pytest.ini

 [pytest]
+testpaths = src tests doc/notebooks
+pythonpath = src
 python_files = test_*.py *_test.py scenario_*.py
 norecursedirs = *.egg-info .git .cache .ipynb_checkpoints htmlcov
-addopts = --doctest-modules --durations=20  --cov-config pytest.ini
+addopts = 
+       --doctest-modules --durations=20
+       --cov-config pytest.ini
+       --ignore=src/lbmpy/custom_code_nodes.py
+       --ignore=src/lbmpy/lookup_tables.py
+       --ignore=src/lbmpy/phasefield_allen_cahn/contact_angle.py
+markers =
+       longrun: tests only run at night since they have large execution time
+       notebook: mark for notebooks
+# these warnings all come from third party libraries.
+filterwarnings =
+       ignore:the imp module is deprecated in favour of importlib:DeprecationWarning
+       ignore:'contextfilter' is renamed to 'pass_context':DeprecationWarning
+       ignore:Persisting input arguments took:UserWarning
+
 
 [run]
 branch = True
-source = lbmpy
-         lbmpy_tests
+source = src/lbmpy
+         tests
 
 omit = doc/*
-       lbmpy_tests/*
+       tests/*
        setup.py
        conftest.py
+       versioneer.py
+       quicktest.py
+       noxfile.py
+       src/lbmpy/_version.py
+       src/lbmpy/_compat.py
+       venv/
 
 [report]
 exclude_lines =
@@ -19,10 +41,12 @@ exclude_lines =
        pragma: no cover
 
        def __repr__
+       def _repr_html_
 
        # Don't complain if tests don't hit defensive assertion code:
        raise AssertionError
        raise NotImplementedError
+       NotImplementedError()
        #raise ValueError
 
        # Don't complain if non-runnable code isn't run:
@@ -31,7 +55,7 @@ exclude_lines =
        if __name__ == .__main__.:
 
 skip_covered = True
-fail_under = 89
+fail_under = 87
 
 [html]
 directory = coverage_report

quicktest.py

+#!/usr/bin/env python3
+
+from contextlib import redirect_stdout
+import io
+from tests.test_quicktests import (
+    test_poiseuille_channel_quicktest,
+    test_entropic_methods,
+    test_cumulant_ldc
+)
+
+quick_tests = [
+    test_poiseuille_channel_quicktest,
+    test_entropic_methods,
+    test_cumulant_ldc,
+]
+
+if __name__ == "__main__":
+    print("Running lbmpy quicktests")
+    for qt in quick_tests:
+        print(f"   -> {qt.__name__}")
+        with redirect_stdout(io.StringIO()):
+            qt()

setup.py

-import os
-import sys
-import io
-from setuptools import setup, find_packages
-import distutils
-from contextlib import redirect_stdout
-from importlib import import_module
-sys.path.insert(0, os.path.abspath('doc'))
-from version_from_git import version_number_from_git
+from setuptools import setup, __version__ as setuptools_version
 
+if int(setuptools_version.split('.')[0]) < 61:
+    raise Exception(
+        "[ERROR] lbmpy requires at least setuptools version 61 to install.\n"
+        "If this error occurs during an installation via pip, it is likely that there is a conflict between "
+        "versions of setuptools installed by pip and the system package manager. "
+        "In this case, it is recommended to install lbmpy into a virtual environment instead."
+    )
 
-quick_tests = [
-    'test_serial_scenarios.test_ldc_mrt',
-    'test_serial_scenarios.test_channel_srt',
-]
+import versioneer
 
 
-class SimpleTestRunner(distutils.cmd.Command):
-    """A custom command to run selected tests"""
+def get_cmdclass():
+    return versioneer.get_cmdclass()
 
-    description = 'run some quick tests'
-    user_options = []
 
-    @staticmethod
-    def _run_tests_in_module(test):
-        """Short test runner function - to work also if py.test is not installed."""
-        test = 'lbmpy_tests.' + test
-        mod, function_name = test.rsplit('.', 1)
-        if isinstance(mod, str):
-            mod = import_module(mod)
-
-        func = getattr(mod, function_name)
-        print("   -> %s in %s" % (function_name, mod.__name__))
-        with redirect_stdout(io.StringIO()):
-            func()
-
-    def initialize_options(self):
-        pass
-
-    def finalize_options(self):
-        pass
-
-    def run(self):
-        """Run command."""
-        for test in quick_tests:
-            self._run_tests_in_module(test)
-
-
-setup(name='lbmpy',
-      version=version_number_from_git(),
-      description='Code Generation for Lattice Boltzmann Methods',
-      author='Martin Bauer',
-      license='AGPLv3',
-      author_email='martin.bauer@fau.de',
-      url='https://i10git.cs.fau.de/pycodegen/lbmpy/',
-      packages=['lbmpy'] + ['lbmpy.' + s for s in find_packages('lbmpy')],
-      install_requires=['pystencils'],
-      classifiers=[
-            'Development Status :: 4 - Beta',
-            'Framework :: Jupyter',
-            'Topic :: Software Development :: Code Generators',
-            'Topic :: Scientific/Engineering :: Physics',
-            'Intended Audience :: Developers',
-            'Intended Audience :: Science/Research',
-            'License :: OSI Approved :: GNU Affero General Public License v3 or later (AGPLv3+)',
-      ],
-      python_requires=">=3.6",
-      extras_require={
-          'gpu': ['pycuda'],
-          'opencl': ['pyopencl'],
-          'alltrafos': ['islpy', 'py-cpuinfo'],
-          'interactive': ['scipy', 'scikit-image', 'cython', 'matplotlib',
-                          'ipy_table', 'imageio', 'jupyter', 'pyevtk'],
-          'doc': ['sphinx', 'sphinx_rtd_theme', 'nbsphinx',
-                  'sphinxcontrib-bibtex', 'sphinx_autodoc_typehints', 'pandoc'],
-      },
-      cmdclass={
-          'quicktest': SimpleTestRunner
-      }
-      )
+setup(
+    version=versioneer.get_version(),
+    cmdclass=get_cmdclass(),
+)

src/lbmpy/__init__.py

+from .creationfunctions import (
+    create_lb_ast,
+    create_lb_collision_rule,
+    create_lb_function,
+    create_lb_method,
+    create_lb_update_rule,
+    LBMConfig,
+    LBMOptimisation,
+)
+from .enums import Stencil, Method, ForceModel, CollisionSpace, SubgridScaleModel
+from .lbstep import LatticeBoltzmannStep
+from .macroscopic_value_kernels import (
+    pdf_initialization_assignments,
+    macroscopic_values_getter,
+    strain_rate_tensor_getter,
+    compile_macroscopic_values_getter,
+    compile_macroscopic_values_setter,
+    create_advanced_velocity_setter_collision_rule,
+)
+from .maxwellian_equilibrium import get_weights
+from .relaxationrates import (
+    relaxation_rate_from_lattice_viscosity,
+    lattice_viscosity_from_relaxation_rate,
+    relaxation_rate_from_magic_number,
+)
+from .scenarios import create_lid_driven_cavity, create_fully_periodic_flow
+from .stencils import LBStencil
+
+
+__all__ = [
+    "create_lb_ast",
+    "create_lb_collision_rule",
+    "create_lb_function",
+    "create_lb_method",
+    "create_lb_update_rule",
+    "LBMConfig",
+    "LBMOptimisation",
+    "Stencil",
+    "Method",
+    "ForceModel",
+    "CollisionSpace",
+    "SubgridScaleModel",
+    "LatticeBoltzmannStep",
+    "pdf_initialization_assignments",
+    "macroscopic_values_getter",
+    "strain_rate_tensor_getter",
+    "compile_macroscopic_values_getter",
+    "compile_macroscopic_values_setter",
+    "create_advanced_velocity_setter_collision_rule",
+    "get_weights",
+    "relaxation_rate_from_lattice_viscosity",
+    "lattice_viscosity_from_relaxation_rate",
+    "relaxation_rate_from_magic_number",
+    "create_lid_driven_cavity",
+    "create_fully_periodic_flow",
+    "LBStencil",
+]
+
+
+from . import _version
+__version__ = _version.get_versions()['version']

src/lbmpy/_compat.py

+from pystencils import __version__ as ps_version
+
+#   Determine if we're running pystencils 1.x or 2.x
+version_tokes = ps_version.split(".")
+
+PYSTENCILS_VERSION_MAJOR = int(version_tokes[0])
+IS_PYSTENCILS_2 = PYSTENCILS_VERSION_MAJOR == 2
+
+if IS_PYSTENCILS_2:
+    from pystencils.defaults import DEFAULTS
+
+    def get_loop_counter_symbol(coord: int):
+        return DEFAULTS.spatial_counters[coord]
+
+    def get_supported_instruction_sets():
+        from pystencils import Target
+        vector_targets = Target.available_vector_cpu_targets()
+        isas = []
+        for target in vector_targets:
+            tokens = target.name.split("_")
+            isas.append(tokens[-1].lower())
+        return isas
+
+else:
+    from pystencils.backends.simd_instruction_sets import (
+        get_supported_instruction_sets as get_supported_instruction_sets_,
+    )
+
+    get_supported_instruction_sets = get_supported_instruction_sets_
+
+    def get_loop_counter_symbol(coord: int):
+        from pystencils.astnodes import LoopOverCoordinate
+
+        return LoopOverCoordinate.get_loop_counter_symbol(coord)
+
+
+def import_guard_pystencils1(feature):
+    if IS_PYSTENCILS_2:
+        raise ImportError(
+            f"The following feature is not yet available when running pystencils 2.x: {feature}"
+        )
+    return True

src/lbmpy/_version.py

+
+# This file helps to compute a version number in source trees obtained from
+# git-archive tarball (such as those provided by githubs download-from-tag
+# feature). Distribution tarballs (built by setup.py sdist) and build
+# directories (produced by setup.py build) will contain a much shorter file
+# that just contains the computed version number.
+
+# This file is released into the public domain.
+# Generated by versioneer-0.29
+# https://github.com/python-versioneer/python-versioneer
+
+"""Git implementation of _version.py."""
+
+import errno
+import os
+import re
+import subprocess
+import sys
+from typing import Any, Callable, Dict, List, Optional, Tuple
+import functools
+
+
+def get_keywords() -> Dict[str, str]:
+    """Get the keywords needed to look up the version information."""
+    # these strings will be replaced by git during git-archive.
+    # setup.py/versioneer.py will grep for the variable names, so they must
+    # each be defined on a line of their own. _version.py will just call
+    # get_keywords().
+    git_refnames = "$Format:%d$"
+    git_full = "$Format:%H$"
+    git_date = "$Format:%ci$"
+    keywords = {"refnames": git_refnames, "full": git_full, "date": git_date}
+    return keywords
+
+
+class VersioneerConfig:
+    """Container for Versioneer configuration parameters."""
+
+    VCS: str
+    style: str
+    tag_prefix: str
+    parentdir_prefix: str
+    versionfile_source: str
+    verbose: bool
+
+
+def get_config() -> VersioneerConfig:
+    """Create, populate and return the VersioneerConfig() object."""
+    # these strings are filled in when 'setup.py versioneer' creates
+    # _version.py
+    cfg = VersioneerConfig()
+    cfg.VCS = "git"
+    cfg.style = "pep440"
+    cfg.tag_prefix = "release/"
+    cfg.parentdir_prefix = "lbmpy-"
+    cfg.versionfile_source = "src/lbmpy/_version.py"
+    cfg.verbose = False
+    return cfg
+
+
+class NotThisMethod(Exception):
+    """Exception raised if a method is not valid for the current scenario."""
+
+
+LONG_VERSION_PY: Dict[str, str] = {}
+HANDLERS: Dict[str, Dict[str, Callable]] = {}
+
+
+def register_vcs_handler(vcs: str, method: str) -> Callable:  # decorator
+    """Create decorator to mark a method as the handler of a VCS."""
+    def decorate(f: Callable) -> Callable:
+        """Store f in HANDLERS[vcs][method]."""
+        if vcs not in HANDLERS:
+            HANDLERS[vcs] = {}
+        HANDLERS[vcs][method] = f
+        return f
+    return decorate
+
+
+def run_command(
+    commands: List[str],
+    args: List[str],
+    cwd: Optional[str] = None,
+    verbose: bool = False,
+    hide_stderr: bool = False,
+    env: Optional[Dict[str, str]] = None,
+) -> Tuple[Optional[str], Optional[int]]:
+    """Call the given command(s)."""
+    assert isinstance(commands, list)
+    process = None
+
+    popen_kwargs: Dict[str, Any] = {}
+    if sys.platform == "win32":
+        # This hides the console window if pythonw.exe is used
+        startupinfo = subprocess.STARTUPINFO()
+        startupinfo.dwFlags |= subprocess.STARTF_USESHOWWINDOW
+        popen_kwargs["startupinfo"] = startupinfo
+
+    for command in commands:
+        try:
+            dispcmd = str([command] + args)
+            # remember shell=False, so use git.cmd on windows, not just git
+            process = subprocess.Popen([command] + args, cwd=cwd, env=env,
+                                       stdout=subprocess.PIPE,
+                                       stderr=(subprocess.PIPE if hide_stderr
+                                               else None), **popen_kwargs)
+            break
+        except OSError as e:
+            if e.errno == errno.ENOENT:
+                continue
+            if verbose:
+                print("unable to run %s" % dispcmd)
+                print(e)
+            return None, None
+    else:
+        if verbose:
+            print("unable to find command, tried %s" % (commands,))
+        return None, None
+    stdout = process.communicate()[0].strip().decode()
+    if process.returncode != 0:
+        if verbose:
+            print("unable to run %s (error)" % dispcmd)
+            print("stdout was %s" % stdout)
+        return None, process.returncode
+    return stdout, process.returncode
+
+
+def versions_from_parentdir(
+    parentdir_prefix: str,
+    root: str,
+    verbose: bool,
+) -> Dict[str, Any]:
+    """Try to determine the version from the parent directory name.
+
+    Source tarballs conventionally unpack into a directory that includes both
+    the project name and a version string. We will also support searching up
+    two directory levels for an appropriately named parent directory
+    """
+    rootdirs = []
+
+    for _ in range(3):
+        dirname = os.path.basename(root)
+        if dirname.startswith(parentdir_prefix):
+            return {"version": dirname[len(parentdir_prefix):],
+                    "full-revisionid": None,
+                    "dirty": False, "error": None, "date": None}
+        rootdirs.append(root)
+        root = os.path.dirname(root)  # up a level
+
+    if verbose:
+        print("Tried directories %s but none started with prefix %s" %
+              (str(rootdirs), parentdir_prefix))
+    raise NotThisMethod("rootdir doesn't start with parentdir_prefix")
+
+
+@register_vcs_handler("git", "get_keywords")
+def git_get_keywords(versionfile_abs: str) -> Dict[str, str]:
+    """Extract version information from the given file."""
+    # the code embedded in _version.py can just fetch the value of these
+    # keywords. When used from setup.py, we don't want to import _version.py,
+    # so we do it with a regexp instead. This function is not used from
+    # _version.py.
+    keywords: Dict[str, str] = {}
+    try:
+        with open(versionfile_abs, "r") as fobj:
+            for line in fobj:
+                if line.strip().startswith("git_refnames ="):
+                    mo = re.search(r'=\s*"(.*)"', line)
+                    if mo:
+                        keywords["refnames"] = mo.group(1)
+                if line.strip().startswith("git_full ="):
+                    mo = re.search(r'=\s*"(.*)"', line)
+                    if mo:
+                        keywords["full"] = mo.group(1)
+                if line.strip().startswith("git_date ="):
+                    mo = re.search(r'=\s*"(.*)"', line)
+                    if mo:
+                        keywords["date"] = mo.group(1)
+    except OSError:
+        pass
+    return keywords
+
+
+@register_vcs_handler("git", "keywords")
+def git_versions_from_keywords(
+    keywords: Dict[str, str],
+    tag_prefix: str,
+    verbose: bool,
+) -> Dict[str, Any]:
+    """Get version information from git keywords."""
+    if "refnames" not in keywords:
+        raise NotThisMethod("Short version file found")
+    date = keywords.get("date")
+    if date is not None:
+        # Use only the last line.  Previous lines may contain GPG signature
+        # information.
+        date = date.splitlines()[-1]
+
+        # git-2.2.0 added "%cI", which expands to an ISO-8601 -compliant
+        # datestamp. However we prefer "%ci" (which expands to an "ISO-8601
+        # -like" string, which we must then edit to make compliant), because
+        # it's been around since git-1.5.3, and it's too difficult to
+        # discover which version we're using, or to work around using an
+        # older one.
+        date = date.strip().replace(" ", "T", 1).replace(" ", "", 1)
+    refnames = keywords["refnames"].strip()
+    if refnames.startswith("$Format"):
+        if verbose:
+            print("keywords are unexpanded, not using")
+        raise NotThisMethod("unexpanded keywords, not a git-archive tarball")
+    refs = {r.strip() for r in refnames.strip("()").split(",")}
+    # starting in git-1.8.3, tags are listed as "tag: foo-1.0" instead of
+    # just "foo-1.0". If we see a "tag: " prefix, prefer those.
+    TAG = "tag: "
+    tags = {r[len(TAG):] for r in refs if r.startswith(TAG)}
+    if not tags:
+        # Either we're using git < 1.8.3, or there really are no tags. We use
+        # a heuristic: assume all version tags have a digit. The old git %d
+        # expansion behaves like git log --decorate=short and strips out the
+        # refs/heads/ and refs/tags/ prefixes that would let us distinguish
+        # between branches and tags. By ignoring refnames without digits, we
+        # filter out many common branch names like "release" and
+        # "stabilization", as well as "HEAD" and "master".
+        tags = {r for r in refs if re.search(r'\d', r)}
+        if verbose:
+            print("discarding '%s', no digits" % ",".join(refs - tags))
+    if verbose:
+        print("likely tags: %s" % ",".join(sorted(tags)))
+    for ref in sorted(tags):
+        # sorting will prefer e.g. "2.0" over "2.0rc1"
+        if ref.startswith(tag_prefix):
+            r = ref[len(tag_prefix):]
+            # Filter out refs that exactly match prefix or that don't start
+            # with a number once the prefix is stripped (mostly a concern
+            # when prefix is '')
+            if not re.match(r'\d', r):
+                continue
+            if verbose:
+                print("picking %s" % r)
+            return {"version": r,
+                    "full-revisionid": keywords["full"].strip(),
+                    "dirty": False, "error": None,
+                    "date": date}
+    # no suitable tags, so version is "0+unknown", but full hex is still there
+    if verbose:
+        print("no suitable tags, using unknown + full revision id")
+    return {"version": "0+unknown",
+            "full-revisionid": keywords["full"].strip(),
+            "dirty": False, "error": "no suitable tags", "date": None}
+
+
+@register_vcs_handler("git", "pieces_from_vcs")
+def git_pieces_from_vcs(
+    tag_prefix: str,
+    root: str,
+    verbose: bool,
+    runner: Callable = run_command
+) -> Dict[str, Any]:
+    """Get version from 'git describe' in the root of the source tree.
+
+    This only gets called if the git-archive 'subst' keywords were *not*
+    expanded, and _version.py hasn't already been rewritten with a short
+    version string, meaning we're inside a checked out source tree.
+    """
+    GITS = ["git"]
+    if sys.platform == "win32":
+        GITS = ["git.cmd", "git.exe"]
+
+    # GIT_DIR can interfere with correct operation of Versioneer.
+    # It may be intended to be passed to the Versioneer-versioned project,
+    # but that should not change where we get our version from.
+    env = os.environ.copy()
+    env.pop("GIT_DIR", None)
+    runner = functools.partial(runner, env=env)
+
+    _, rc = runner(GITS, ["rev-parse", "--git-dir"], cwd=root,
+                   hide_stderr=not verbose)
+    if rc != 0:
+        if verbose:
+            print("Directory %s not under git control" % root)
+        raise NotThisMethod("'git rev-parse --git-dir' returned error")
+
+    # if there is a tag matching tag_prefix, this yields TAG-NUM-gHEX[-dirty]
+    # if there isn't one, this yields HEX[-dirty] (no NUM)
+    describe_out, rc = runner(GITS, [
+        "describe", "--tags", "--dirty", "--always", "--long",
+        "--match", f"{tag_prefix}[[:digit:]]*"
+    ], cwd=root)
+    # --long was added in git-1.5.5
+    if describe_out is None:
+        raise NotThisMethod("'git describe' failed")
+    describe_out = describe_out.strip()
+    full_out, rc = runner(GITS, ["rev-parse", "HEAD"], cwd=root)
+    if full_out is None:
+        raise NotThisMethod("'git rev-parse' failed")
+    full_out = full_out.strip()
+
+    pieces: Dict[str, Any] = {}
+    pieces["long"] = full_out
+    pieces["short"] = full_out[:7]  # maybe improved later
+    pieces["error"] = None
+
+    branch_name, rc = runner(GITS, ["rev-parse", "--abbrev-ref", "HEAD"],
+                             cwd=root)
+    # --abbrev-ref was added in git-1.6.3
+    if rc != 0 or branch_name is None:
+        raise NotThisMethod("'git rev-parse --abbrev-ref' returned error")
+    branch_name = branch_name.strip()
+
+    if branch_name == "HEAD":
+        # If we aren't exactly on a branch, pick a branch which represents
+        # the current commit. If all else fails, we are on a branchless
+        # commit.
+        branches, rc = runner(GITS, ["branch", "--contains"], cwd=root)
+        # --contains was added in git-1.5.4
+        if rc != 0 or branches is None:
+            raise NotThisMethod("'git branch --contains' returned error")
+        branches = branches.split("\n")
+
+        # Remove the first line if we're running detached
+        if "(" in branches[0]:
+            branches.pop(0)
+
+        # Strip off the leading "* " from the list of branches.
+        branches = [branch[2:] for branch in branches]
+        if "master" in branches:
+            branch_name = "master"
+        elif not branches:
+            branch_name = None
+        else:
+            # Pick the first branch that is returned. Good or bad.
+            branch_name = branches[0]
+
+    pieces["branch"] = branch_name
+
+    # parse describe_out. It will be like TAG-NUM-gHEX[-dirty] or HEX[-dirty]
+    # TAG might have hyphens.
+    git_describe = describe_out
+
+    # look for -dirty suffix
+    dirty = git_describe.endswith("-dirty")
+    pieces["dirty"] = dirty
+    if dirty:
+        git_describe = git_describe[:git_describe.rindex("-dirty")]
+
+    # now we have TAG-NUM-gHEX or HEX
+
+    if "-" in git_describe:
+        # TAG-NUM-gHEX
+        mo = re.search(r'^(.+)-(\d+)-g([0-9a-f]+)$', git_describe)
+        if not mo:
+            # unparsable. Maybe git-describe is misbehaving?
+            pieces["error"] = ("unable to parse git-describe output: '%s'"
+                               % describe_out)
+            return pieces
+
+        # tag
+        full_tag = mo.group(1)
+        if not full_tag.startswith(tag_prefix):
+            if verbose:
+                fmt = "tag '%s' doesn't start with prefix '%s'"
+                print(fmt % (full_tag, tag_prefix))
+            pieces["error"] = ("tag '%s' doesn't start with prefix '%s'"
+                               % (full_tag, tag_prefix))
+            return pieces
+        pieces["closest-tag"] = full_tag[len(tag_prefix):]
+
+        # distance: number of commits since tag
+        pieces["distance"] = int(mo.group(2))
+
+        # commit: short hex revision ID
+        pieces["short"] = mo.group(3)
+
+    else:
+        # HEX: no tags
+        pieces["closest-tag"] = None
+        out, rc = runner(GITS, ["rev-list", "HEAD", "--left-right"], cwd=root)
+        pieces["distance"] = len(out.split())  # total number of commits
+
+    # commit date: see ISO-8601 comment in git_versions_from_keywords()
+    date = runner(GITS, ["show", "-s", "--format=%ci", "HEAD"], cwd=root)[0].strip()
+    # Use only the last line.  Previous lines may contain GPG signature
+    # information.
+    date = date.splitlines()[-1]
+    pieces["date"] = date.strip().replace(" ", "T", 1).replace(" ", "", 1)
+
+    return pieces
+
+
+def plus_or_dot(pieces: Dict[str, Any]) -> str:
+    """Return a + if we don't already have one, else return a ."""
+    if "+" in pieces.get("closest-tag", ""):
+        return "."
+    return "+"
+
+
+def render_pep440(pieces: Dict[str, Any]) -> str:
+    """Build up version string, with post-release "local version identifier".
+
+    Our goal: TAG[+DISTANCE.gHEX[.dirty]] . Note that if you
+    get a tagged build and then dirty it, you'll get TAG+0.gHEX.dirty
+
+    Exceptions:
+    1: no tags. git_describe was just HEX. 0+untagged.DISTANCE.gHEX[.dirty]
+    """
+    if pieces["closest-tag"]:
+        rendered = pieces["closest-tag"]
+        if pieces["distance"] or pieces["dirty"]:
+            rendered += plus_or_dot(pieces)
+            rendered += "%d.g%s" % (pieces["distance"], pieces["short"])
+            if pieces["dirty"]:
+                rendered += ".dirty"
+    else:
+        # exception #1
+        rendered = "0+untagged.%d.g%s" % (pieces["distance"],
+                                          pieces["short"])
+        if pieces["dirty"]:
+            rendered += ".dirty"
+    return rendered
+
+
+def render_pep440_branch(pieces: Dict[str, Any]) -> str:
+    """TAG[[.dev0]+DISTANCE.gHEX[.dirty]] .
+
+    The ".dev0" means not master branch. Note that .dev0 sorts backwards
+    (a feature branch will appear "older" than the master branch).
+
+    Exceptions:
+    1: no tags. 0[.dev0]+untagged.DISTANCE.gHEX[.dirty]
+    """
+    if pieces["closest-tag"]:
+        rendered = pieces["closest-tag"]
+        if pieces["distance"] or pieces["dirty"]:
+            if pieces["branch"] != "master":
+                rendered += ".dev0"
+            rendered += plus_or_dot(pieces)
+            rendered += "%d.g%s" % (pieces["distance"], pieces["short"])
+            if pieces["dirty"]:
+                rendered += ".dirty"
+    else:
+        # exception #1
+        rendered = "0"
+        if pieces["branch"] != "master":
+            rendered += ".dev0"
+        rendered += "+untagged.%d.g%s" % (pieces["distance"],
+                                          pieces["short"])
+        if pieces["dirty"]:
+            rendered += ".dirty"
+    return rendered
+
+
+def pep440_split_post(ver: str) -> Tuple[str, Optional[int]]:
+    """Split pep440 version string at the post-release segment.
+
+    Returns the release segments before the post-release and the
+    post-release version number (or -1 if no post-release segment is present).
+    """
+    vc = str.split(ver, ".post")
+    return vc[0], int(vc[1] or 0) if len(vc) == 2 else None
+
+
+def render_pep440_pre(pieces: Dict[str, Any]) -> str:
+    """TAG[.postN.devDISTANCE] -- No -dirty.
+
+    Exceptions:
+    1: no tags. 0.post0.devDISTANCE
+    """
+    if pieces["closest-tag"]:
+        if pieces["distance"]:
+            # update the post release segment
+            tag_version, post_version = pep440_split_post(pieces["closest-tag"])
+            rendered = tag_version
+            if post_version is not None:
+                rendered += ".post%d.dev%d" % (post_version + 1, pieces["distance"])
+            else:
+                rendered += ".post0.dev%d" % (pieces["distance"])
+        else:
+            # no commits, use the tag as the version
+            rendered = pieces["closest-tag"]
+    else:
+        # exception #1
+        rendered = "0.post0.dev%d" % pieces["distance"]
+    return rendered
+
+
+def render_pep440_post(pieces: Dict[str, Any]) -> str:
+    """TAG[.postDISTANCE[.dev0]+gHEX] .
+
+    The ".dev0" means dirty. Note that .dev0 sorts backwards
+    (a dirty tree will appear "older" than the corresponding clean one),
+    but you shouldn't be releasing software with -dirty anyways.
+
+    Exceptions:
+    1: no tags. 0.postDISTANCE[.dev0]
+    """
+    if pieces["closest-tag"]:
+        rendered = pieces["closest-tag"]
+        if pieces["distance"] or pieces["dirty"]:
+            rendered += ".post%d" % pieces["distance"]
+            if pieces["dirty"]:
+                rendered += ".dev0"
+            rendered += plus_or_dot(pieces)
+            rendered += "g%s" % pieces["short"]
+    else:
+        # exception #1
+        rendered = "0.post%d" % pieces["distance"]
+        if pieces["dirty"]:
+            rendered += ".dev0"
+        rendered += "+g%s" % pieces["short"]
+    return rendered
+
+
+def render_pep440_post_branch(pieces: Dict[str, Any]) -> str:
+    """TAG[.postDISTANCE[.dev0]+gHEX[.dirty]] .
+
+    The ".dev0" means not master branch.
+
+    Exceptions:
+    1: no tags. 0.postDISTANCE[.dev0]+gHEX[.dirty]
+    """
+    if pieces["closest-tag"]:
+        rendered = pieces["closest-tag"]
+        if pieces["distance"] or pieces["dirty"]:
+            rendered += ".post%d" % pieces["distance"]
+            if pieces["branch"] != "master":
+                rendered += ".dev0"
+            rendered += plus_or_dot(pieces)
+            rendered += "g%s" % pieces["short"]
+            if pieces["dirty"]:
+                rendered += ".dirty"
+    else:
+        # exception #1
+        rendered = "0.post%d" % pieces["distance"]
+        if pieces["branch"] != "master":
+            rendered += ".dev0"
+        rendered += "+g%s" % pieces["short"]
+        if pieces["dirty"]:
+            rendered += ".dirty"
+    return rendered
+
+
+def render_pep440_old(pieces: Dict[str, Any]) -> str:
+    """TAG[.postDISTANCE[.dev0]] .
+
+    The ".dev0" means dirty.
+
+    Exceptions:
+    1: no tags. 0.postDISTANCE[.dev0]
+    """
+    if pieces["closest-tag"]:
+        rendered = pieces["closest-tag"]
+        if pieces["distance"] or pieces["dirty"]:
+            rendered += ".post%d" % pieces["distance"]
+            if pieces["dirty"]:
+                rendered += ".dev0"
+    else:
+        # exception #1
+        rendered = "0.post%d" % pieces["distance"]
+        if pieces["dirty"]:
+            rendered += ".dev0"
+    return rendered
+
+
+def render_git_describe(pieces: Dict[str, Any]) -> str:
+    """TAG[-DISTANCE-gHEX][-dirty].
+
+    Like 'git describe --tags --dirty --always'.
+
+    Exceptions:
+    1: no tags. HEX[-dirty]  (note: no 'g' prefix)
+    """
+    if pieces["closest-tag"]:
+        rendered = pieces["closest-tag"]
+        if pieces["distance"]:
+            rendered += "-%d-g%s" % (pieces["distance"], pieces["short"])
+    else:
+        # exception #1
+        rendered = pieces["short"]
+    if pieces["dirty"]:
+        rendered += "-dirty"
+    return rendered
+
+
+def render_git_describe_long(pieces: Dict[str, Any]) -> str:
+    """TAG-DISTANCE-gHEX[-dirty].
+
+    Like 'git describe --tags --dirty --always -long'.
+    The distance/hash is unconditional.
+
+    Exceptions:
+    1: no tags. HEX[-dirty]  (note: no 'g' prefix)
+    """
+    if pieces["closest-tag"]:
+        rendered = pieces["closest-tag"]
+        rendered += "-%d-g%s" % (pieces["distance"], pieces["short"])
+    else:
+        # exception #1
+        rendered = pieces["short"]
+    if pieces["dirty"]:
+        rendered += "-dirty"
+    return rendered
+
+
+def render(pieces: Dict[str, Any], style: str) -> Dict[str, Any]:
+    """Render the given version pieces into the requested style."""
+    if pieces["error"]:
+        return {"version": "unknown",
+                "full-revisionid": pieces.get("long"),
+                "dirty": None,
+                "error": pieces["error"],
+                "date": None}
+
+    if not style or style == "default":
+        style = "pep440"  # the default
+
+    if style == "pep440":
+        rendered = render_pep440(pieces)
+    elif style == "pep440-branch":
+        rendered = render_pep440_branch(pieces)
+    elif style == "pep440-pre":
+        rendered = render_pep440_pre(pieces)
+    elif style == "pep440-post":
+        rendered = render_pep440_post(pieces)
+    elif style == "pep440-post-branch":
+        rendered = render_pep440_post_branch(pieces)
+    elif style == "pep440-old":
+        rendered = render_pep440_old(pieces)
+    elif style == "git-describe":
+        rendered = render_git_describe(pieces)
+    elif style == "git-describe-long":
+        rendered = render_git_describe_long(pieces)
+    else:
+        raise ValueError("unknown style '%s'" % style)
+
+    return {"version": rendered, "full-revisionid": pieces["long"],
+            "dirty": pieces["dirty"], "error": None,
+            "date": pieces.get("date")}
+
+
+def get_versions() -> Dict[str, Any]:
+    """Get version information or return default if unable to do so."""
+    # I am in _version.py, which lives at ROOT/VERSIONFILE_SOURCE. If we have
+    # __file__, we can work backwards from there to the root. Some
+    # py2exe/bbfreeze/non-CPython implementations don't do __file__, in which
+    # case we can only use expanded keywords.
+
+    cfg = get_config()
+    verbose = cfg.verbose
+
+    try:
+        return git_versions_from_keywords(get_keywords(), cfg.tag_prefix,
+                                          verbose)
+    except NotThisMethod:
+        pass
+
+    try:
+        root = os.path.realpath(__file__)
+        # versionfile_source is the relative path from the top of the source
+        # tree (where the .git directory might live) to this file. Invert
+        # this to find the root from __file__.
+        for _ in cfg.versionfile_source.split('/'):
+            root = os.path.dirname(root)
+    except NameError:
+        return {"version": "0+unknown", "full-revisionid": None,
+                "dirty": None,
+                "error": "unable to find root of source tree",
+                "date": None}
+
+    try:
+        pieces = git_pieces_from_vcs(cfg.tag_prefix, root, verbose)
+        return render(pieces, cfg.style)
+    except NotThisMethod:
+        pass
+
+    try:
+        if cfg.parentdir_prefix:
+            return versions_from_parentdir(cfg.parentdir_prefix, root, verbose)
+    except NotThisMethod:
+        pass
+
+    return {"version": "0+unknown", "full-revisionid": None,
+            "dirty": None,
+            "error": "unable to compute version", "date": None}

src/lbmpy/advanced_streaming/__init__.py

+from .indexing import BetweenTimestepsIndexing
+from .communication import get_communication_slices, LBMPeriodicityHandling
+from .utility import Timestep, get_accessor, is_inplace, get_timesteps, \
+    numeric_index, numeric_offsets, inverse_dir_index, AccessPdfValues
+
+__all__ = ['BetweenTimestepsIndexing',
+           'get_communication_slices', 'LBMPeriodicityHandling',
+           'Timestep', 'get_accessor', 'is_inplace', 'get_timesteps',
+           'numeric_index', 'numeric_offsets', 'inverse_dir_index', 'AccessPdfValues']

src/lbmpy/advanced_streaming/communication.py

+import itertools
+from pystencils import CreateKernelConfig, Field, Assignment, AssignmentCollection, Target
+from pystencils.slicing import (
+    shift_slice,
+    get_slice_before_ghost_layer,
+    normalize_slice,
+)
+from lbmpy.advanced_streaming.utility import (
+    is_inplace,
+    get_accessor,
+    numeric_index,
+    Timestep,
+    get_timesteps,
+    numeric_offsets,
+)
+from pystencils.datahandling import SerialDataHandling
+from itertools import chain
+
+
+class LBMPeriodicityHandling:
+
+    def __init__(
+        self,
+        stencil,
+        data_handling,
+        pdf_field_name,
+        streaming_pattern="pull",
+        ghost_layers=1,
+        cupy_direct_copy=True,
+    ):
+        """
+        Periodicity Handling for Lattice Boltzmann Streaming.
+
+        **On the usage with cuda:**
+        - cupy allows the copying of sliced arrays within device memory using the numpy syntax,
+        e.g. `dst[:,0] = src[:,-1]`. In this implementation, this is the default for periodicity
+        handling. Alternatively, if you set `cupy_direct_copy=False`, GPU kernels are generated and
+        compiled. The compiled kernels are almost twice as fast in execution as cupy array copying,
+        but especially for large stencils like D3Q27, their compilation can take up to 20 seconds.
+        Choose your weapon depending on your use case.
+        """
+        if not isinstance(data_handling, SerialDataHandling):
+            raise ValueError("Only serial data handling is supported!")
+
+        self.stencil = stencil
+        self.dim = stencil.D
+        self.dh = data_handling
+
+        assert data_handling.default_target in [Target.CPU, Target.GPU]
+        self.target = data_handling.default_target
+
+        self.pdf_field_name = pdf_field_name
+        self.ghost_layers = ghost_layers
+        self.periodicity = data_handling.periodicity
+        self.inplace_pattern = is_inplace(streaming_pattern)
+
+        self.cpu = self.target == Target.CPU
+        self.cupy_direct_copy = self.target == Target.GPU and cupy_direct_copy
+
+        def is_copy_direction(direction):
+            s = 0
+            for d, p in zip(direction, self.periodicity):
+                s += abs(d)
+                if d != 0 and not p:
+                    return False
+
+            return s != 0
+
+        full_stencil = itertools.product(*([-1, 0, 1] for _ in range(self.dim)))
+        copy_directions = tuple(filter(is_copy_direction, full_stencil))
+        self.comm_slices = []
+        timesteps = get_timesteps(streaming_pattern)
+        for timestep in timesteps:
+            slices_per_comm_dir = get_communication_slices(
+                stencil=stencil,
+                comm_stencil=copy_directions,
+                streaming_pattern=streaming_pattern,
+                prev_timestep=timestep,
+                ghost_layers=ghost_layers,
+            )
+            self.comm_slices.append(
+                list(chain.from_iterable(v for k, v in slices_per_comm_dir.items()))
+            )
+
+        if self.target == Target.GPU and not cupy_direct_copy:
+            self.device_copy_kernels = list()
+            for timestep in timesteps:
+                self.device_copy_kernels.append(self._compile_copy_kernels(timestep))
+
+    def __call__(self, prev_timestep=Timestep.BOTH):
+        if self.cpu:
+            self._periodicity_handling_cpu(prev_timestep)
+        else:
+            self._periodicity_handling_gpu(prev_timestep)
+
+    def _periodicity_handling_cpu(self, prev_timestep):
+        arr = self.dh.cpu_arrays[self.pdf_field_name]
+        comm_slices = self.comm_slices[prev_timestep.idx]
+        for src, dst in comm_slices:
+            arr[dst] = arr[src]
+
+    def _compile_copy_kernels(self, timestep):
+        assert self.target == Target.GPU
+        pdf_field = self.dh.fields[self.pdf_field_name]
+        kernels = []
+        for src, dst in self.comm_slices[timestep.idx]:
+            kernels.append(periodic_pdf_gpu_copy_kernel(pdf_field, src, dst))
+        return kernels
+
+    def _periodicity_handling_gpu(self, prev_timestep):
+        arr = self.dh.gpu_arrays[self.pdf_field_name]
+        if self.cupy_direct_copy:
+            for src, dst in self.comm_slices[prev_timestep.idx]:
+                arr[dst] = arr[src]
+        else:
+            kernel_args = {self.pdf_field_name: arr}
+            for kernel in self.device_copy_kernels[prev_timestep.idx]:
+                kernel(**kernel_args)
+
+
+def get_communication_slices(
+    stencil,
+    comm_stencil=None,
+    streaming_pattern="pull",
+    prev_timestep=Timestep.BOTH,
+    ghost_layers=1,
+):
+    """
+    Return the source and destination slices for periodicity handling or communication between blocks.
+
+    :param stencil: The stencil used by the LB method.
+    :param comm_stencil: The stencil defining the communication directions. If None, it will be set to the
+                         full stencil (D2Q9 in 2D, D3Q27 in 3D, etc.).
+    :param streaming_pattern: The streaming pattern.
+    :param prev_timestep: Timestep after which communication is run.
+    :param ghost_layers: Number of ghost layers in each direction.
+
+    """
+
+    if comm_stencil is None:
+        comm_stencil = itertools.product(*([-1, 0, 1] for _ in range(stencil.D)))
+
+    pdfs = Field.create_generic(
+        "pdfs", spatial_dimensions=len(stencil[0]), index_shape=(stencil.Q,)
+    )
+    write_accesses = get_accessor(streaming_pattern, prev_timestep).write(pdfs, stencil)
+    slices_per_comm_direction = dict()
+
+    for comm_dir in comm_stencil:
+        if all(d == 0 for d in comm_dir):
+            continue
+
+        slices_for_dir = []
+
+        for streaming_dir in set(_extend_dir(comm_dir)) & set(stencil):
+            d = stencil.index(streaming_dir)
+            write_index = numeric_index(write_accesses[d])[0]
+
+            origin_slice = get_slice_before_ghost_layer(
+                comm_dir, ghost_layers=ghost_layers, thickness=1
+            )
+            src_slice = _fix_length_one_slices(origin_slice)
+
+            write_offsets = numeric_offsets(write_accesses[d])
+            tangential_dir = tuple(s - c for s, c in zip(streaming_dir, comm_dir))
+
+            # TODO: this is just a hotfix. _trim_slice_in_direction breaks FreeSlip BC with adjacent periodic side
+            if streaming_pattern != "pull":
+                src_slice = shift_slice(
+                    _trim_slice_in_direction(src_slice, tangential_dir), write_offsets
+                )
+
+            neighbour_transform = _get_neighbour_transform(comm_dir, ghost_layers)
+            dst_slice = shift_slice(src_slice, neighbour_transform)
+
+            src_slice = src_slice + (write_index,)
+            dst_slice = dst_slice + (write_index,)
+
+            slices_for_dir.append((src_slice, dst_slice))
+
+        slices_per_comm_direction[comm_dir] = slices_for_dir
+    return slices_per_comm_direction
+
+
+def periodic_pdf_gpu_copy_kernel(pdf_field, src_slice, dst_slice, domain_size=None):
+    """Generate a GPU kernel which copies all values from one slice of a field
+    to another non-overlapping slice."""
+    from pystencils import create_kernel
+
+    pdf_idx = src_slice[-1]
+    assert isinstance(pdf_idx, int), "PDF index needs to be an integer constant"
+    assert pdf_idx == dst_slice[-1], "Source and Destination PDF indices must be equal"
+    src_slice = src_slice[:-1]
+    dst_slice = dst_slice[:-1]
+
+    # TODO this is the domain_size with GL
+    if domain_size is None:
+        domain_size = pdf_field.spatial_shape
+
+    normalized_from_slice = normalize_slice(src_slice, domain_size)
+    normalized_to_slice = normalize_slice(dst_slice, domain_size)
+
+    def _start(s):
+        return s.start if isinstance(s, slice) else s
+
+    def _stop(s):
+        return s.stop if isinstance(s, slice) else s
+
+    offset = [
+        _start(s1) - _start(s2)
+        for s1, s2 in zip(normalized_from_slice, normalized_to_slice)
+    ]
+    assert offset == [
+        _stop(s1) - _stop(s2)
+        for s1, s2 in zip(normalized_from_slice, normalized_to_slice)
+    ], "Slices have to have same size"
+
+    copy_eq = AssignmentCollection(
+        main_assignments=[
+            Assignment(pdf_field(pdf_idx), pdf_field[tuple(offset)](pdf_idx))
+        ]
+    )
+    config = CreateKernelConfig(
+        iteration_slice=dst_slice,
+        skip_independence_check=True,
+        target=Target.GPU,
+    )
+
+    ast = create_kernel(copy_eq, config=config)
+    return ast.compile()
+
+
+def _extend_dir(direction):
+    if len(direction) == 0:
+        yield tuple()
+    elif direction[0] == 0:
+        for d in [-1, 0, 1]:
+            for rest in _extend_dir(direction[1:]):
+                yield (d,) + rest
+    else:
+        for rest in _extend_dir(direction[1:]):
+            yield (direction[0],) + rest
+
+
+def _get_neighbour_transform(direction, ghost_layers):
+    return tuple(d * (ghost_layers + 1) for d in direction)
+
+
+def _fix_length_one_slices(slices):
+    """Slices of length one are replaced by their start value for correct periodic shifting"""
+    if isinstance(slices, int):
+        return slices
+    elif isinstance(slices, slice):
+        if slices.stop is not None and abs(slices.start - slices.stop) == 1:
+            return slices.start
+        elif slices.stop is None and slices.start == -1:
+            return -1  # [-1:] also has length one
+        else:
+            return slices
+    else:
+        return tuple(_fix_length_one_slices(s) for s in slices)
+
+
+def _trim_slice_in_direction(slices, direction):
+    assert len(slices) == len(direction)
+
+    result = []
+    for s, d in zip(slices, direction):
+        if isinstance(s, int):
+            result.append(s)
+            continue
+        start = s.start + 1 if d == -1 else s.start
+        stop = s.stop - 1 if d == 1 else s.stop
+        result.append(slice(start, stop, s.step))
+
+    return tuple(result)

src/lbmpy/advanced_streaming/indexing.py

+import numpy as np
+import sympy as sp
+import pystencils as ps
+
+from .._compat import IS_PYSTENCILS_2
+
+if IS_PYSTENCILS_2:
+    from pystencils import TypedSymbol, create_type
+    from pystencils.types.quick import Arr
+    from lbmpy.lookup_tables import TranslationArraysNode
+else:
+    from pystencils.typing import TypedSymbol, create_type
+    from ..custom_code_nodes import TranslationArraysNode
+
+from lbmpy.advanced_streaming.utility import get_accessor, inverse_dir_index, is_inplace, Timestep
+from itertools import product
+
+
+class BetweenTimestepsIndexing:
+
+    #   ==============================================
+    #       Symbols for usage in kernel definitions
+    #   ==============================================
+
+    @property
+    def proxy_fields(self):
+        return ps.fields(f"f_out({self._q}), f_in({self._q}): [{self._dim}D]")
+
+    @property
+    def dir_symbol(self):
+        return TypedSymbol('dir', create_type(self._index_dtype))
+
+    @property
+    def inverse_dir_symbol(self):
+        """Symbol denoting the inversion of a PDF field index.
+        Use only at top-level of index to f_out or f_in, otherwise it can't be correctly replaced."""
+        return sp.IndexedBase('invdir')
+
+    #   =============================
+    #       Constructor and State
+    #   =============================
+
+    def __init__(self, pdf_field, stencil, prev_timestep=Timestep.BOTH, streaming_pattern='pull',
+                 index_dtype=np.int32, offsets_dtype=np.int32):
+        if prev_timestep == Timestep.BOTH and is_inplace(streaming_pattern):
+            raise ValueError('Cannot create index arrays for both kinds of timesteps for inplace streaming pattern '
+                             + streaming_pattern)
+
+        prev_accessor = get_accessor(streaming_pattern, prev_timestep)
+        next_accessor = get_accessor(streaming_pattern, prev_timestep.next())
+
+        outward_accesses = prev_accessor.write(pdf_field, stencil)
+        inward_accesses = next_accessor.read(pdf_field, stencil)
+
+        self._accesses = {'out': outward_accesses, 'in': inward_accesses}
+
+        self._pdf_field = pdf_field
+        self._stencil = stencil
+        self._dim = stencil.D
+        self._q = stencil.Q
+        self._coordinate_names = ['x', 'y', 'z'][:self._dim]
+
+        self._index_dtype = create_type(index_dtype)
+        self._offsets_dtype = create_type(offsets_dtype)
+
+        self._required_index_arrays = set()
+        self._required_offset_arrays = set()
+        self._trivial_index_translations, self._trivial_offset_translations = self._collect_trivial_translations()
+
+    def _index_array_symbol(self, f_dir, inverse):
+        assert f_dir in ['in', 'out']
+        inv = '_inv' if inverse else ''
+        name = f"f_{f_dir}{inv}_dir_idx"
+        if IS_PYSTENCILS_2:
+            return TypedSymbol(name, Arr(self._index_dtype, self._q))
+        else:
+            return TypedSymbol(name, self._index_dtype)
+
+    def _offset_array_symbols(self, f_dir, inverse):
+        assert f_dir in ['in', 'out']
+        inv = '_inv' if inverse else ''
+        name_base = f"f_{f_dir}{inv}_offsets_"
+
+        if IS_PYSTENCILS_2:
+            symbols = [TypedSymbol(name_base + d, Arr(self._index_dtype, self._q)) for d in self._coordinate_names]
+        else:
+            symbols = [TypedSymbol(name_base + d, self._index_dtype) for d in self._coordinate_names]
+        
+        return symbols
+
+    def _array_symbols(self, f_dir, inverse, index):
+        if (f_dir, inverse) in self._trivial_index_translations:
+            translated_index = index
+        else:
+            index_array_symbol = self._index_array_symbol(f_dir, inverse)
+            translated_index = sp.IndexedBase(index_array_symbol, shape=(1,))[index]
+            self._required_index_arrays.add((f_dir, inverse))
+
+        if (f_dir, inverse) in self._trivial_offset_translations:
+            offsets = (0, ) * self._dim
+        else:
+            offset_array_symbols = self._offset_array_symbols(f_dir, inverse)
+            offsets = tuple(sp.IndexedBase(s, shape=(1,))[index] for s in offset_array_symbols)
+            self._required_offset_arrays.add((f_dir, inverse))
+
+        return {'index': translated_index, 'offsets': offsets}
+
+    #   =================================
+    #       Proxy fields substitution
+    #   =================================
+
+    def substitute_proxies(self, assignments):
+        if isinstance(assignments, ps.Assignment):
+            assignments = [assignments]
+
+        if not isinstance(assignments, ps.AssignmentCollection):
+            assignments = ps.AssignmentCollection(assignments)
+
+        accesses = self._accesses
+        f_out, f_in = self.proxy_fields
+        inv_dir = self.inverse_dir_symbol
+
+        accessor_subs = dict()
+
+        for fa in assignments.atoms(ps.Field.Access):
+            if fa.field == f_out:
+                f_dir = 'out'
+            elif fa.field == f_in:
+                f_dir = 'in'
+            else:
+                continue
+
+            inv = False
+            idx = fa.index[0]
+            if isinstance(idx, sp.Indexed) and idx.base == inv_dir:
+                idx = idx.indices[0]
+                if isinstance(sp.sympify(idx), sp.Integer):
+                    idx = inverse_dir_index(self._stencil, idx)
+                inv = True
+
+            if isinstance(sp.sympify(idx), sp.Integer):
+                accessor_subs[fa] = accesses[f_dir][idx].get_shifted(*fa.offsets)
+            else:
+                arr = self._array_symbols(f_dir, inv, idx)
+                accessor_subs[fa] = self._pdf_field[arr['offsets']](arr['index']).get_shifted(*fa.offsets)
+
+        return assignments.new_with_substitutions(accessor_subs)
+
+    #   =================
+    #       Internals
+    #   =================
+
+    def _get_translated_indices_and_offsets(self, f_dir, inv):
+        accesses = self._accesses[f_dir]
+
+        if inv:
+            inverse_indices = [inverse_dir_index(self._stencil, i)
+                               for i in range(len(self._stencil))]
+            accesses = [accesses[idx] for idx in inverse_indices]
+
+        indices = [a.index[0] for a in accesses]
+        offsets = []
+        for d in range(self._dim):
+            offsets.append([a.offsets[d] for a in accesses])
+        return indices, offsets
+
+    def _collect_trivial_translations(self):
+        trivial_index_translations = set()
+        trivial_offset_translations = set()
+        trivial_indices = list(range(self._q))
+        trivial_offsets = [[0] * self._q] * self._dim
+        for f_dir, inv in product(['in', 'out'], [False, True]):
+            indices, offsets = self._get_translated_indices_and_offsets(f_dir, inv)
+            if indices == trivial_indices:
+                trivial_index_translations.add((f_dir, inv))
+            if offsets == trivial_offsets:
+                trivial_offset_translations.add((f_dir, inv))
+        return trivial_index_translations, trivial_offset_translations
+
+    def create_code_node(self):
+        array_content = list()
+        symbols_defined = set()
+        for f_dir, inv in self._required_index_arrays:
+            indices, offsets = self._get_translated_indices_and_offsets(f_dir, inv)
+            index_array_symbol = self._index_array_symbol(f_dir, inv)
+            symbols_defined.add(index_array_symbol)
+
+            if IS_PYSTENCILS_2:
+                array_content.append((index_array_symbol, indices))
+            else:
+                array_content.append((self._index_dtype, index_array_symbol.name, indices))
+
+        for f_dir, inv in self._required_offset_arrays:
+            indices, offsets = self._get_translated_indices_and_offsets(f_dir, inv)
+            offset_array_symbols = self._offset_array_symbols(f_dir, inv)
+            symbols_defined |= set(offset_array_symbols)
+            for d, arrsymb in enumerate(offset_array_symbols):
+                if IS_PYSTENCILS_2:
+                    array_content.append((arrsymb, offsets[d]))
+                else:
+                    array_content.append((self._offsets_dtype, arrsymb.name, offsets[d]))
+
+        if IS_PYSTENCILS_2:
+            return TranslationArraysNode(array_content)
+        else:
+            return TranslationArraysNode(array_content, symbols_defined)
+
+#   end class AdvancedStreamingIndexing

src/lbmpy/advanced_streaming/utility.py

+from lbmpy.fieldaccess import PdfFieldAccessor, \
+    StreamPullTwoFieldsAccessor, \
+    StreamPushTwoFieldsAccessor, \
+    AAEvenTimeStepAccessor, \
+    AAOddTimeStepAccessor, \
+    EsoTwistEvenTimeStepAccessor, \
+    EsoTwistOddTimeStepAccessor, \
+    EsoPullEvenTimeStepAccessor, \
+    EsoPullOddTimeStepAccessor, \
+    EsoPushEvenTimeStepAccessor, \
+    EsoPushOddTimeStepAccessor
+
+import numpy as np
+import pystencils as ps
+from enum import IntEnum
+
+
+class Timestep(IntEnum):
+    EVEN = 0
+    ODD = 1
+    BOTH = 2
+
+    def next(self):
+        return self if self == Timestep.BOTH else Timestep((self + 1) % 2)
+
+    @property
+    def idx(self):
+        """To use this timestep as an array index"""
+        return self % 2
+
+    def __str__(self):
+        if self == Timestep.EVEN:
+            return 'Even'
+        elif self == Timestep.ODD:
+            return 'Odd'
+        else:
+            return 'Both'
+
+
+streaming_patterns = ['push', 'pull', 'aa', 'esotwist', 'esopull', 'esopush']
+
+even_accessors = {
+    'pull': StreamPullTwoFieldsAccessor,
+    'push': StreamPushTwoFieldsAccessor,
+    'aa': AAEvenTimeStepAccessor,
+    'esotwist': EsoTwistEvenTimeStepAccessor,
+    'esopull': EsoPullEvenTimeStepAccessor,
+    'esopush': EsoPushEvenTimeStepAccessor
+}
+
+odd_accessors = {
+    'pull': StreamPullTwoFieldsAccessor,
+    'push': StreamPushTwoFieldsAccessor,
+    'aa': AAOddTimeStepAccessor,
+    'esotwist': EsoTwistOddTimeStepAccessor,
+    'esopull': EsoPullOddTimeStepAccessor,
+    'esopush': EsoPushOddTimeStepAccessor
+}
+
+
+def is_inplace(streaming_pattern):
+    if streaming_pattern not in streaming_patterns:
+        raise ValueError('Invalid streaming pattern', streaming_pattern)
+
+    return streaming_pattern in ['aa', 'esotwist', 'esopull', 'esopush']
+
+
+def get_accessor(streaming_pattern: str, timestep: Timestep) -> PdfFieldAccessor:
+    if streaming_pattern not in streaming_patterns:
+        raise ValueError(
+            "Invalid value of parameter 'streaming_pattern'.", streaming_pattern)
+
+    if is_inplace(streaming_pattern) and (timestep == Timestep.BOTH):
+        raise ValueError(f"Invalid timestep for streaming pattern {streaming_pattern}: {str(timestep)}")
+
+    if timestep == Timestep.EVEN:
+        return even_accessors[streaming_pattern]
+    else:
+        return odd_accessors[streaming_pattern]
+
+
+def get_timesteps(streaming_pattern):
+    return (Timestep.EVEN, Timestep.ODD) if is_inplace(streaming_pattern) else (Timestep.BOTH, )
+
+
+def numeric_offsets(field_access: ps.Field.Access):
+    return tuple(int(o) for o in field_access.offsets)
+
+
+def numeric_index(field_access: ps.Field.Access):
+    return tuple(int(i) for i in field_access.index)
+
+
+def inverse_dir_index(stencil, direction):
+    return stencil.index(tuple(-d for d in stencil[direction]))
+
+
+class AccessPdfValues:
+    """Allows to access values from a PDF array correctly depending on 
+    the streaming pattern."""
+
+    def __init__(self, stencil,
+                 streaming_pattern='pull', timestep=Timestep.BOTH, streaming_dir='out',
+                 accessor=None):
+        if streaming_dir not in ['in', 'out']:
+            raise ValueError('Invalid streaming direction.', streaming_dir)
+
+        pdf_field = ps.Field.create_generic('pdfs', len(stencil[0]), index_shape=(stencil.Q,))
+
+        if accessor is None:
+            accessor = get_accessor(streaming_pattern, timestep)
+        self.accs = accessor.read(pdf_field, stencil) \
+            if streaming_dir == 'in' \
+            else accessor.write(pdf_field, stencil)
+
+    def write_pdf(self, pdf_arr, pos, d, value):
+        offsets = numeric_offsets(self.accs[d])
+        pos = tuple(p + o for p, o in zip(pos, offsets))
+        i = numeric_index(self.accs[d])[0]
+        pdf_arr[pos + (i,)] = value
+
+    def read_pdf(self, pdf_arr, pos, d):
+        offsets = numeric_offsets(self.accs[d])
+        pos = tuple(p + o for p, o in zip(pos, offsets))
+        i = numeric_index(self.accs[d])[0]
+        return pdf_arr[pos + (i,)]
+
+    def read_multiple(self, pdf_arr, indices):
+        """Returns PDF values for a list of index tuples (x, y, [z,] dir)"""
+        return np.array([self.read_pdf(pdf_arr, idx[:-1], idx[-1]) for idx in indices])
+
+    def collect_from_index_list(self, pdf_arr, index_list):
+        """To collect PDF values according to an pystencils boundary handling index list"""
+        def to_index_tuple(idx):
+            return tuple(idx[v] for v in ('x', 'y', 'z')[:len(idx) - 1] + ('dir',))
+
+        return self.read_multiple(pdf_arr, (to_index_tuple(idx) for idx in index_list))

src/lbmpy/analytical_solutions.py

+from typing import Union
+from numpy.typing import NDArray
+
+
+def poiseuille_flow(middle_distance: Union[float, NDArray], height,
+                    ext_force_density: float, dyn_visc: float) -> Union[float, NDArray]:
+    """
+    Analytical solution for plane Poiseuille flow.
+
+    Args:
+        middle_distance: Distance to the middle plane of the channel.
+        height: Distance between the boundaries.
+        ext_force_density: Force density on the fluid normal to the boundaries.
+        dyn_visc: dyn_visc
+
+    Returns:
+        A numpy array of the poiseuille profile if middle_distance is given as array otherwise of velocity of
+        the position given with middle_distance
+    """
+    return ext_force_density * 1. / (2 * dyn_visc) * (height**2.0 / 4.0 - middle_distance**2.0)

src/lbmpy/boundaries/__init__.py

+from lbmpy.boundaries.boundaryconditions import (
+    UBB, FixedDensity, DiffusionDirichlet, SimpleExtrapolationOutflow, WallFunctionBounce,
+    ExtrapolationOutflow, NeumannByCopy, NoSlip, NoSlipLinearBouzidi, QuadraticBounceBack, StreamInConstant, FreeSlip)
+from lbmpy.boundaries.boundaryhandling import LatticeBoltzmannBoundaryHandling
+from lbmpy.boundaries.wall_function_models import MoninObukhovSimilarityTheory, LogLaw, MuskerLaw, SpaldingsLaw
+
+__all__ = ['NoSlip', 'NoSlipLinearBouzidi', 'QuadraticBounceBack', 'FreeSlip', 'WallFunctionBounce',
+           'UBB', 'FixedDensity',
+           'SimpleExtrapolationOutflow', 'ExtrapolationOutflow',
+           'DiffusionDirichlet', 'NeumannByCopy', 'StreamInConstant',
+           'LatticeBoltzmannBoundaryHandling',
+           'MoninObukhovSimilarityTheory', 'LogLaw', 'MuskerLaw', 'SpaldingsLaw']

src/lbmpy/boundaries/boundaries_in_kernel.py

+import sympy as sp
+
+from .._compat import IS_PYSTENCILS_2
+
+from lbmpy.advanced_streaming.indexing import BetweenTimestepsIndexing
+from lbmpy.advanced_streaming.utility import Timestep, get_accessor
+from pystencils.boundaries.boundaryhandling import BoundaryOffsetInfo
+from pystencils import Assignment
+from pystencils.simp import AssignmentCollection, sympy_cse_on_assignment_list
+from pystencils.stencil import inverse_direction
+from pystencils.sympyextensions import fast_subs
+
+if IS_PYSTENCILS_2:
+    from lbmpy.lookup_tables import LbmWeightInfo
+else:
+    from lbmpy.custom_code_nodes import LbmWeightInfo
+    from pystencils.astnodes import Block, Conditional, LoopOverCoordinate, SympyAssignment  # TODO replace
+
+
+def direction_indices_in_direction(direction, stencil):
+    for i, offset in enumerate(stencil):
+        for d_i, o_i in zip(direction, offset):
+            if (d_i == 1 and o_i == 1) or (d_i == -1 and o_i == -1):
+                yield i
+                break
+
+
+def boundary_substitutions(lb_method):
+    stencil = lb_method.stencil
+    w = lb_method.weights
+    replacements = {}
+    for idx, offset in enumerate(stencil):
+        symbolic_offset = BoundaryOffsetInfo.offset_from_dir(idx, dim=lb_method.dim)
+        for sym, value in zip(symbolic_offset, offset):
+            replacements[sym] = value
+
+        replacements[BoundaryOffsetInfo.inv_dir(idx)] = stencil.index(inverse_direction(offset))
+        replacements[LbmWeightInfo.weight_of_direction(idx)] = w[idx]
+    return replacements
+
+
+def border_conditions(direction, field, ghost_layers=1):
+    abs_direction = tuple(-e if e < 0 else e for e in direction)
+    assert sum(abs_direction) == 1
+    idx = abs_direction.index(1)
+    val = direction[idx]
+
+    loop_ctrs = [LoopOverCoordinate.get_loop_counter_symbol(i) for i in range(len(direction))]
+    loop_ctr = loop_ctrs[idx]
+
+    gl = ghost_layers
+    border_condition = sp.Eq(loop_ctr, gl if val < 0 else field.shape[idx] - gl - 1)
+
+    if ghost_layers == 0:
+        return border_condition
+    else:
+        other_min = [sp.Ge(c, gl)
+                     for c in loop_ctrs if c != loop_ctr]
+        other_max = [sp.Lt(c, field.shape[i] - gl)
+                     for i, c in enumerate(loop_ctrs) if c != loop_ctr]
+        result = sp.And(border_condition, *other_min, *other_max)
+        return result
+
+
+def boundary_conditional(boundary, direction, streaming_pattern, prev_timestep, lb_method, output_field, cse=False):
+    if IS_PYSTENCILS_2:
+        raise NotImplementedError("In-Kernel Boundaries are not yet available on pystencils 2.0")
+
+    stencil = lb_method.stencil
+
+    dir_indices = direction_indices_in_direction(direction, stencil)
+    indexing = BetweenTimestepsIndexing(output_field, lb_method.stencil, prev_timestep, streaming_pattern)
+    f_out, f_in = indexing.proxy_fields
+    inv_dir = indexing.inverse_dir_symbol
+
+    assignments = []
+    for direction_idx in dir_indices:
+        rule = boundary(f_out, f_in, direction_idx, inv_dir, lb_method, index_field=None, force_vector=None)
+
+        #   rhs: replace f_out by post collision symbols.
+        rhs_substitutions = {f_out(i): sym for i, sym in enumerate(lb_method.post_collision_pdf_symbols)}
+        rule = AssignmentCollection([rule]).new_with_substitutions(rhs_substitutions)
+        rule = indexing.substitute_proxies(rule)
+
+        ac = rule.new_without_subexpressions()
+        assignments += ac.main_assignments
+
+    border_cond = border_conditions(direction, output_field, ghost_layers=1)
+    if cse:
+        assignments = sympy_cse_on_assignment_list(assignments)
+    assignments = [SympyAssignment(a.lhs, a.rhs) for a in assignments]
+    return Conditional(border_cond, Block(assignments))
+
+
+def update_rule_with_push_boundaries(collision_rule, field, boundary_spec, 
+                                     streaming_pattern='pull', timestep=Timestep.BOTH):
+    method = collision_rule.method
+    accessor = get_accessor(streaming_pattern, timestep)
+    loads = [Assignment(a, b) for a, b in zip(method.pre_collision_pdf_symbols, accessor.read(field, method.stencil))]
+    stores = [Assignment(a, b) for a, b in
+              zip(accessor.write(field, method.stencil), method.post_collision_pdf_symbols)]
+
+    result = collision_rule.copy()
+    result.subexpressions = loads + result.subexpressions
+    result.main_assignments += stores
+    for direction, boundary in boundary_spec.items():
+        cond = boundary_conditional(boundary, direction, streaming_pattern, timestep, method, field)
+        result.main_assignments.append(cond)
+
+    if 'split_groups' in result.simplification_hints:
+        substitutions = {b: a for a, b in zip(accessor.write(field, method.stencil), method.post_collision_pdf_symbols)}
+        new_split_groups = []
+        for split_group in result.simplification_hints['split_groups']:
+            new_split_groups.append([fast_subs(e, substitutions) for e in split_group])
+        result.simplification_hints['split_groups'] = new_split_groups
+
+    return result

src/lbmpy/boundaries/boundaryconditions.py

+import abc
+from enum import Enum, auto
+from warnings import warn
+
+from pystencils import Assignment, AssignmentCollection, Field, TypedSymbol
+from pystencils.stencil import offset_to_direction_string, direction_string_to_offset, inverse_direction
+from pystencils.sympyextensions import get_symmetric_part, simplify_by_equality, scalar_product
+
+from lbmpy.advanced_streaming.utility import AccessPdfValues, Timestep
+from lbmpy.maxwellian_equilibrium import discrete_equilibrium
+from lbmpy.simplificationfactory import create_simplification_strategy
+
+import sympy as sp
+import numpy as np
+
+from .._compat import IS_PYSTENCILS_2
+
+if IS_PYSTENCILS_2:
+    from pystencils import create_type
+    from pystencils.sympyextensions.typed_sympy import CastFunc
+    from pystencils.types.quick import Arr
+    from lbmpy.lookup_tables import (
+        NeighbourOffsetArrays,
+        MirroredStencilDirections,
+        LbmWeightInfo,
+        TranslationArraysNode
+    )
+else:
+    from pystencils.typing import create_type, CastFunc
+    from lbmpy.custom_code_nodes import (
+        NeighbourOffsetArrays,
+        MirroredStencilDirections,
+        LbmWeightInfo,
+        TranslationArraysNode
+    )
+
+
+class LbBoundary(abc.ABC):
+    """Base class that all boundaries should derive from.
+
+    Args:
+        name: optional name of the boundary.
+    """
+
+    inner_or_boundary = True
+    single_link = False
+
+    def __init__(self, name=None, calculate_force_on_boundary=False):
+        self._name = name
+        self.calculate_force_on_boundary = calculate_force_on_boundary
+
+    def __call__(self, f_out, f_in, dir_symbol, inv_dir, lb_method, index_field, force_vector):
+        """
+        This function defines the boundary behavior and must therefore be implemented by all boundaries.
+        The boundary is defined through a list of sympy equations from which a boundary kernel is generated.
+
+        Args:
+        f_out:          a pystencils field acting as a proxy to access the populations streaming out of the current
+                        cell, i.e. the post-collision PDFs of the previous LBM step
+        f_in:           a pystencils field acting as a proxy to access the populations streaming into the current
+                        cell, i.e. the pre-collision PDFs for the next LBM step
+        dir_symbol:     a sympy symbol that can be used as an index to f_out and f_in. It describes the direction
+                        pointing from the fluid to the boundary cell.
+        inv_dir:        an indexed sympy symbol which describes the inversion of a direction index. It can be used in
+                        the indices of f_out and f_in for retrieving the PDF of the inverse direction.
+        lb_method:      an instance of the LB method used. Use this to adapt the boundary to the method
+                        (e.g. compressibility)
+        index_field:    the boundary index field that can be used to retrieve and update boundary data
+        force_vector:   vector to store the force on the boundary. Has the same size as the index field and
+                        D-entries per cell
+
+        Returns:
+            list of pystencils assignments, or pystencils.AssignmentCollection
+        """
+        raise NotImplementedError("Boundary class has to overwrite __call__")
+
+    @property
+    def additional_data(self):
+        """Return a list of (name, type) tuples for additional data items required in this boundary
+        These data items can either be initialized in separate kernel see additional_data_kernel_init or by
+        Python callbacks - see additional_data_callback """
+        return []
+
+    @property
+    def additional_data_init_callback(self):
+        """Return a callback function called with a boundary data setter object and returning a dict of
+        data-name to data for each element that should be initialized"""
+        return None
+
+    def get_additional_code_nodes(self, lb_method):
+        """Return a list of code nodes that will be added in the generated code before the index field loop.
+
+        Args:
+            lb_method: lattice Boltzmann method. See :func:`lbmpy.creationfunctions.create_lb_method`
+        """
+        return []
+
+    @property
+    def name(self):
+        if self._name:
+            return self._name
+        else:
+            return type(self).__name__
+
+    @name.setter
+    def name(self, new_value):
+        self._name = new_value
+
+    def __hash__(self):
+        return hash(self.name)
+
+    def __eq__(self, other):
+        if not isinstance(other, type(self)):
+            return False
+        return self.__dict__ == other.__dict__
+
+
+# end class Boundary
+
+
+class NoSlip(LbBoundary):
+    r"""
+    No-Slip, (half-way) simple bounce back boundary condition, enforcing zero velocity at obstacle.
+    Populations leaving the boundary node :math:`\mathbf{x}_b` at time :math:`t` are reflected
+    back with :math:`\mathbf{c}_{\overline{i}} = -\mathbf{c}_{i}`
+
+    .. math ::
+        f_{\overline{i}}(\mathbf{x}_b, t + \Delta t) = f^{\star}_{i}(\mathbf{x}_b, t)
+
+    Args:
+        name: optional name of the boundary.
+        calculate_force_on_boundary: stores the force for each PDF at the boundary in a force vector
+    """
+
+    def __init__(self, name=None, calculate_force_on_boundary=False):
+        """Set an optional name here, to mark boundaries, for example for force evaluations"""
+        super(NoSlip, self).__init__(name, calculate_force_on_boundary)
+
+    def get_additional_code_nodes(self, lb_method):
+        if self.calculate_force_on_boundary:
+            return [NeighbourOffsetArrays(lb_method.stencil)]
+        else:
+            return []
+
+    def __call__(self, f_out, f_in, dir_symbol, inv_dir, lb_method, index_field, force_vector):
+        if self.calculate_force_on_boundary:
+            force = sp.Symbol("f")
+            subexpressions = [Assignment(force, sp.Float(2.0) * f_out(dir_symbol))]
+            offset = NeighbourOffsetArrays.neighbour_offset(dir_symbol, lb_method.stencil)
+            if IS_PYSTENCILS_2:
+                offset = [CastFunc.as_numeric(o) for o in offset]
+            for i in range(lb_method.stencil.D):
+                subexpressions.append(Assignment(force_vector[0](f'F_{i}'), force * offset[i]))
+        else:
+            subexpressions = []
+
+        boundary_assignments = [Assignment(f_in(inv_dir[dir_symbol]), f_out(dir_symbol))]
+        return AssignmentCollection(boundary_assignments, subexpressions=subexpressions)
+
+
+class NoSlipLinearBouzidi(LbBoundary):
+    """
+    No-Slip, (half-way) simple bounce back boundary condition with interpolation
+    to increase accuracy: :cite:`BouzidiBC`. In order to make the boundary condition work properly a
+    Python callback function needs to be provided to calculate the distance from the wall for each cell near to the
+    boundary. If this is not done the boundary condition will fall back to a simple NoSlip boundary.
+    Furthermore, for this boundary condition a second fluid cell away from the wall is needed. If the second fluid
+    cell is not available (e.g. because it is marked as boundary as well), the boundary condition should fall back to
+    a NoSlip boundary as well.
+
+    Args:
+        name: optional name of the boundary.
+        init_wall_distance: Python callback function to calculate the wall distance for each cell near to the  boundary
+        data_type: data type of the wall distance q
+    """
+
+    def __init__(self, name=None, init_wall_distance=None, data_type='double', calculate_force_on_boundary=False):
+        self.data_type = data_type
+        self.init_wall_distance = init_wall_distance
+        super(NoSlipLinearBouzidi, self).__init__(name, calculate_force_on_boundary)
+
+    @property
+    def additional_data(self):
+        """Used internally only. For the NoSlipLinearBouzidi boundary the distance to the obstacle of every
+        direction is needed. This information is stored in the index vector."""
+        return [('q', create_type(self.data_type))]
+
+    def get_additional_code_nodes(self, lb_method):
+        if self.calculate_force_on_boundary:
+            return [NeighbourOffsetArrays(lb_method.stencil)]
+        else:
+            return []
+
+    @property
+    def additional_data_init_callback(self):
+        def default_callback(boundary_data, **_):
+            for cell in boundary_data.index_array:
+                cell['q'] = -1
+
+        if self.init_wall_distance:
+            return self.init_wall_distance
+        else:
+            warn("No callback function provided to initialise the wall distance for each cell "
+                 "(init_wall_distance=None). The boundary condition will fall back to a simple NoSlip BC")
+            return default_callback
+
+    def __call__(self, f_out, f_in, dir_symbol, inv_dir, lb_method, index_field, force_vector):
+        f_xf = sp.Symbol("f_xf")
+        f_xf_inv = sp.Symbol("f_xf_inv")
+        d_x2f = sp.Symbol("d_x2f")
+        q = sp.Symbol("q")
+        one = sp.Float(1.0)
+        two = sp.Float(2.0)
+        half = sp.Rational(1, 2)
+
+        subexpressions = [Assignment(f_xf, f_out(dir_symbol)),
+                          Assignment(f_xf_inv, f_out(inv_dir[dir_symbol])),
+                          Assignment(d_x2f, f_in(dir_symbol)),
+                          Assignment(q, index_field[0]('q'))]
+
+        case_one = (half * (f_xf + f_xf_inv * (two * q - one))) / q
+        case_two = two * q * f_xf + (one - two * q) * d_x2f
+        case_three = f_xf
+
+        rhs = sp.Piecewise((case_one, sp.Ge(q, 0.5)),
+                           (case_two, sp.And(sp.Gt(q, 0), sp.Lt(q, 0.5))),
+                           (case_three, True))
+
+        if self.calculate_force_on_boundary:
+            force = sp.Symbol("f")
+            subexpressions.append(Assignment(force, f_xf + rhs))
+            offset = NeighbourOffsetArrays.neighbour_offset(dir_symbol, lb_method.stencil)
+            if IS_PYSTENCILS_2:
+                offset = [CastFunc.as_numeric(o) for o in offset]
+            for i in range(lb_method.stencil.D):
+                subexpressions.append(Assignment(force_vector[0](f'F_{i}'), force * offset[i]))
+
+        boundary_assignments = [Assignment(f_in(inv_dir[dir_symbol]), rhs)]
+
+        return AssignmentCollection(boundary_assignments, subexpressions=subexpressions)
+
+
+# end class NoSlipLinearBouzidi
+
+class QuadraticBounceBack(LbBoundary):
+    """
+    Second order accurate bounce back boundary condition. Implementation details are provided in a demo notebook here:
+    https://pycodegen.pages.i10git.cs.fau.de/lbmpy/notebooks/demo_interpolation_boundary_conditions.html
+
+    Args:
+        relaxation_rate: relaxation rate to realise a BGK scheme for recovering the pre collision PDF value.
+        name: optional name of the boundary.
+        init_wall_distance: Python callback function to calculate the wall distance for each cell near to the  boundary
+        data_type: data type of the wall distance q
+    """
+
+    def __init__(self, relaxation_rate, name=None, init_wall_distance=None, data_type='double',
+                 calculate_force_on_boundary=False):
+        self.relaxation_rate = relaxation_rate
+        self.data_type = data_type
+        self.init_wall_distance = init_wall_distance
+        self.equilibrium_values_name = "f_eq"
+
+        super(QuadraticBounceBack, self).__init__(name, calculate_force_on_boundary)
+
+    def inv_dir_symbol(self, stencil):
+        if IS_PYSTENCILS_2:
+            return TypedSymbol("inv_dir", Arr(create_type("int32"), stencil.Q))
+        else:
+            return TypedSymbol("inv_dir", create_type("int32"))
+
+    @property
+    def additional_data(self):
+        """Used internally only. For the NoSlipLinearBouzidi boundary the distance to the obstacle of every
+        direction is needed. This information is stored in the index vector."""
+        return [('q', create_type(self.data_type))]
+
+    @property
+    def additional_data_init_callback(self):
+        def default_callback(boundary_data, **_):
+            for cell in boundary_data.index_array:
+                cell['q'] = 0.5
+
+        if self.init_wall_distance:
+            return self.init_wall_distance
+        else:
+            warn("No callback function provided to initialise the wall distance for each cell "
+                 "(init_wall_distance=None). The boundary condition will fall back to a simple NoSlip BC")
+            return default_callback
+
+    def get_additional_code_nodes(self, lb_method):
+        """Return a list of code nodes that will be added in the generated code before the index field loop.
+
+        Args:
+            lb_method: Lattice Boltzmann method. See :func:`lbmpy.creationfunctions.create_lb_method`
+
+        Returns:
+            list containing LbmWeightInfo
+        """
+        stencil = lb_method.stencil
+        inv_directions = [str(stencil.index(inverse_direction(direction))) for direction in stencil]
+        
+        if IS_PYSTENCILS_2:
+            inverse_dir_node = TranslationArraysNode([(self.inv_dir_symbol(stencil), inv_directions), ])
+        else:
+            inv_dir_symbol = self.inv_dir_symbol(stencil)
+            dtype = inv_dir_symbol.dtype
+            name = inv_dir_symbol.name
+            inverse_dir_node = TranslationArraysNode([(dtype, name, inv_directions), ], {inv_dir_symbol})
+        
+        return [LbmWeightInfo(lb_method, self.data_type), inverse_dir_node, NeighbourOffsetArrays(lb_method.stencil)]
+
+    @staticmethod
+    def get_equilibrium(v, u, rho, drho, weight, compressible, zero_centered):
+        rho_background = sp.Integer(1)
+
+        result = discrete_equilibrium(v, u, rho, weight,
+                                      order=2, c_s_sq=sp.Rational(1, 3), compressible=compressible)
+        if zero_centered:
+            shift = discrete_equilibrium(v, [0] * len(u), rho_background, weight,
+                                         order=0, c_s_sq=sp.Rational(1, 3), compressible=False)
+            result = simplify_by_equality(result - shift, rho, drho, rho_background)
+
+        return result
+
+    def __call__(self, f_out, f_in, dir_symbol, inv_dir, lb_method, index_field, force_vector):
+        omega = self.relaxation_rate
+        inv = sp.IndexedBase(self.inv_dir_symbol(lb_method.stencil), shape=(1,))[dir_symbol]
+        weight_info = LbmWeightInfo(lb_method, data_type=self.data_type)
+        weight_of_direction = weight_info.weight_of_direction
+        pdf_field_accesses = [f_out(i) for i in range(len(lb_method.stencil))]
+
+        pdf_symbols = [sp.Symbol(f"pdf_{i}") for i in range(len(lb_method.stencil))]
+        f_xf = sp.Symbol("f_xf")
+        f_xf_inv = sp.Symbol("f_xf_inv")
+        q = sp.Symbol("q")
+        feq = sp.Symbol("f_eq")
+        weight = sp.Symbol("w")
+        weight_inv = sp.Symbol("w_inv")
+        v = [TypedSymbol(f"c_{i}", self.data_type) for i in range(lb_method.stencil.D)]
+        v_inv = [TypedSymbol(f"c_inv_{i}", self.data_type) for i in range(lb_method.stencil.D)]
+        one = sp.Float(1.0)
+        half = sp.Rational(1, 2)
+
+        subexpressions = [Assignment(pdf_symbols[i], pdf) for i, pdf in enumerate(pdf_field_accesses)]
+        subexpressions.append(Assignment(f_xf, f_out(dir_symbol)))
+        subexpressions.append(Assignment(f_xf_inv, f_out(inv_dir[dir_symbol])))
+        subexpressions.append(Assignment(q, index_field[0]('q')))
+        subexpressions.append(Assignment(weight, weight_of_direction(dir_symbol, lb_method)))
+        subexpressions.append(Assignment(weight_inv, weight_of_direction(inv, lb_method)))
+
+        if IS_PYSTENCILS_2:
+            cast_offset = CastFunc.as_numeric
+        else:
+            def cast_offset(x):
+                return x
+
+        for i in range(lb_method.stencil.D):
+            offset = NeighbourOffsetArrays.neighbour_offset(dir_symbol, lb_method.stencil)
+            subexpressions.append(Assignment(v[i], cast_offset(offset[i])))
+
+        for i in range(lb_method.stencil.D):
+            offset = NeighbourOffsetArrays.neighbour_offset(inv, lb_method.stencil)
+            subexpressions.append(Assignment(v_inv[i], cast_offset(offset[i])))
+
+        cqc = lb_method.conserved_quantity_computation
+        rho = cqc.density_symbol
+        drho = cqc.density_deviation_symbol
+        u = sp.Matrix(cqc.velocity_symbols)
+        compressible = cqc.compressible
+        zero_centered = cqc.zero_centered_pdfs
+
+        cqe = cqc.equilibrium_input_equations_from_pdfs(pdf_symbols, False)
+        subexpressions.append(cqe.all_assignments)
+
+        eq_dir = self.get_equilibrium(v, u, rho, drho, weight, compressible, zero_centered)
+        eq_inv = self.get_equilibrium(v_inv, u, rho, drho, weight_inv, compressible, zero_centered)
+
+        subexpressions.append(Assignment(feq, eq_dir + eq_inv))
+
+        t1 = (f_xf - f_xf_inv + (f_xf + f_xf_inv - feq * omega) / (one - omega))
+        t2 = (q * (f_xf + f_xf_inv)) / (one + q)
+        result = (one - q) / (one + q) * t1 * half + t2
+
+        if self.calculate_force_on_boundary:
+            force = sp.Symbol("f")
+            subexpressions.append(Assignment(force, f_xf + result))
+            offset = NeighbourOffsetArrays.neighbour_offset(dir_symbol, lb_method.stencil)
+            if IS_PYSTENCILS_2:
+                offset = [CastFunc.as_numeric(o) for o in offset]
+            for i in range(lb_method.stencil.D):
+                subexpressions.append(Assignment(force_vector[0](f'F_{i}'), force * offset[i]))
+
+        boundary_assignments = [Assignment(f_in(inv_dir[dir_symbol]), result)]
+        return AssignmentCollection(boundary_assignments, subexpressions=subexpressions)
+
+
+# end class QuadraticBounceBack
+
+class FreeSlip(LbBoundary):
+    """
+    Free-Slip boundary condition, which enforces a zero normal fluid velocity :math:`u_n = 0` but places no restrictions
+    on the tangential fluid velocity :math:`u_t`.
+
+    Args:
+        stencil: LBM stencil which is used for the simulation
+        normal_direction: optional normal direction pointing from wall to fluid.
+                          If the Free slip boundary is applied to a certain side in the domain it is not necessary
+                          to calculate the normal direction since it can be stated for all boundary cells.
+                          This reduces the memory space for the index array significantly.
+        name: optional name of the boundary.
+    """
+
+    def __init__(self, stencil, normal_direction=None, name=None):
+        """Set an optional name here, to mark boundaries, for example for force evaluations"""
+        self.stencil = stencil
+
+        if normal_direction and len(normal_direction) - normal_direction.count(0) != 1:
+            raise ValueError("It is only possible to pre specify the normal direction for simple situations."
+                             "This means if the free slip boundary is applied to a straight wall or side in the "
+                             "simulation domain. A possible value for example would be (0, 1, 0) if the "
+                             "free slip boundary is applied to the northern wall. For more complex situations "
+                             "the normal direction has to be calculated for each cell. This is done when "
+                             "the normal direction is not defined for this class")
+
+        if normal_direction:
+            normal_direction = tuple([int(n) for n in normal_direction])
+            assert all([n in [-1, 0, 1] for n in normal_direction]), \
+                "Only -1, 0 and 1 allowed for defining the normal direction"
+            self.mirror_axis = normal_direction.index(*[d for d in normal_direction if d != 0])
+
+        self.normal_direction = normal_direction
+        self.dim = len(stencil[0])
+
+        if name is None and normal_direction:
+            name = f"Free Slip : {offset_to_direction_string([-x for x in normal_direction])}"
+
+        super(FreeSlip, self).__init__(name, calculate_force_on_boundary=False)
+
+    def init_callback(self, boundary_data, **_):
+        if len(boundary_data.index_array) > 1e6:
+            warn(f"The calculation of the normal direction for each cell might take a long time, because "
+                 f"{len(boundary_data.index_array)} cells are marked as Free Slip boundary cells. Consider specifying "
+                 f" the normal direction beforehand, which is possible if it is equal for all cells (e.g. at a wall)")
+
+        dim = boundary_data.dim
+        coords = [coord for coord, _ in zip(['x', 'y', 'z'], range(dim))]
+
+        boundary_cells = set()
+
+        # get a set containing all boundary cells
+        for cell in boundary_data.index_array:
+            fluid_cell = tuple([cell[coord] for coord in coords])
+            direction = self.stencil[cell['dir']]
+            boundary_cell = tuple([i + d for i, d in zip(fluid_cell, direction)])
+            boundary_cells.add(boundary_cell)
+
+        for cell in boundary_data.index_array:
+            fluid_cell = tuple([cell[coord] for coord in coords])
+            direction = self.stencil[cell['dir']]
+            ref_direction = direction
+            normal_direction = [0] * dim
+
+            for i in range(dim):
+                sub_direction = [0] * dim
+                sub_direction[i] = direction[i]
+                test_cell = tuple([x + y for x, y in zip(fluid_cell, sub_direction)])
+
+                if test_cell in boundary_cells:
+                    normal_direction[i] = direction[i]
+                    ref_direction = MirroredStencilDirections.mirror_stencil(ref_direction, i)
+
+            # convex corner special case:
+            if all(n == 0 for n in normal_direction):
+                normal_direction = direction
+            else:
+                ref_direction = inverse_direction(ref_direction)
+
+            for i, cell_name in zip(range(dim), self.additional_data):
+                cell[cell_name[0]] = -normal_direction[i]
+            cell['ref_dir'] = self.stencil.index(ref_direction)
+
+    @property
+    def additional_data(self):
+        """Used internally only. For the FreeSlip boundary the information of the normal direction for each pdf
+        direction is needed. This information is stored in the index vector."""
+        if self.normal_direction:
+            return []
+        else:
+            data_type = create_type('int32')
+            wnz = [] if self.dim == 2 else [('wnz', data_type)]
+            data = [('wnx', data_type), ('wny', data_type)] + wnz
+            return data + [('ref_dir', data_type)]
+
+    @property
+    def additional_data_init_callback(self):
+        if self.normal_direction:
+            return None
+        else:
+            return self.init_callback
+
+    def get_additional_code_nodes(self, lb_method):
+        if self.normal_direction:
+            return [MirroredStencilDirections(self.stencil, self.mirror_axis), NeighbourOffsetArrays(lb_method.stencil)]
+        else:
+            return [NeighbourOffsetArrays(lb_method.stencil)]
+
+    def __call__(self, f_out, f_in, dir_symbol, inv_dir, lb_method, index_field, force_vector):
+        neighbor_offset = NeighbourOffsetArrays.neighbour_offset(dir_symbol, lb_method.stencil)
+        if self.normal_direction:
+            tangential_offset = tuple(offset + normal for offset, normal in zip(neighbor_offset, self.normal_direction))
+            mirrored_stencil_symbol = MirroredStencilDirections._mirrored_symbol(self.mirror_axis, self.stencil)
+            mirrored_direction = inv_dir[sp.IndexedBase(mirrored_stencil_symbol, shape=(1,))[dir_symbol]]
+        else:
+            normal_direction = list()
+            for i, cell_name in zip(range(self.dim), self.additional_data):
+                normal_direction.append(index_field[0](cell_name[0]))
+            normal_direction = tuple(normal_direction)
+            tangential_offset = tuple(offset + normal for offset, normal in zip(neighbor_offset, normal_direction))
+
+            mirrored_direction = index_field[0]('ref_dir')
+
+        return Assignment(f_in.center(inv_dir[dir_symbol]), f_out[tangential_offset](mirrored_direction))
+
+
+# end class FreeSlip
+
+
+class WallFunctionBounce(LbBoundary):
+    """
+    Wall function based on the bounce back idea, cf. :cite:`Han2021`. Its implementation is extended to the D3Q27
+    stencil, whereas different weights of the drag distribution are proposed.
+
+    Args:
+        lb_method: LB method which is used for the simulation
+        pdfs: Symbolic representation of the particle distribution functions.
+        normal_direction: Normal direction of the wall. Currently, only straight and axis-aligned walls are supported.
+        wall_function_model: Wall function that is used to retrieve the wall stress :math:`tau_w` during the simulation.
+                             See :class:`lbmpy.boundaries.wall_treatment.WallFunctionModel` for more details
+        mean_velocity: Optional field or field access for the mean velocity. As wall functions are typically defined
+                       in terms of the mean velocity, it is recommended to provide this variable. Per default, the
+                       instantaneous velocity obtained from pdfs is used for the wall function.
+        sampling_shift: Optional sampling shift for the velocity sampling. Can be provided as symbolic variable or
+                        integer. In both cases, the user must assure that the sampling shift is at least 1, as sampling
+                        in boundary cells is not physical. Per default, a sampling shift of 1 is employed which
+                        corresponds to a sampling in the first fluid cell normal to the wall. For lower friction
+                        Reynolds numbers, choosing a sampling shift >1 has shown to improve the results for higher
+                        resolutions.
+                        Mutually exclusive with the Maronga sampling shift.
+        maronga_sampling_shift: Optionally, apply a correction factor to the wall shear stress proposed by Maronga et
+                                al. :cite:`Maronga2020`. Has only been tested and validated for the MOST wall function.
+                                No guarantee is given that it also works with other wall functions.
+                                Mutually exclusive with the standard sampling shift.
+        dt: time discretisation. Usually one in LB units
+        dy: space discretisation. Usually one in LB units
+        y: distance from the wall
+        target_friction_velocity: A target friction velocity can be given if an estimate is known a priori. This target
+                                  friction velocity will be used as initial guess for implicit wall functions to ensure
+                                  convergence of the Newton algorithm.
+        weight_method: The extension of the WFB to a D3Q27 stencil is non-unique. Different weights can be chosen to
+                       define the drag distribution onto the pdfs. Per default, weights corresponding to the weights
+                       in the D3Q27 stencil are chosen.
+        name: Optional name of the boundary.
+        data_type: Floating-point precision. Per default, double.
+    """
+
+    class WeightMethod(Enum):
+        LATTICE_WEIGHT = auto(),
+        GEOMETRIC_WEIGHT = auto()
+
+    def __init__(self, lb_method, pdfs, normal_direction, wall_function_model,
+                 mean_velocity=None, sampling_shift=1, maronga_sampling_shift=None,
+                 dt=1, dy=1, y=0.5,
+                 target_friction_velocity=None,
+                 weight_method=WeightMethod.LATTICE_WEIGHT,
+                 name=None, data_type='double'):
+        """Set an optional name here, to mark boundaries, for example for force evaluations"""
+        self.stencil = lb_method.stencil
+        if not (self.stencil.Q == 19 or self.stencil.Q == 27):
+            raise ValueError("WFB boundary is currently only defined for D3Q19 and D3Q27 stencils.")
+        self.pdfs = pdfs
+
+        self.wall_function_model = wall_function_model
+
+        if mean_velocity:
+            if isinstance(mean_velocity, Field):
+                self.mean_velocity = mean_velocity.center_vector
+            elif isinstance(mean_velocity, Field.Access):
+                self.mean_velocity = mean_velocity.field.neighbor_vector(mean_velocity.offsets)
+            else:
+                raise ValueError("Mean velocity field has to be a pystencils Field or Field.Access")
+        else:
+            self.mean_velocity = None
+
+        if not isinstance(sampling_shift, int):
+            self.sampling_shift = TypedSymbol(sampling_shift.name, np.uint32)
+        else:
+            assert sampling_shift >= 1, "The sampling shift must be greater than 1."
+            self.sampling_shift = sampling_shift
+
+        if maronga_sampling_shift:
+            assert self.mean_velocity, "Mean velocity field must be provided when using the Maronga correction"
+            if not isinstance(maronga_sampling_shift, int):
+                self.maronga_sampling_shift = TypedSymbol(maronga_sampling_shift.name, np.uint32)
+            else:
+                assert maronga_sampling_shift >= 1, "The Maronga sampling shift must be greater than 1."
+                self.maronga_sampling_shift = maronga_sampling_shift
+        else:
+            self.maronga_sampling_shift = None
+
+        if (self.sampling_shift != 1) and self.maronga_sampling_shift:
+            raise ValueError("Both sampling shift and Maronga offset are set. This is currently not supported.")
+
+        self.dt = dt
+        self.dy = dy
+        self.y = y
+        self.data_type = data_type
+
+        self.target_friction_velocity = target_friction_velocity
+
+        self.weight_method = weight_method
+
+        if len(normal_direction) - normal_direction.count(0) != 1:
+            raise ValueError("Only normal directions for straight walls are supported for example (0, 1, 0) for "
+                             "a WallFunctionBounce applied to the southern boundary of the domain")
+
+        self.mirror_axis = normal_direction.index(*[direction for direction in normal_direction if direction != 0])
+
+        self.normal_direction = normal_direction
+        assert all([n in [-1, 0, 1] for n in self.normal_direction]), \
+            "Only -1, 0 and 1 allowed for defining the normal direction"
+        tangential_component = [int(not n) for n in self.normal_direction]
+        self.normal_axis = tangential_component.index(0)
+        self.tangential_axis = [0, 1, 2]
+        self.tangential_axis.remove(self.normal_axis)
+
+        self.dim = self.stencil.D
+
+        if name is None:
+            name = f"WFB : {offset_to_direction_string([-x for x in normal_direction])}"
+
+        super(WallFunctionBounce, self).__init__(name, calculate_force_on_boundary=False)
+
+    def get_additional_code_nodes(self, lb_method):
+        return [MirroredStencilDirections(self.stencil, self.mirror_axis),
+                NeighbourOffsetArrays(lb_method.stencil)]
+
+    def __call__(self, f_out, f_in, dir_symbol, inv_dir, lb_method, index_field, force_vector):
+        # needed symbols for offsets and indices
+        # neighbour offset symbols are basically the stencil directions defined in stencils.py:L130ff.
+        neighbor_offset = NeighbourOffsetArrays.neighbour_offset(dir_symbol, lb_method.stencil)
+        tangential_offset = tuple(offset + normal for offset, normal in zip(neighbor_offset, self.normal_direction))
+        mirrored_stencil_symbol = MirroredStencilDirections._mirrored_symbol(self.mirror_axis, self.stencil)
+        mirrored_direction = inv_dir[sp.IndexedBase(mirrored_stencil_symbol, shape=(1,))[dir_symbol]]
+
+        name_base = "f_in_inv_offsets_"
+        offset_array_symbols = [TypedSymbol(name_base + d, mirrored_stencil_symbol.dtype) for d in ['x', 'y', 'z']]
+        mirrored_offset = sp.IndexedBase(mirrored_stencil_symbol, shape=(1,))[dir_symbol]
+        offsets = tuple(sp.IndexedBase(s, shape=(1,))[mirrored_offset] for s in offset_array_symbols)
+
+        # needed symbols in the Assignments
+        u_m = sp.Symbol("u_m")
+        tau_w = sp.Symbol("tau_w")
+        wall_stress = sp.symbols("tau_w_x tau_w_y tau_w_z")
+
+        # if the mean velocity field is not given, or the Maronga correction is applied, density and velocity values
+        # will be calculated from pdfs
+        cqc = lb_method.conserved_quantity_computation
+
+        result = []
+        if (not self.mean_velocity) or self.maronga_sampling_shift:
+            pdf_center_vector = sp.Matrix([0] * self.stencil.Q)
+
+            for i in range(self.stencil.Q):
+                pdf_center_vector[i] = self.pdfs[offsets[0] + self.normal_direction[0],
+                                                 offsets[1] + self.normal_direction[1],
+                                                 offsets[2] + self.normal_direction[2]](i)
+
+            eq_equations = cqc.equilibrium_input_equations_from_pdfs(pdf_center_vector)
+            result.append(eq_equations.all_assignments)
+
+        # sample velocity which will be used in the wall stress calculation
+        if self.mean_velocity:
+            if self.maronga_sampling_shift:
+                u_for_tau_wall = tuple(u_mean_i.get_shifted(
+                    self.maronga_sampling_shift * self.normal_direction[0],
+                    self.maronga_sampling_shift * self.normal_direction[1],
+                    self.maronga_sampling_shift * self.normal_direction[2]
+                ) for u_mean_i in self.mean_velocity)
+            else:
+                u_for_tau_wall = tuple(u_mean_i.get_shifted(
+                    self.sampling_shift * self.normal_direction[0],
+                    self.sampling_shift * self.normal_direction[1],
+                    self.sampling_shift * self.normal_direction[2]
+                ) for u_mean_i in self.mean_velocity)
+
+            rho_for_tau_wall = sp.Float(1)
+        else:
+            rho_for_tau_wall = cqc.density_symbol
+            u_for_tau_wall = cqc.velocity_symbols
+
+        # calculate Maronga factor in case of correction
+        maronga_fix = sp.Symbol("maronga_fix")
+        if self.maronga_sampling_shift:
+            inst_first_cell_vel = cqc.velocity_symbols
+            mean_first_cell_vel = tuple(u_mean_i.get_shifted(*self.normal_direction) for u_mean_i in self.mean_velocity)
+
+            mag_inst_vel_first_cell = sp.sqrt(sum([inst_first_cell_vel[i] ** 2 for i in self.tangential_axis]))
+            mag_mean_vel_first_cell = sp.sqrt(sum([mean_first_cell_vel[i] ** 2 for i in self.tangential_axis]))
+
+            result.append(Assignment(maronga_fix, mag_inst_vel_first_cell / mag_mean_vel_first_cell))
+        else:
+            maronga_fix = 1
+
+        # store which direction is tangential component (only those are used for the wall shear stress)
+        red_u_mag = sp.sqrt(sum([u_for_tau_wall[i]**2 for i in self.tangential_axis]))
+
+        u_mag = Assignment(u_m, red_u_mag)
+        result.append(u_mag)
+
+        wall_distance = self.maronga_sampling_shift if self.maronga_sampling_shift else self.sampling_shift
+
+        # using wall function model
+        wall_law_assignments = self.wall_function_model.shear_stress_assignments(
+            density_symbol=rho_for_tau_wall, velocity_symbol=u_m, shear_stress_symbol=tau_w,
+            wall_distance=(wall_distance - sp.Rational(1, 2) * self.dy),
+            u_tau_target=self.target_friction_velocity)
+        result.append(wall_law_assignments)
+
+        # calculate wall stress components and use them to calculate the drag
+        for i in self.tangential_axis:
+            result.append(Assignment(wall_stress[i], - u_for_tau_wall[i] / u_m * tau_w * maronga_fix))
+
+        weight, inv_weight_sq = sp.symbols("wfb_weight inverse_weight_squared")
+
+        if self.stencil.Q == 19:
+            result.append(Assignment(weight, sp.Rational(1, 2)))
+        elif self.stencil.Q == 27:
+            result.append(
+                Assignment(
+                    inv_weight_sq,
+                    sum([CastFunc(neighbor_offset[i], self.data_type)**2 for i in self.tangential_axis])
+                )
+            )
+            a, b = sp.symbols("wfb_a wfb_b")
+
+            if self.weight_method == self.WeightMethod.LATTICE_WEIGHT:
+                res_ab = sp.solve([2 * a + 4 * b - 1, a - 4 * b], [a, b])  # lattice weight scaling
+            elif self.weight_method == self.WeightMethod.GEOMETRIC_WEIGHT:
+                res_ab = sp.solve([2 * a + 4 * b - 1, a - sp.sqrt(2) * b], [a, b])  # geometric scaling
+            else:
+                raise ValueError("Unknown weighting method for the WFB D3Q27 extension. Currently, only lattice "
+                                 "weights and geometric weights are supported.")
+
+            result.append(Assignment(weight, sp.Piecewise((sp.Float(0), sp.Equality(inv_weight_sq, 0)),
+                                                          (res_ab[a], sp.Equality(inv_weight_sq, 1)),
+                                                          (res_ab[b], True))))
+
+        factor = self.dt / self.dy * weight
+        drag = sum(
+            [
+                CastFunc(neighbor_offset[i], self.data_type) * factor * wall_stress[i]
+                for i in self.tangential_axis
+            ]
+        )
+
+        result.append(Assignment(f_in.center(inv_dir[dir_symbol]), f_out[tangential_offset](mirrored_direction) - drag))
+
+        return result
+
+# end class WallFunctionBounce
+
+
+class UBB(LbBoundary):
+    r"""Velocity bounce back boundary condition, enforcing specified velocity at obstacle. Furthermore, a density
+        at the wall can be implied. The boundary condition is implemented with the following formula:
+
+    .. math ::
+        f_{\overline{i}}(\mathbf{x}_b, t + \Delta t) = f^{\star}_{i}(\mathbf{x}_b, t) -
+        2 w_{i} \rho_{w} \frac{\mathbf{c}_i \cdot \mathbf{u}_w}{c_s^2}
+
+
+    Args:
+        velocity: Prescribe the fluid velocity :math:`\mathbf{u}_w` at the wall.
+                  Can either be a constant, an access into a field, or a callback function.
+                  The callback functions gets a numpy record array with members, ``x``, ``y``, ``z``, ``dir``
+                  (direction) and ``velocity`` which has to be set to the desired velocity of the corresponding link
+        density: Prescribe the fluid density :math:`\rho_{w}` at the wall. If not prescribed the density is
+                 calculated from the PDFs at the wall. The density can only be set constant.
+        adapt_velocity_to_force: adapts the velocity to the correct equilibrium when the lattice Boltzmann method holds
+                                 a forcing term. If no forcing term is set and adapt_velocity_to_force is set to True
+                                 it has no effect.
+        dim: number of spatial dimensions
+        name: optional name of the boundary.
+    """
+
+    def __init__(self, velocity, density=None, adapt_velocity_to_force=False, dim=None, name=None, data_type='double'):
+        self._velocity = velocity
+        self._density = density
+        self._adaptVelocityToForce = adapt_velocity_to_force
+        if callable(self._velocity) and not dim:
+            raise ValueError("When using a velocity callback the dimension has to be specified with the dim parameter")
+        elif not callable(self._velocity):
+            dim = len(velocity)
+        self.dim = dim
+        self.data_type = data_type
+
+        super(UBB, self).__init__(name, calculate_force_on_boundary=False)
+
+    @property
+    def additional_data(self):
+        """ In case of the UBB boundary additional data is a velocity vector. This vector is added to each cell to
+            realize velocity profiles for the inlet."""
+        if self.velocity_is_callable:
+            return [(f'vel_{i}', create_type(self.data_type)) for i in range(self.dim)]
+        else:
+            return []
+
+    @property
+    def additional_data_init_callback(self):
+        """Initialise additional data of the boundary. For an example see
+            `tutorial 02 <https://pycodegen.pages.i10git.cs.fau.de/lbmpy/notebooks/02_tutorial_boundary_setup.html>`_
+            or lbmpy.geometry.add_pipe_inflow_boundary"""
+        if callable(self._velocity):
+            return self._velocity
+
+    def get_additional_code_nodes(self, lb_method):
+        """Return a list of code nodes that will be added in the generated code before the index field loop.
+
+        Args:
+            lb_method: Lattice Boltzmann method. See :func:`lbmpy.creationfunctions.create_lb_method`
+
+        Returns:
+            list containing LbmWeightInfo and NeighbourOffsetArrays
+        """
+        return [LbmWeightInfo(lb_method, self.data_type), NeighbourOffsetArrays(lb_method.stencil)]
+
+    @property
+    def velocity_is_callable(self):
+        """Returns True is velocity is callable. This means the velocity should be initialised via a callback function.
+        This is useful if the inflow velocity should have a certain profile for instance"""
+        return callable(self._velocity)
+
+    def __call__(self, f_out, f_in, dir_symbol, inv_dir, lb_method, index_field, force_vector):
+        dtype = create_type(self.data_type)
+        vel_from_idx_field = callable(self._velocity)
+        vel = [index_field(f'vel_{i}') for i in range(self.dim)] if vel_from_idx_field else self._velocity
+
+        assert self.dim == lb_method.dim, \
+            f"Dimension of UBB ({self.dim}) does not match dimension of method ({lb_method.dim})"
+
+        neighbor_offset = NeighbourOffsetArrays.neighbour_offset(dir_symbol, lb_method.stencil)
+
+        velocity = tuple(v_i.get_shifted(*neighbor_offset)
+                         if isinstance(v_i, Field.Access) and not vel_from_idx_field
+                         else v_i
+                         for v_i in vel)
+
+        if self._adaptVelocityToForce:
+            cqc = lb_method.conserved_quantity_computation
+            shifted_vel_eqs = cqc.equilibrium_input_equations_from_init_values(velocity=velocity)
+            shifted_vel_eqs = shifted_vel_eqs.new_without_subexpressions()
+            velocity = [eq.rhs for eq in shifted_vel_eqs.new_filtered(cqc.velocity_symbols).main_assignments]
+
+        c_s_sq = sp.Rational(1, 3)
+        weight_info = LbmWeightInfo(lb_method, data_type=self.data_type)
+        weight_of_direction = weight_info.weight_of_direction
+        vel_term = (
+            2 / c_s_sq
+            * sum([CastFunc(d_i, dtype) * v_i for d_i, v_i in zip(neighbor_offset, velocity)]) 
+            * weight_of_direction(dir_symbol, lb_method)
+        )
+
+        # Better alternative: in conserved value computation
+        # rename what is currently called density to "virtual_density"
+        # provide a new quantity density, which is constant in case of incompressible models
+        if lb_method.conserved_quantity_computation.compressible:
+            cqc = lb_method.conserved_quantity_computation
+            density_symbol = sp.Symbol("rho")
+            pdf_field_accesses = [f_out(i) for i in range(len(lb_method.stencil))]
+            density_equations = cqc.output_equations_from_pdfs(pdf_field_accesses, {'density': density_symbol})
+            density_symbol = lb_method.conserved_quantity_computation.density_symbol
+            if self._density:
+                result = [Assignment(density_symbol, self._density)]
+            else:
+                result = density_equations.all_assignments
+            result += [Assignment(f_in(inv_dir[dir_symbol]),
+                                  f_out(dir_symbol) - vel_term * density_symbol)]
+            return result
+        else:
+            return [Assignment(f_in(inv_dir[dir_symbol]),
+                               f_out(dir_symbol) - vel_term)]
+
+
+# end class UBB
+
+
+class SimpleExtrapolationOutflow(LbBoundary):
+    r"""
+    Simple Outflow boundary condition :cite:`geier2015`, equation F.1 (listed below).
+    This boundary condition extrapolates missing populations from the last layer of
+    fluid cells onto the boundary by copying them in the normal direction.
+
+    .. math ::
+        f_{\overline{1}jkxyzt} = f_{\overline{1}jk(x - \Delta x)yzt}
+
+
+    Args:
+        normal_direction: direction vector normal to the outflow
+        stencil: stencil used by the lattice boltzmann method
+        name: optional name of the boundary.
+    """
+
+    def __init__(self, normal_direction, stencil, name=None):
+        if isinstance(normal_direction, str):
+            normal_direction = direction_string_to_offset(normal_direction, dim=len(stencil[0]))
+
+        if name is None:
+            name = f"Simple Outflow: {offset_to_direction_string(normal_direction)}"
+
+        self.normal_direction = tuple([int(n) for n in normal_direction])
+        assert all([n in [-1, 0, 1] for n in self.normal_direction]), \
+            "Only -1, 0 and 1 allowed for defining the normal direction"
+        super(SimpleExtrapolationOutflow, self).__init__(name, calculate_force_on_boundary=False)
+
+    def get_additional_code_nodes(self, lb_method):
+        """Return a list of code nodes that will be added in the generated code before the index field loop.
+
+        Args:
+            lb_method: Lattice Boltzmann method. See :func:`lbmpy.creationfunctions.create_lb_method`
+
+        Returns:
+            list containing NeighbourOffsetArrays
+
+        """
+        return [NeighbourOffsetArrays(lb_method.stencil)]
+
+    def __call__(self, f_out, f_in, dir_symbol, inv_dir, lb_method, index_field, force_vector):
+        neighbor_offset = NeighbourOffsetArrays.neighbour_offset(dir_symbol, lb_method.stencil)
+        tangential_offset = tuple(offset - normal for offset, normal in zip(neighbor_offset, self.normal_direction))
+
+        return Assignment(f_in.center(inv_dir[dir_symbol]), f_out[tangential_offset](inv_dir[dir_symbol]))
+
+
+# end class SimpleExtrapolationOutflow
+
+
+class ExtrapolationOutflow(LbBoundary):
+    r"""
+    Outflow boundary condition :cite:`geier2015`, equation F.2, with u neglected (listed below).
+    This boundary condition interpolates populations missing on the boundary in normal direction.
+    For this interpolation, the PDF values of the last time step are used. They are interpolated
+    between fluid cell and boundary cell. To get the PDF values from the last time step an index
+    array is used which stores them.
+
+    .. math ::
+        f_{\overline{1}jkxyzt} = f_{\overline{1}jk(x - \Delta x)yz(t - \Delta t)} c \theta^{\frac{1}{2}}
+        \frac{\Delta t}{\Delta x} + \left(1 - c \theta^{\frac{1}{2}} \frac{\Delta t}{\Delta x} \right)
+         f_{\overline{1}jk(x - \Delta x)yzt}
+
+
+    Args:
+        normal_direction: direction vector normal to the outflow
+        lb_method: the lattice Boltzmann method to be used in the simulation
+        dt: lattice time step size
+        dx: lattice spacing distance
+        name: optional name of the boundary.
+        streaming_pattern: Streaming pattern to be used in the simulation
+        zeroth_timestep: for in-place patterns, whether the initial setup corresponds to an even or odd time step
+        initial_density: floating point constant or callback taking spatial coordinates (x, y [,z]) as
+                         positional arguments, specifying the initial density on boundary nodes
+        initial_velocity: tuple of floating point constants or callback taking spatial coordinates (x, y [,z]) as
+                          positional arguments, specifying the initial velocity on boundary nodes
+    """
+
+    def __init__(self, normal_direction, lb_method, dt=1, dx=1, name=None,
+                 streaming_pattern='pull', zeroth_timestep=Timestep.BOTH,
+                 initial_density=None, initial_velocity=None, data_type='double'):
+
+        self.lb_method = lb_method
+        self.stencil = lb_method.stencil
+        self.dim = len(self.stencil[0])
+
+        if isinstance(normal_direction, str):
+            normal_direction = direction_string_to_offset(normal_direction, dim=self.dim)
+
+        if name is None:
+            name = f"Outflow: {offset_to_direction_string(normal_direction)}"
+
+        self.normal_direction = tuple([int(n) for n in normal_direction])
+        assert all([n in [-1, 0, 1] for n in self.normal_direction]), \
+            "Only -1, 0 and 1 allowed for defining the normal direction"
+        self.streaming_pattern = streaming_pattern
+        self.zeroth_timestep = zeroth_timestep
+        self.dx = sp.Number(dx)
+        self.dt = sp.Number(dt)
+        self.c = sp.sqrt(sp.Rational(1, 3)) * (self.dx / self.dt)
+
+        self.initial_density = initial_density
+        self.initial_velocity = initial_velocity
+        self.equilibrium_calculation = None
+
+        self.data_type = data_type
+
+        if initial_density and initial_velocity:
+            equilibrium = lb_method.get_equilibrium(conserved_quantity_equations=AssignmentCollection([]))
+            rho = lb_method.zeroth_order_equilibrium_moment_symbol
+            u_vec = lb_method.first_order_equilibrium_moment_symbols
+            eq_lambda = equilibrium.lambdify((rho,) + u_vec)
+            post_pdf_symbols = lb_method.post_collision_pdf_symbols
+
+            def calc_eq_pdfs(density, velocity, j):
+                return eq_lambda(density, *velocity)[post_pdf_symbols[j]]
+
+            self.equilibrium_calculation = calc_eq_pdfs
+
+        super(ExtrapolationOutflow, self).__init__(name, calculate_force_on_boundary=False)
+
+    def init_callback(self, boundary_data, **_):
+        dim = boundary_data.dim
+        coord_names = ['x', 'y', 'z'][:dim]
+        pdf_acc = AccessPdfValues(self.stencil, streaming_pattern=self.streaming_pattern,
+                                  timestep=self.zeroth_timestep, streaming_dir='out')
+
+        def get_boundary_cell_pdfs(f_cell, b_cell, direction):
+            if self.equilibrium_calculation is not None:
+                density = self.initial_density(
+                    *b_cell) if callable(self.initial_density) else self.initial_density
+                velocity = self.initial_velocity(
+                    *b_cell) if callable(self.initial_velocity) else self.initial_velocity
+                return self.equilibrium_calculation(density, velocity, direction)
+            else:
+                return pdf_acc.read_pdf(boundary_data.pdf_array, f_cell, direction)
+
+        for entry in boundary_data.index_array:
+            center = tuple(entry[c] for c in coord_names)
+            direction = self.stencil[entry["dir"]]
+            inv_dir = self.stencil.index(inverse_direction(direction))
+            tangential_offset = tuple(offset - normal for offset, normal in zip(direction, self.normal_direction))
+            domain_cell = tuple(f + o for f, o in zip(center, tangential_offset))
+            outflow_cell = tuple(f + o for f, o in zip(center, direction))
+
+            #   Initial fluid cell PDF values
+            entry['pdf'] = pdf_acc.read_pdf(boundary_data.pdf_array, domain_cell, inv_dir)
+            entry['pdf_nd'] = get_boundary_cell_pdfs(domain_cell, outflow_cell, inv_dir)
+
+    @property
+    def additional_data(self):
+        """Used internally only. For the ExtrapolationOutflow information of the previous PDF values is needed. This
+        information is stored in the index vector."""
+        data = [('pdf', create_type(self.data_type)), ('pdf_nd', create_type(self.data_type))]
+        return data
+
+    @property
+    def additional_data_init_callback(self):
+        return self.init_callback
+
+    def get_additional_code_nodes(self, lb_method):
+        """Return a list of code nodes that will be added in the generated code before the index field loop.
+
+        Args:
+            lb_method: Lattice Boltzmann method. See :func:`lbmpy.creationfunctions.create_lb_method`
+
+        Returns:
+            list containing NeighbourOffsetArrays
+
+        """
+        return [NeighbourOffsetArrays(lb_method.stencil)]
+
+    def __call__(self, f_out, f_in, dir_symbol, inv_dir, lb_method, index_field, force_vector):
+        subexpressions = []
+        boundary_assignments = []
+        dtdx = sp.Rational(self.dt, self.dx)
+
+        neighbor_offset = NeighbourOffsetArrays.neighbour_offset(dir_symbol, lb_method.stencil)
+        tangential_offset = tuple(offset - normal for offset, normal in zip(neighbor_offset, self.normal_direction))
+
+        interpolated_pdf_sym = sp.Symbol('pdf_inter')
+        interpolated_pdf_asm = Assignment(interpolated_pdf_sym, (index_field[0]('pdf') * (self.c * dtdx))
+                                          + ((sp.Number(1) - self.c * dtdx) * index_field[0]('pdf_nd')))
+        subexpressions.append(interpolated_pdf_asm)
+
+        asm = Assignment(f_in.center(inv_dir[dir_symbol]), interpolated_pdf_sym)
+        boundary_assignments.append(asm)
+
+        asm = Assignment(index_field[0]('pdf'), f_out[tangential_offset](inv_dir[dir_symbol]))
+        boundary_assignments.append(asm)
+
+        asm = Assignment(index_field[0]('pdf_nd'), interpolated_pdf_sym)
+        boundary_assignments.append(asm)
+
+        return AssignmentCollection(boundary_assignments, subexpressions=subexpressions)
+
+
+# end class ExtrapolationOutflow
+
+
+class FixedDensity(LbBoundary):
+    r"""Boundary condition for prescribing a density at the wall. Through :math:`p = c_s^2 \rho` this boundary condition
+        can also function as a pressure boundary condition.
+
+    .. math ::
+        f_{\overline{i}}(\mathbf{x}_b, t + \Delta t) = - f^{\star}_{i}(\mathbf{x}_b, t) +
+        2 w_{i} \rho_{w} (1 + \frac{(\mathbf{c}_i \cdot \mathbf{u}_w)^2}{2c_s^4} + \frac{\mathbf{u}_w^2}{2c_s^2})
+
+    Args:
+        density: value of the density which should be set.
+        name: optional name of the boundary.
+    """
+
+    def __init__(self, density, name=None):
+        if name is None:
+            name = "Fixed Density " + str(density)
+        self.density = density
+
+        super(FixedDensity, self).__init__(name, calculate_force_on_boundary=False)
+
+    def __call__(self, f_out, f_in, dir_symbol, inv_dir, lb_method, index_field, force_vector):
+        def remove_asymmetric_part_of_main_assignments(assignment_collection, degrees_of_freedom):
+            new_main_assignments = [Assignment(a.lhs, get_symmetric_part(a.rhs, degrees_of_freedom))
+                                    for a in assignment_collection.main_assignments]
+            return assignment_collection.copy(new_main_assignments)
+
+        cqc = lb_method.conserved_quantity_computation
+        velocity = cqc.velocity_symbols
+        symmetric_eq = remove_asymmetric_part_of_main_assignments(lb_method.get_equilibrium(),
+                                                                  degrees_of_freedom=velocity)
+        substitutions = {sym: f_out(i) for i, sym in enumerate(lb_method.pre_collision_pdf_symbols)}
+        symmetric_eq = symmetric_eq.new_with_substitutions(substitutions)
+
+        simplification = create_simplification_strategy(lb_method)
+        symmetric_eq = simplification(symmetric_eq)
+
+        density = self.density
+        equilibrium_input = cqc.equilibrium_input_equations_from_init_values(density=density)
+        equilibrium_input = equilibrium_input.new_without_subexpressions()
+        equilibrium_input = equilibrium_input.main_assignments_dict
+
+        subexpressions_dict = symmetric_eq.subexpressions_dict
+        subexpressions_dict[cqc.density_symbol] = equilibrium_input[cqc.density_symbol]
+        subexpressions_dict[cqc.density_deviation_symbol] = equilibrium_input[cqc.density_deviation_symbol]
+
+        conditions = [(eq_i.rhs, sp.Equality(dir_symbol, i))
+                      for i, eq_i in enumerate(symmetric_eq.main_assignments)] + [(0, True)]
+        eq_component = sp.Piecewise(*conditions)
+
+        main_assignments = [Assignment(f_in(inv_dir[dir_symbol]), 2 * eq_component - f_out(dir_symbol))]
+
+        ac = AssignmentCollection(main_assignments, subexpressions=subexpressions_dict)
+        ac = ac.new_without_unused_subexpressions()
+        ac.topological_sort()
+
+        return ac
+
+
+# end class FixedDensity
+
+class DiffusionDirichlet(LbBoundary):
+    """Concentration boundary which is used for concentration or thermal boundary conditions of convection-diffusion
+    equation Base on https://doi.org/10.1103/PhysRevE.85.016701.
+
+    Args:
+        concentration: can either be a constant, an access into a field, or a callback function.
+                       The callback functions gets a numpy record array with members, ``x``, ``y``, ``z``, ``dir``
+                       (direction) and ``concentration`` which has to be set to the desired
+                       velocity of the corresponding link
+        velocity_field: if velocity field is given the boundary value is approximated by using the discrete equilibrium.
+        name: optional name of the boundary.
+        data_type: data type of the concentration value. default is double
+    """
+
+    def __init__(self, concentration, velocity_field=None, name=None, data_type='double'):
+        if name is None:
+            name = "DiffusionDirichlet"
+        self.concentration = concentration
+        self._data_type = data_type
+        self.concentration_is_callable = callable(self.concentration)
+        self.velocity_field = velocity_field
+
+        super(DiffusionDirichlet, self).__init__(name, calculate_force_on_boundary=False)
+
+    @property
+    def additional_data(self):
+        """ In case of the UBB boundary additional data is a velocity vector. This vector is added to each cell to
+            realize velocity profiles for the inlet."""
+        if self.concentration_is_callable:
+            return [('concentration', create_type(self._data_type))]
+        else:
+            return []
+
+    @property
+    def additional_data_init_callback(self):
+        """Initialise additional data of the boundary. For an example see
+            `tutorial 02 <https://pycodegen.pages.i10git.cs.fau.de/lbmpy/notebooks/02_tutorial_boundary_setup.html>`_
+            or lbmpy.geometry.add_pipe_inflow_boundary"""
+        if self.concentration_is_callable:
+            return self.concentration
+
+    def get_additional_code_nodes(self, lb_method):
+        """Return a list of code nodes that will be added in the generated code before the index field loop.
+
+        Args:
+            lb_method: Lattice Boltzmann method. See :func:`lbmpy.creationfunctions.create_lb_method`
+
+        Returns:
+            list containing LbmWeightInfo
+        """
+        if self.velocity_field:
+            return [LbmWeightInfo(lb_method, self._data_type), NeighbourOffsetArrays(lb_method.stencil)]
+        else:
+            return [LbmWeightInfo(lb_method, self._data_type)]
+
+    def __call__(self, f_out, f_in, dir_symbol, inv_dir, lb_method, index_field, force_vector):
+        assert lb_method.conserved_quantity_computation.zero_centered_pdfs is False, \
+            "DiffusionDirichlet only works for methods with normal pdfs storage -> set zero_centered=False"
+        weight_info = LbmWeightInfo(lb_method, self._data_type)
+        w_dir = weight_info.weight_of_direction(dir_symbol, lb_method)
+
+        if self.concentration_is_callable:
+            concentration = index_field[0]('concentration')
+        else:
+            concentration = self.concentration
+
+        if self.velocity_field:
+            neighbour_offset = NeighbourOffsetArrays.neighbour_offset(dir_symbol, lb_method.stencil)
+            u = self.velocity_field
+            cs = sp.Rational(1, 3)
+
+            equilibrium = (1 + scalar_product(neighbour_offset, u.center_vector)**2 / (2 * cs**4)
+                           - scalar_product(u.center_vector, u.center_vector) / (2 * cs**2))
+        else:
+            equilibrium = sp.Rational(1, 1)
+
+        result = [Assignment(f_in(inv_dir[dir_symbol]), 2.0 * w_dir * concentration * equilibrium - f_out(dir_symbol))]
+        return result
+
+
+# end class DiffusionDirichlet
+
+
+class NeumannByCopy(LbBoundary):
+    """Neumann boundary condition which is implemented by coping the PDF values to achieve similar values at the fluid
+       and the boundary node"""
+
+    def get_additional_code_nodes(self, lb_method):
+        """Return a list of code nodes that will be added in the generated code before the index field loop.
+
+        Args:
+            lb_method: Lattice Boltzmann method. See :func:`lbmpy.creationfunctions.create_lb_method`
+
+        Returns:
+            list containing NeighbourOffsetArrays
+        """
+        return [NeighbourOffsetArrays(lb_method.stencil)]
+
+    def __call__(self, f_out, f_in, dir_symbol, inv_dir, lb_method, index_field, force_vector):
+        neighbour_offset = NeighbourOffsetArrays.neighbour_offset(dir_symbol, lb_method.stencil)
+        return [Assignment(f_in(inv_dir[dir_symbol]), f_out(inv_dir[dir_symbol])),
+                Assignment(f_out[neighbour_offset](dir_symbol), f_out(dir_symbol))]
+
+
+# end class NeumannByCopy
+
+
+class StreamInConstant(LbBoundary):
+    """Boundary condition that takes a constant and overrides the boundary PDFs with this value. This is used for
+    debugging mainly.
+
+    Args:
+        constant: value which should be set for the PDFs at the boundary cell.
+        name: optional name of the boundary.
+    """
+
+    def __init__(self, constant, name=None):
+        super(StreamInConstant, self).__init__(name, calculate_force_on_boundary=False)
+        self.constant = constant
+
+    def get_additional_code_nodes(self, lb_method):
+        """Return a list of code nodes that will be added in the generated code before the index field loop.
+
+        Args:
+            lb_method: Lattice Boltzmann method. See :func:`lbmpy.creationfunctions.create_lb_method`
+
+        Returns:
+            list containing NeighbourOffsetArrays
+        """
+        return [NeighbourOffsetArrays(lb_method.stencil)]
+
+    def __call__(self, f_out, f_in, dir_symbol, inv_dir, lb_method, index_field, force_vector):
+        neighbour_offset = NeighbourOffsetArrays.neighbour_offset(dir_symbol, lb_method.stencil)
+        return [Assignment(f_in(inv_dir[dir_symbol]), self.constant),
+                Assignment(f_out[neighbour_offset](dir_symbol), self.constant)]
+
+# end class StreamInConstant

src/lbmpy/boundaries/boundaryhandling.py

+from dataclasses import replace
+import numpy as np
+
+from pystencils import Assignment, CreateKernelConfig, create_kernel, Field, Target, FieldType
+from pystencils.boundaries import BoundaryHandling
+from pystencils.boundaries.createindexlist import numpy_data_type_for_boundary_object
+from pystencils.simp import add_subexpressions_for_field_reads
+from pystencils.stencil import inverse_direction
+
+from lbmpy.advanced_streaming.indexing import BetweenTimestepsIndexing
+from lbmpy.advanced_streaming.utility import is_inplace, Timestep, AccessPdfValues
+
+from .._compat import IS_PYSTENCILS_2
+
+if IS_PYSTENCILS_2:
+    from pystencils.types import PsNumericType
+
+
+class LatticeBoltzmannBoundaryHandling(BoundaryHandling):
+    """
+    Enables boundary handling for LBM simulations with advanced streaming patterns.
+    For the in-place patterns AA and EsoTwist, two kernels are generated for a boundary
+    object and the right one selected depending on the time step.
+    """
+
+    def __init__(self, lb_method, data_handling, pdf_field_name, streaming_pattern='pull',
+                 name="boundary_handling", flag_interface=None, target=Target.CPU, openmp=False, **kwargs):
+        self._lb_method = lb_method
+        self._streaming_pattern = streaming_pattern
+        self._inplace = is_inplace(streaming_pattern)
+        self._prev_timestep = None
+        super(LatticeBoltzmannBoundaryHandling, self).__init__(
+            data_handling, pdf_field_name, lb_method.stencil,
+            name, flag_interface, target=target, openmp=openmp,
+            **kwargs
+        )
+
+    #   ------------------------- Overridden methods of pystencils.BoundaryHandling -------------------------
+
+    @property
+    def prev_timestep(self):
+        return self._prev_timestep
+
+    def __call__(self, prev_timestep=Timestep.BOTH, **kwargs):
+        self._prev_timestep = prev_timestep
+        super(LatticeBoltzmannBoundaryHandling, self).__call__(**kwargs)
+        self._prev_timestep = None
+
+    def add_fixed_steps(self, fixed_loop, **kwargs):
+        if self._inplace:  # Fixed Loop can't do timestep selection
+            raise NotImplementedError("Adding to fixed loop is currently not supported for inplace kernels")
+        super(LatticeBoltzmannBoundaryHandling, self).add_fixed_steps(fixed_loop, **kwargs)
+
+    def _add_boundary(self, boundary_obj, flag=None):
+        if self._inplace:
+            return self._add_inplace_boundary(boundary_obj, flag)
+        else:
+            return super(LatticeBoltzmannBoundaryHandling, self)._add_boundary(boundary_obj, flag)
+
+    def _add_inplace_boundary(self, boundary_obj, flag=None):
+        if boundary_obj not in self._boundary_object_to_boundary_info:
+            sym_index_field = Field.create_generic('indexField', spatial_dimensions=1, field_type=FieldType.INDEXED,
+                                                   dtype=numpy_data_type_for_boundary_object(boundary_obj, self.dim))
+
+            ast_even = self._create_boundary_kernel(self._data_handling.fields[self._field_name], sym_index_field,
+                                                    boundary_obj, Timestep.EVEN)
+            ast_odd = self._create_boundary_kernel(self._data_handling.fields[self._field_name], sym_index_field,
+                                                   boundary_obj, Timestep.ODD)
+            kernels = [ast_even.compile(), ast_odd.compile()]
+            if flag is None:
+                flag = self.flag_interface.reserve_next_flag()
+            boundary_info = self.InplaceStreamingBoundaryInfo(self, boundary_obj, flag, kernels)
+            self._boundary_object_to_boundary_info[boundary_obj] = boundary_info
+        return self._boundary_object_to_boundary_info[boundary_obj].flag
+
+    def _create_boundary_kernel(self, symbolic_field, symbolic_index_field, boundary_obj, prev_timestep=Timestep.BOTH):
+        if IS_PYSTENCILS_2:
+            additional_args = {"default_dtype": self._default_dtype}
+        else:
+            additional_args = dict()
+            
+        return create_lattice_boltzmann_boundary_kernel(
+            symbolic_field, symbolic_index_field, self._lb_method, boundary_obj,
+            prev_timestep=prev_timestep, streaming_pattern=self._streaming_pattern,
+            target=self._target, cpu_openmp=self._openmp, **additional_args)
+
+    class InplaceStreamingBoundaryInfo(object):
+
+        @property
+        def kernel(self):
+            prev_timestep = self._boundary_handling.prev_timestep
+            if prev_timestep is None:
+                raise Exception(
+                    "The boundary kernel property was accessed while "
+                    + "there was no boundary handling in progress.")
+            return self._kernels[prev_timestep]
+
+        def __init__(self, boundary_handling, boundary_obj, flag, kernels):
+            self._boundary_handling = boundary_handling
+            self.boundary_object = boundary_obj
+            self.flag = flag
+            self._kernels = kernels
+
+    #   end class InplaceStreamingBoundaryInfo
+
+    # ------------------------------ Force On Boundary ------------------------------------------------------------
+
+    def force_on_boundary(self, boundary_obj, prev_timestep=Timestep.BOTH):
+        from lbmpy.boundaries import NoSlip
+        self.__call__(prev_timestep=prev_timestep)
+        if isinstance(boundary_obj, NoSlip):
+            return self._force_on_no_slip(boundary_obj, prev_timestep)
+        else:
+            return self._force_on_boundary(boundary_obj, prev_timestep)
+
+    def _force_on_no_slip(self, boundary_obj, prev_timestep):
+        dh = self._data_handling
+        ff_ghost_layers = dh.ghost_layers_of_field(self.flag_interface.flag_field_name)
+        method = self._lb_method
+        stencil = np.array(method.stencil)
+        result = np.zeros(self.dim)
+
+        for b in dh.iterate(ghost_layers=ff_ghost_layers):
+            obj_to_ind_list = b[self._index_array_name].boundary_object_to_index_list
+            pdf_array = b[self._field_name]
+            if boundary_obj in obj_to_ind_list:
+                ind_arr = obj_to_ind_list[boundary_obj]
+                acc = AccessPdfValues(self._lb_method.stencil,
+                                      streaming_pattern=self._streaming_pattern, timestep=prev_timestep,
+                                      streaming_dir='out')
+                values = 2 * acc.collect_from_index_list(pdf_array, ind_arr)
+                forces = stencil[ind_arr['dir']] * values[:, np.newaxis]
+                result += forces.sum(axis=0)
+        return dh.reduce_float_sequence(list(result), 'sum')
+
+    def _force_on_boundary(self, boundary_obj, prev_timestep):
+        dh = self._data_handling
+        ff_ghost_layers = dh.ghost_layers_of_field(self.flag_interface.flag_field_name)
+        method = self._lb_method
+        stencil = np.array(method.stencil)
+        inv_direction = np.array([method.stencil.index(inverse_direction(d))
+                                  for d in method.stencil])
+        result = np.zeros(self.dim)
+
+        for b in dh.iterate(ghost_layers=ff_ghost_layers):
+            obj_to_ind_list = b[self._index_array_name].boundary_object_to_index_list
+            pdf_array = b[self._field_name]
+            if boundary_obj in obj_to_ind_list:
+                ind_arr = obj_to_ind_list[boundary_obj]
+                inverse_ind_arr = ind_arr.copy()
+                inverse_ind_arr['dir'] = inv_direction[inverse_ind_arr['dir']]
+                acc_out = AccessPdfValues(self._lb_method.stencil,
+                                          streaming_pattern=self._streaming_pattern, timestep=prev_timestep,
+                                          streaming_dir='out')
+                acc_in = AccessPdfValues(self._lb_method.stencil,
+                                         streaming_pattern=self._streaming_pattern, timestep=prev_timestep.next(),
+                                         streaming_dir='in')
+                acc_fluid = acc_out if boundary_obj.inner_or_boundary else acc_in
+                acc_boundary = acc_in if boundary_obj.inner_or_boundary else acc_out
+                fluid_values = acc_fluid.collect_from_index_list(pdf_array, ind_arr)
+                boundary_values = acc_boundary.collect_from_index_list(pdf_array, inverse_ind_arr)
+                values = fluid_values + boundary_values
+                forces = stencil[ind_arr['dir']] * values[:, np.newaxis]
+                result += forces.sum(axis=0)
+
+        return dh.reduce_float_sequence(list(result), 'sum')
+
+
+# end class LatticeBoltzmannBoundaryHandling
+
+def create_lattice_boltzmann_boundary_kernel(pdf_field, index_field, lb_method, boundary_functor,
+                                             prev_timestep=Timestep.BOTH, streaming_pattern='pull',
+                                             target=Target.CPU, force_vector=None, **kernel_creation_args):
+    from .._compat import IS_PYSTENCILS_2
+
+    indexing = BetweenTimestepsIndexing(
+        pdf_field, lb_method.stencil, prev_timestep, streaming_pattern, np.int32, np.int32)
+
+    dim = lb_method.stencil.D
+    f_out, f_in = indexing.proxy_fields
+    dir_symbol = indexing.dir_symbol
+    inv_dir = indexing.inverse_dir_symbol
+
+    if IS_PYSTENCILS_2:
+        from pystencils.types.quick import SInt
+        config = CreateKernelConfig(
+            index_field=index_field,
+            target=target,
+            index_dtype=SInt(32),
+            skip_independence_check=True,
+            **kernel_creation_args
+        )
+
+        default_data_type: PsNumericType = config.get_option("default_dtype")
+
+        if force_vector is None:
+            force_vector_type = np.dtype([(f"F_{i}", default_data_type.numpy_dtype) for i in range(dim)], align=True)
+            force_vector = Field.create_generic('force_vector', spatial_dimensions=1,
+                                                dtype=force_vector_type, field_type=FieldType.INDEXED)
+
+        boundary_assignments = boundary_functor(f_out, f_in, dir_symbol, inv_dir, lb_method, index_field, force_vector)
+        boundary_assignments = indexing.substitute_proxies(boundary_assignments)
+
+        if pdf_field.dtype != default_data_type:
+            boundary_assignments = add_subexpressions_for_field_reads(boundary_assignments, data_type=default_data_type)
+
+        elements: list[Assignment] = []
+
+        index_arrs_node = indexing.create_code_node()
+        elements += index_arrs_node.get_array_declarations()
+        
+        for node in boundary_functor.get_additional_code_nodes(lb_method)[::-1]:
+            elements += node.get_array_declarations()
+            
+        elements += [Assignment(dir_symbol, index_field[0]('dir'))]
+        elements += boundary_assignments.all_assignments
+
+        kernel = create_kernel(elements, config=config)
+        return kernel
+    else:
+        config = CreateKernelConfig(index_fields=[index_field], target=target, default_number_int="int32",
+                                    skip_independence_check=True, **kernel_creation_args)
+
+        default_data_type = config.data_type.default_factory()
+
+        if force_vector is None:
+            force_vector_type = np.dtype([(f"F_{i}", default_data_type.c_name) for i in range(dim)], align=True)
+            force_vector = Field.create_generic('force_vector', spatial_dimensions=1,
+                                                dtype=force_vector_type, field_type=FieldType.INDEXED)
+
+        config = replace(config, index_fields=[index_field, force_vector])
+
+        boundary_assignments = boundary_functor(f_out, f_in, dir_symbol, inv_dir, lb_method, index_field, force_vector)
+        boundary_assignments = indexing.substitute_proxies(boundary_assignments)
+
+        if pdf_field.dtype != default_data_type:
+            boundary_assignments = add_subexpressions_for_field_reads(boundary_assignments, data_type=default_data_type)
+
+        elements = [Assignment(dir_symbol, index_field[0]('dir'))]
+        elements += boundary_assignments.all_assignments
+
+        kernel = create_kernel(elements, config=config)
+
+        #   Code Elements ahead of the loop
+        index_arrs_node = indexing.create_code_node()
+        for node in boundary_functor.get_additional_code_nodes(lb_method)[::-1]:
+            kernel.body.insert_front(node)
+        kernel.body.insert_front(index_arrs_node)
+        return kernel

src/lbmpy/boundaries/wall_function_models.py

+import sympy as sp
+from abc import ABC, abstractmethod
+
+from pystencils import Assignment
+
+
+class WallFunctionModel(ABC):
+    def __init__(self, name):
+        self._name = name
+
+    @abstractmethod
+    def shear_stress_assignments(self, density_symbol: sp.Symbol, shear_stress_symbol: sp.Symbol,
+                                 velocity_symbol: sp.Symbol, wall_distance, u_tau_target):
+        """
+        Computes a symbolic representation for the log law.
+
+        Args:
+            density_symbol: symbol density, should be provided by the LB method's conserved quantity computation
+            shear_stress_symbol: symbolic wall shear stress to which the calculated shear stress will be assigned
+            velocity_symbol: symbolic velocity that is taken as a reference in the wall functions
+            wall_distance: distance to the wall, equals to 0.5 in standard cell-centered LBM
+            u_tau_target: in implicit wall functions, a target friction velocity can be provided which will be used as
+                          initial guess in the Newton iteration. This target friction velocity can be obtained, e.g.,
+                          from the target friction Reynolds number
+        """
+        pass
+
+
+# end class WallFunctionModel
+
+
+class ExplicitWallFunctionModel(WallFunctionModel, ABC):
+    """
+    Abstract base class for explicit wall functions that can be solved directly for the wall shear stress.
+    """
+
+    def __init__(self, name):
+        super(ExplicitWallFunctionModel, self).__init__(name=name)
+
+
+class MoninObukhovSimilarityTheory(ExplicitWallFunctionModel):
+    def __init__(self, z0, kappa=0.41, phi=0, name="MOST"):
+        self.z0 = z0
+        self.kappa = kappa
+        self.phi = phi
+
+        super(MoninObukhovSimilarityTheory, self).__init__(name=name)
+
+    def shear_stress_assignments(self, density_symbol: sp.Symbol, shear_stress_symbol: sp.Symbol,
+                                 velocity_symbol: sp.Symbol, wall_distance, u_tau_target=None):
+        u_tau = velocity_symbol * self.kappa / sp.ln(wall_distance / self.z0 + self.phi)
+        return [Assignment(shear_stress_symbol, u_tau ** 2 * density_symbol)]
+
+
+class ImplicitWallFunctionModel(WallFunctionModel, ABC):
+    """
+    Abstract base class for implicit wall functions that require a Newton procedure to solve for the wall shear stress.
+    """
+
+    def __init__(self, name, newton_steps, viscosity):
+        self.newton_steps = newton_steps
+        self.u_tau = sp.symbols(f"wall_function_u_tau_:{self.newton_steps + 1}")
+        self.delta = sp.symbols(f"wall_function_delta_:{self.newton_steps}")
+
+        self.viscosity = viscosity
+
+        super(ImplicitWallFunctionModel, self).__init__(name=name)
+
+    def newton_iteration(self, wall_law):
+        m = -wall_law / wall_law.diff(self.u_tau[0])
+
+        assignments = []
+        for i in range(self.newton_steps):
+            assignments.append(Assignment(self.delta[i], m.subs({self.u_tau[0]: self.u_tau[i]})))
+            assignments.append(Assignment(self.u_tau[i + 1], self.u_tau[i] + self.delta[i]))
+
+        return assignments
+
+
+class LogLaw(ImplicitWallFunctionModel):
+    """
+    Analytical model for the velocity profile inside the boundary layer, obtained from the mean velocity gradient.
+    Only valid in the log-law region.
+    """
+
+    def __init__(self, viscosity, newton_steps=5, kappa=0.41, b=5.2, name="LogLaw"):
+        self.kappa = kappa
+        self.b = b
+
+        super(LogLaw, self).__init__(name=name, newton_steps=newton_steps, viscosity=viscosity)
+
+    def shear_stress_assignments(self, density_symbol: sp.Symbol, shear_stress_symbol: sp.Symbol,
+                                 velocity_symbol: sp.Symbol, wall_distance, u_tau_target=None):
+        def law(u_p, y_p):
+            return 1 / self.kappa * sp.ln(y_p) + self.b - u_p
+
+        u_plus = velocity_symbol / self.u_tau[0]
+        y_plus = (wall_distance * self.u_tau[0]) / self.viscosity
+
+        u_tau_init = u_tau_target if u_tau_target else velocity_symbol / sp.Float(100)
+
+        wall_law = law(u_plus, y_plus)
+        assignments = [Assignment(self.u_tau[0], u_tau_init),  # initial guess
+                       *self.newton_iteration(wall_law),  # newton iterations
+                       Assignment(shear_stress_symbol, self.u_tau[-1] ** 2 * density_symbol)]  # final result
+
+        return assignments
+
+
+class SpaldingsLaw(ImplicitWallFunctionModel):
+    """
+    Single formula for the velocity profile inside the boundary layer, proposed by Spalding :cite:`spalding1961`.
+    Valid in the inner and the outer layer.
+    """
+
+    def __init__(self, viscosity, newton_steps=5, kappa=0.41, b=5.5, name="Spalding"):
+        self.kappa = kappa
+        self.b = b
+
+        super(SpaldingsLaw, self).__init__(name=name, newton_steps=newton_steps, viscosity=viscosity)
+
+    def shear_stress_assignments(self, density_symbol: sp.Symbol, shear_stress_symbol: sp.Symbol,
+                                 velocity_symbol: sp.Symbol, wall_distance, u_tau_target=None):
+        def law(u_p, y_p):
+            k_times_u = self.kappa * u_p
+            frac_1 = (k_times_u ** 2) / sp.Float(2)
+            frac_2 = (k_times_u ** 3) / sp.Float(6)
+            return (u_p + sp.exp(-self.kappa * self.b) * (sp.exp(k_times_u) - sp.Float(1) - k_times_u - frac_1 - frac_2)
+                    - y_p)
+
+        u_plus = velocity_symbol / self.u_tau[0]
+        y_plus = (wall_distance * self.u_tau[0]) / self.viscosity
+
+        u_tau_init = u_tau_target if u_tau_target else velocity_symbol / sp.Float(100)
+
+        wall_law = law(u_plus, y_plus)
+        assignments = [Assignment(self.u_tau[0], u_tau_init),  # initial guess
+                       *self.newton_iteration(wall_law),  # newton iterations
+                       Assignment(shear_stress_symbol, self.u_tau[-1] ** 2 * density_symbol)]  # final result
+
+        return assignments
+
+
+class MuskerLaw(ImplicitWallFunctionModel):
+    """
+    Quasi-analytical model for the velocity profile inside the boundary layer, proposed by Musker. Valid in the inner
+    and the outer layer.
+    Formulation taken from :cite:`malaspinas2015`, Equation (59).
+    """
+
+    def __init__(self, viscosity, newton_steps=5, name="Musker"):
+
+        super(MuskerLaw, self).__init__(name=name, newton_steps=newton_steps, viscosity=viscosity)
+
+    def shear_stress_assignments(self, density_symbol: sp.Symbol, shear_stress_symbol: sp.Symbol,
+                                 velocity_symbol: sp.Symbol, wall_distance, u_tau_target=None):
+        def law(u_p, y_p):
+            arctan = sp.Float(5.424) * sp.atan(sp.Float(0.119760479041916168) * y_p - sp.Float(0.488023952095808383))
+            logarithm = (sp.Float(0.434) * sp.log((y_p + sp.Float(10.6)) ** sp.Float(9.6)
+                                                  / (y_p ** 2 - sp.Float(8.15) * y_p + sp.Float(86)) ** 2))
+            return (arctan + logarithm - sp.Float(3.50727901936264842)) - u_p
+
+        u_plus = velocity_symbol / self.u_tau[0]
+        y_plus = (wall_distance * self.u_tau[0]) / self.viscosity
+
+        u_tau_init = u_tau_target if u_tau_target else velocity_symbol / sp.Float(100)
+
+        wall_law = law(u_plus, y_plus)
+        assignments = [Assignment(self.u_tau[0], u_tau_init),  # initial guess
+                       *self.newton_iteration(wall_law),  # newton iterations
+                       Assignment(shear_stress_symbol, self.u_tau[-1] ** 2 * density_symbol)]  # final result
+
+        return assignments

lbmpy/chapman_enskog/chapman_enskog.py → src/lbmpy/chapman_enskog/chapman_enskog.py

@@ -21,8 +21,8 @@ class ChapmanEnskogAnalysis:
         cqc = method.conserved_quantity_computation
         self._method = method
         self._moment_cache = LbMethodEqMoments(method)
-        self.rho = cqc.defined_symbols(order=0)[1]
-        self.u = cqc.defined_symbols(order=1)[1]
+        self.rho = cqc.density_symbol
+        self.u = cqc.velocity_symbols
         self.t = sp.Symbol("t")
         self.epsilon = sp.Symbol("epsilon")
 
@@ -370,7 +370,7 @@ def take_moments(eqn, pdf_to_moment_name=(('f', '\\Pi'), ('\\Omega f', '\\Upsilo
                 if new_f_index is None:
                     rest *= factor
                 else:
-                    assert not(new_f_index and f_index)
+                    assert not (new_f_index and f_index)
                     f_index = new_f_index
 
         moment_tuple = [0] * len(velocity_terms)

lbmpy/chapman_enskog/chapman_enskog_steady_state.py → src/lbmpy/chapman_enskog/chapman_enskog_steady_state.py

 import functools
 
+import numpy as np
 import sympy as sp
 
 from lbmpy.chapman_enskog.chapman_enskog import (
@@ -150,7 +151,8 @@ class SteadyStateChapmanEnskogAnalysis:
 
                 have_shape = hasattr(arg, 'shape') and hasattr(new_prod, 'shape')
                 if have_shape and arg.shape == new_prod.shape and arg.shape[1] == 1:
-                    new_prod = sp.matrix_multiply_elementwise(new_prod, arg)
+                    # since sympy 1.9 sp.matrix_multiply_elementwise does not work anymore in this case
+                    new_prod = sp.Matrix(np.multiply(new_prod, arg))
                 else:
                     new_prod = arg * new_prod
                 if new_prod == 0: