lbmpy_tests/test_force_on_boundary.py → tests/test_force_on_boundary.py

 import numpy as np
 
 from lbmpy.boundaries import UBB, NoSlip
+from lbmpy.enums import ForceModel
 from lbmpy.scenarios import create_channel
 from pystencils import make_slice
 
-try:
-    import waLBerla as wLB
-except ImportError:
-    wLB = None
+# try:
+#     import waLBerla as wLB
+# except ImportError:
+wLB = None
 
 
 def calculate_force(step, obstacle):
@@ -26,10 +27,11 @@ def test_force_on_boundary():
 
     for parallel in (False, True) if wLB else (False,):
         for boundary_obj in boundaries:
-            print("Testing parallel %d, boundary %s" % (parallel, boundary_obj.name))
-            step = create_channel(domain_size, force=1e-5, relaxation_rate=1.5, parallel=parallel, force_model='buick')
+            print(f"Testing parallel {parallel}, boundary {boundary_obj.name}")
+            step = create_channel(domain_size, force=1e-5, relaxation_rate=1.5, parallel=parallel,
+                                  force_model=ForceModel.BUICK)
             force = calculate_force(step, boundary_obj)
-            print("  -> force = ", force)
+            print(f"  -> force = {force}")
             results.append(force)
 
     for res in results[1:]:

tests/test_free_slip.py

+from dataclasses import replace
+
+import pystencils as ps
+import lbmpy as lp
+from pystencils.slicing import slice_from_direction
+
+from lbmpy.boundaries.boundaryhandling import LatticeBoltzmannBoundaryHandling
+from lbmpy.boundaries.boundaryconditions import FreeSlip, NoSlip, ExtrapolationOutflow, UBB
+
+from lbmpy.creationfunctions import create_lb_method, create_lb_update_rule
+from lbmpy.macroscopic_value_kernels import pdf_initialization_assignments
+
+import numpy as np
+
+
+def velocity_info_callback(boundary_data, **_):
+    boundary_data['vel_1'] = 0
+    boundary_data['vel_2'] = 0
+    u_max = 0.1
+    x, y = boundary_data.link_positions(0), boundary_data.link_positions(1)
+    dist = (15 - y) / 15
+    boundary_data['vel_0'] = u_max * (1 - dist)
+
+
+def test_free_slip():
+    stencil = lp.LBStencil(lp.Stencil.D3Q27)
+    domain_size = (30, 15, 30)
+    dim = len(domain_size)
+
+    dh = ps.create_data_handling(domain_size=domain_size)
+
+    src = dh.add_array('src', values_per_cell=stencil.Q)
+    dh.fill('src', 0.0, ghost_layers=True)
+    dst = dh.add_array('dst', values_per_cell=stencil.Q)
+    dh.fill('dst', 0.0, ghost_layers=True)
+
+    velField = dh.add_array('velField', values_per_cell=stencil.D)
+    dh.fill('velField', 0.0, ghost_layers=True)
+
+    lbm_config = lp.LBMConfig(stencil=stencil, method=lp.Method.SRT, relaxation_rate=1.8,
+                              output={'velocity': velField}, kernel_type='stream_pull_collide')
+    method = create_lb_method(lbm_config=lbm_config)
+
+    init = pdf_initialization_assignments(method, 1.0, (0, 0, 0), src.center_vector)
+
+    config = ps.CreateKernelConfig(target=dh.default_target, cpu_openmp=False)
+    ast_init = ps.create_kernel(init, config=config)
+    kernel_init = ast_init.compile()
+
+    dh.run_kernel(kernel_init)
+
+    lbm_opt = lp.LBMOptimisation(symbolic_field=src, symbolic_temporary_field=dst)
+    lbm_config = replace(lbm_config, lb_method=method)
+
+    update = create_lb_update_rule(lbm_config=lbm_config, lbm_optimisation=lbm_opt)
+
+    ast_kernel = ps.create_kernel(update, config=config)
+    kernel = ast_kernel.compile()
+
+    bh = LatticeBoltzmannBoundaryHandling(method, dh, 'src', name="bh")
+
+    inflow = UBB(velocity_info_callback, dim=dim)
+    outflow = ExtrapolationOutflow(stencil[4], method)
+    wall = NoSlip("wall")
+    freeslip = FreeSlip(stencil, (0, -1, 0))
+
+    bh.set_boundary(inflow, slice_from_direction('W', dim))
+    bh.set_boundary(outflow, slice_from_direction('E', dim))
+    bh.set_boundary(wall, slice_from_direction('S', dim))
+    bh.set_boundary(wall, slice_from_direction('T', dim))
+    bh.set_boundary(wall, slice_from_direction('B', dim))
+    bh.set_boundary(freeslip, slice_from_direction('N', dim))
+
+    for i in range(2000):
+        bh()
+        dh.run_kernel(kernel)
+        dh.swap("src", "dst")
+
+    vel_profile = dh.gather_array('velField')[-2, :, domain_size[2] // 2, 0]
+    np.testing.assert_almost_equal(np.gradient(vel_profile)[-1], 0, decimal=3)

lbmpy_tests/test_geometry_setup_serial.py → tests/test_geometry_setup_serial.py

 import os
 
 import numpy as np
+import pytest
 
 from lbmpy.boundaries import NoSlip
+from lbmpy.enums import Method
 from lbmpy.geometry import add_black_and_white_image, add_pipe_walls
 from lbmpy.lbstep import LatticeBoltzmannStep
+import lbmpy.plot as plt
 from pystencils.slicing import make_slice
 
 
@@ -22,23 +25,20 @@ def test_pipe():
     plot = False
     for domain_size in [(30, 10, 10), (30, 10)]:
         for diameter in [5, 10, diameter_callback]:
-            sc = LatticeBoltzmannStep(domain_size=domain_size, method='srt', relaxation_rate=1.9,
-                                      optimization={})
+            sc = LatticeBoltzmannStep(domain_size=domain_size, method=Method.SRT, relaxation_rate=1.9)
             add_pipe_walls(sc.boundary_handling, diameter)
             if plot:
-                import lbmpy.plot as plt
-                from pystencils.slicing import make_slice
                 if len(domain_size) == 2:
                     plt.boundary_handling(sc.boundary_handling)
-                    plt.title("2D, diameter=%s" % (str(diameter,)))
+                    plt.title(f"2D, diameter={str(diameter,)}")
                     plt.show()
                 elif len(domain_size) == 3:
                     plt.subplot(1, 2, 1)
                     plt.boundary_handling(sc.boundary_handling, make_slice[0.5, :, :])
-                    plt.title("3D, diameter=%s" % (str(diameter,)))
+                    plt.title(f"3D, diameter={str(diameter,)}")
                     plt.subplot(1, 2, 2)
                     plt.boundary_handling(sc.boundary_handling, make_slice[:, 0.5, :])
-                    plt.title("3D, diameter=%s" % (str(diameter, )))
+                    plt.title(f"3D, diameter={str(diameter, )}")
                     plt.show()
 
 
@@ -49,20 +49,19 @@ def get_test_image_path():
 
 
 def test_image():
-    sc = LatticeBoltzmannStep(domain_size=(50, 40), method='srt', relaxation_rate=1.9,
-                              optimization={})
+    pytest.importorskip('scipy.ndimage')
+    sc = LatticeBoltzmannStep(domain_size=(50, 40), method=Method.SRT, relaxation_rate=1.9)
     add_black_and_white_image(sc.boundary_handling, get_test_image_path(), keep_aspect_ratio=True)
 
 
 def test_slice_mask_combination():
-    sc = LatticeBoltzmannStep(domain_size=(30, 30), method='srt', relaxation_rate=1.9,
-                              optimization={})
+    sc = LatticeBoltzmannStep(domain_size=(30, 30), method=Method.SRT, relaxation_rate=1.9)
 
     def callback(*coordinates):
         x = coordinates[0]
         print("x", coordinates[0][:, 0])
         print("y", coordinates[1][0, :])
         print(x.shape)
-        return np.ones_like(x, dtype=np.bool)
+        return np.ones_like(x, dtype=bool)
 
     sc.boundary_handling.set_boundary(NoSlip(), make_slice[6:7, -1], callback)

tests/test_gpu_block_size_limiting.py

+from lbmpy.creationfunctions import create_lb_ast, LBMConfig
+from lbmpy.enums import Method, Stencil
+from lbmpy.stencils import LBStencil
+from lbmpy._compat import IS_PYSTENCILS_2
+import pytest
+from pystencils import Target, CreateKernelConfig
+
+
+@pytest.mark.xfail(IS_PYSTENCILS_2, reason="GPU block size limiting by registers is not available yet")
+def test_gpu_block_size_limiting():    
+    pytest.importorskip("cupy")
+    too_large = 2048*2048
+    lbm_config = LBMConfig(method=Method.CUMULANT, stencil=LBStencil(Stencil.D3Q19),
+                           relaxation_rate=1.8, compressible=True)
+    config = CreateKernelConfig(target=Target.GPU,
+                                gpu_indexing_params={'block_size': (too_large, too_large, too_large)})
+    ast = create_lb_ast(lbm_config=lbm_config, config=config)
+    limited_block_size = ast.indexing.call_parameters((1024, 1024, 1024))
+    kernel = ast.compile()
+    assert all(b < too_large for b in limited_block_size['block'])
+    bs = [too_large, too_large, too_large]
+    bs = ast.indexing.limit_block_size_by_register_restriction(bs, kernel.num_regs)
+    assert all(b < too_large for b in bs)

lbmpy_tests/test_html_output.py → tests/test_html_output.py

-from lbmpy.creationfunctions import create_lb_method
+import pytest
+
+from lbmpy.creationfunctions import create_lb_method, LBMConfig
+from lbmpy.enums import Stencil
 from lbmpy.methods.creationfunctions import compare_moment_based_lb_methods
 from lbmpy.moments import (
     moment_equality_table, moment_equality_table_by_stencil, moments_up_to_component_order)
-from lbmpy.stencils import get_stencil
+from lbmpy.stencils import LBStencil
 
 
 def test_moment_comparison_table():
-    new = create_lb_method(stencil='D3Q19', maxwellian_moments=True)
-    old = create_lb_method(stencil='D3Q19', maxwellian_moments=False)
+    pytest.importorskip('ipy_table')
+
+    lbm_config_new = LBMConfig(stencil=LBStencil(Stencil.D3Q19), continuous_equilibrium=True)
+    lbm_config_old = LBMConfig(stencil=LBStencil(Stencil.D3Q19), continuous_equilibrium=False)
+
+    new = create_lb_method(lbm_config=lbm_config_new)
+    old = create_lb_method(lbm_config=lbm_config_old)
 
     assert old.zeroth_order_equilibrium_moment_symbol == new.zeroth_order_equilibrium_moment_symbol
 
@@ -19,17 +27,18 @@ def test_moment_comparison_table():
     res_all = compare_moment_based_lb_methods(old, new, show_deviations_only=False)
     assert len(res_all.array) == 20
 
-    d3q27 = create_lb_method(stencil='D3Q27')
+    d3q27 = create_lb_method(LBMConfig(stencil=LBStencil(Stencil.D3Q27)))
     compare_moment_based_lb_methods(d3q27, new, show_deviations_only=False)
     compare_moment_based_lb_methods(new, d3q27, show_deviations_only=False)
 
 
 def test_moment_equality_table():
-    d3q19 = get_stencil('D3Q19')
+    pytest.importorskip('ipy_table')
+    d3q19 = LBStencil(Stencil.D3Q19)
     table1 = moment_equality_table(d3q19, max_order=3)
     assert len(table1.array) == 5
 
-    table2 = moment_equality_table_by_stencil({'D3Q19': d3q19, 'D3Q27': get_stencil("D3Q27")},
+    table2 = moment_equality_table_by_stencil({'D3Q19': d3q19, 'D3Q27': LBStencil(Stencil.D3Q27)},
                                               moments_up_to_component_order(2, dim=3))
     assert len(table2.array) == 11
     assert len(table2.array[0]) == 2 + 2

tests/test_hydro_maxwellian_class.py

+import pytest
+import sympy as sp
+from itertools import chain
+
+from pystencils.sympyextensions import remove_higher_order_terms
+
+from lbmpy.stencils import Stencil, LBStencil
+from lbmpy.equilibrium import ContinuousHydrodynamicMaxwellian, DiscreteHydrodynamicMaxwellian
+from lbmpy.moments import moments_up_to_component_order, moments_up_to_order
+from lbmpy.maxwellian_equilibrium import get_equilibrium_values_of_maxwell_boltzmann_function
+
+from lbmpy.methods.default_moment_sets import cascaded_moment_sets_literature, mrt_orthogonal_modes_literature
+
+
+def test_compressible_raw_moment_values():
+    stencil = LBStencil("D3Q27")
+    equilibrium = ContinuousHydrodynamicMaxwellian(dim=stencil.D, compressible=True, deviation_only=False)
+
+    raw_moments = list(chain.from_iterable(mrt_orthogonal_modes_literature(stencil, False)))
+
+    values_a = equilibrium.moments(raw_moments)
+
+    values_b = get_equilibrium_values_of_maxwell_boltzmann_function(raw_moments, stencil.D, space="moment")
+
+    for m, a, b in zip(raw_moments, values_a, values_b):
+        assert (a - b).expand() == sp.Integer(0), f"Mismatch at moment {m}."
+
+
+def test_compressible_central_moment_values():
+    stencil = LBStencil("D3Q27")
+    equilibrium = ContinuousHydrodynamicMaxwellian(dim=stencil.D, compressible=True, deviation_only=False)
+
+    central_moments = list(chain.from_iterable(cascaded_moment_sets_literature(stencil)))
+
+    values_a = equilibrium.central_moments(central_moments)
+
+    values_b = get_equilibrium_values_of_maxwell_boltzmann_function(central_moments, stencil.D, space="central moment")
+
+    for m, a, b in zip(central_moments, values_a, values_b):
+        assert (a - b).expand() == sp.Integer(0), f"Mismatch at moment {m}."
+
+
+def test_compressible_cumulant_values():
+    stencil = LBStencil("D3Q27")
+    equilibrium = ContinuousHydrodynamicMaxwellian(dim=stencil.D, compressible=True, deviation_only=False)
+
+    cumulants = list(chain.from_iterable(cascaded_moment_sets_literature(stencil)))
+
+    values_a = equilibrium.cumulants(cumulants, rescale=False)
+
+    values_b = get_equilibrium_values_of_maxwell_boltzmann_function(cumulants, stencil.D, space="cumulant")
+
+    for m, a, b in zip(cumulants, values_a, values_b):
+        assert (a - b).expand() == sp.Integer(0), f"Mismatch at cumulant {m}."
+
+
+@pytest.mark.parametrize('stencil', [Stencil.D2Q9, Stencil.D3Q15, Stencil.D3Q19, Stencil.D3Q27])
+@pytest.mark.parametrize('compressible', [False, True])
+@pytest.mark.parametrize('deviation_only', [False, True])
+def test_continuous_discrete_moment_equivalence(stencil, compressible, deviation_only):
+    stencil = LBStencil(stencil)
+    c_s_sq = sp.Rational(1, 3)
+    moments = tuple(moments_up_to_order(3, dim=stencil.D, include_permutations=False))
+    cd = ContinuousHydrodynamicMaxwellian(dim=stencil.D, compressible=compressible, deviation_only=deviation_only,
+                                          order=2, c_s_sq=c_s_sq)
+    cm = sp.Matrix(cd.moments(moments))
+    dd = DiscreteHydrodynamicMaxwellian(stencil, compressible=compressible, deviation_only=deviation_only,
+                                        order=2, c_s_sq=c_s_sq)
+    dm = sp.Matrix(dd.moments(moments))
+
+    rho = cd.density
+    delta_rho = cd.density_deviation
+    rho_0 = cd.background_density
+
+    subs = { delta_rho : rho - rho_0 }
+
+    assert (cm - dm).subs(subs).expand() == sp.Matrix((0,) * len(moments))
+
+
+@pytest.mark.parametrize('stencil', [Stencil.D2Q9, Stencil.D3Q15, Stencil.D3Q19, Stencil.D3Q27])
+@pytest.mark.parametrize('compressible', [False, True])
+@pytest.mark.parametrize('deviation_only', [False, True])
+def test_continuous_discrete_central_moment_equivalence(stencil, compressible, deviation_only):
+    stencil = LBStencil(stencil)
+    c_s_sq = sp.Rational(1, 3)
+    moments = tuple(moments_up_to_order(3, dim=stencil.D, include_permutations=False))
+    cd = ContinuousHydrodynamicMaxwellian(dim=stencil.D, compressible=compressible, deviation_only=deviation_only,
+                                          order=2, c_s_sq=c_s_sq)
+    cm = sp.Matrix(cd.central_moments(moments))
+    dd = DiscreteHydrodynamicMaxwellian(stencil, compressible=compressible, deviation_only=deviation_only,
+                                        order=2, c_s_sq=c_s_sq)
+    dm = sp.Matrix(dd.central_moments(moments))
+    dm = sp.Matrix([remove_higher_order_terms(t, dd.velocity, order=2) for t in dm])
+
+    rho = cd.density
+    delta_rho = cd.density_deviation
+    rho_0 = cd.background_density
+
+    subs = { delta_rho : rho - rho_0 }
+
+    assert (cm - dm).subs(subs).expand() == sp.Matrix((0,) * len(moments))
+
+
+@pytest.mark.parametrize('stencil', [Stencil.D2Q9, Stencil.D3Q15, Stencil.D3Q19, Stencil.D3Q27])
+def test_continuous_discrete_cumulant_equivalence(stencil):
+    stencil = LBStencil(stencil)
+    c_s_sq = sp.Rational(1, 3)
+    compressible = True
+    deviation_only = False
+    moments = tuple(moments_up_to_order(3, dim=stencil.D, include_permutations=False))
+    cd = ContinuousHydrodynamicMaxwellian(dim=stencil.D, compressible=compressible, deviation_only=deviation_only,
+                                          order=2, c_s_sq=c_s_sq)
+    cm = sp.Matrix(cd.cumulants(moments))
+    dd = DiscreteHydrodynamicMaxwellian(stencil, compressible=compressible, deviation_only=deviation_only,
+                                        order=2, c_s_sq=c_s_sq)
+    dm = sp.Matrix(dd.cumulants(moments))
+    dm = sp.Matrix([remove_higher_order_terms(t, dd.velocity, order=2) for t in dm])
+
+    rho = cd.density
+    delta_rho = cd.density_deviation
+    rho_0 = cd.background_density
+
+    subs = { delta_rho : rho - rho_0 }
+
+    assert (cm - dm).subs(subs).expand() == sp.Matrix((0,) * len(moments))

tests/test_interpolation_boundaries.py

+import pytest
+import numpy as np
+from pystencils.slicing import slice_from_direction
+
+from lbmpy import LBMConfig, LBStencil, Stencil, Method
+from lbmpy.boundaries.boundaryconditions import NoSlip, NoSlipLinearBouzidi, QuadraticBounceBack, UBB
+from lbmpy.lbstep import LatticeBoltzmannStep
+
+
+def check_velocity(noslip_velocity, interpolated_velocity, wall_distance):
+    # First we check if the flow is fully developed
+    np.testing.assert_almost_equal(np.gradient(np.gradient(noslip_velocity)), 0, decimal=8)
+    np.testing.assert_almost_equal(np.gradient(np.gradient(interpolated_velocity)), 0, decimal=8)
+
+    # If the wall is closer to the first fluid cell we expect a lower velocity at the first fluid cell
+    if wall_distance < 0.5:
+        assert noslip_velocity[0] > interpolated_velocity[0]
+    # If the wall is further away from the first fluid cell we expect a higher velocity at the first fluid cell
+    if wall_distance > 0.5:
+        assert noslip_velocity[0] < interpolated_velocity[0]
+    # If the wall cuts the cell halfway the interpolation BC should approximately fall back to a noslip boundary
+    if wall_distance == 0.5:
+        np.testing.assert_almost_equal(noslip_velocity[0], interpolated_velocity[0], decimal=2)
+
+
+def couette_flow(stencil, method_enum, zero_centered, wall_distance, compressible):
+    dim = stencil.D
+    if dim == 2:
+        domain_size = (50, 25)
+        wall_velocity = (0.01, 0)
+        periodicity = (True, False)
+    else:
+        domain_size = (50, 25, 25)
+        wall_velocity = (0.01, 0, 0)
+        periodicity = (True, False, True)
+
+    timesteps = 10000
+    omega = 1.1
+
+    lbm_config = LBMConfig(stencil=stencil,
+                           method=method_enum,
+                           relaxation_rate=omega,
+                           zero_centered=zero_centered,
+                           compressible=compressible,
+                           weighted=True)
+
+    lb_step_noslip = LatticeBoltzmannStep(domain_size=domain_size, periodicity=periodicity,
+                                          lbm_config=lbm_config, compute_velocity_in_every_step=True)
+    lb_step_bouzidi = LatticeBoltzmannStep(domain_size=domain_size, periodicity=periodicity,
+                                           lbm_config=lbm_config, compute_velocity_in_every_step=True)
+
+    lb_step_quadratic_bb = LatticeBoltzmannStep(domain_size=domain_size, periodicity=periodicity,
+                                                lbm_config=lbm_config, compute_velocity_in_every_step=True)
+
+    def init_wall_distance(boundary_data, **_):
+        for cell in boundary_data.index_array:
+            cell['q'] = wall_distance
+
+    moving_wall = UBB(wall_velocity)
+    noslip = NoSlip("wall")
+    bouzidi = NoSlipLinearBouzidi("wall", init_wall_distance=init_wall_distance)
+    quadratic_bb = QuadraticBounceBack(omega, "wall", init_wall_distance=init_wall_distance)
+
+    lb_step_noslip.boundary_handling.set_boundary(noslip, slice_from_direction('S', dim))
+    lb_step_noslip.boundary_handling.set_boundary(moving_wall, slice_from_direction('N', dim))
+
+    lb_step_bouzidi.boundary_handling.set_boundary(bouzidi, slice_from_direction('S', dim))
+    lb_step_bouzidi.boundary_handling.set_boundary(moving_wall, slice_from_direction('N', dim))
+
+    lb_step_quadratic_bb.boundary_handling.set_boundary(quadratic_bb, slice_from_direction('S', dim))
+    lb_step_quadratic_bb.boundary_handling.set_boundary(moving_wall, slice_from_direction('N', dim))
+
+    lb_step_noslip.run(timesteps)
+    lb_step_bouzidi.run(timesteps)
+    lb_step_quadratic_bb.run(timesteps)
+
+    if dim == 2:
+        noslip_velocity = lb_step_noslip.velocity[domain_size[0] // 2, :, 0]
+        bouzidi_velocity = lb_step_bouzidi.velocity[domain_size[0] // 2, :, 0]
+        quadratic_bb_velocity = lb_step_quadratic_bb.velocity[domain_size[0] // 2, :, 0]
+    else:
+        noslip_velocity = lb_step_noslip.velocity[domain_size[0] // 2, :, domain_size[2] // 2, 0]
+        bouzidi_velocity = lb_step_bouzidi.velocity[domain_size[0] // 2, :, domain_size[2] // 2, 0]
+        quadratic_bb_velocity = lb_step_quadratic_bb.velocity[domain_size[0] // 2, :, domain_size[2] // 2, 0]
+
+    check_velocity(noslip_velocity, bouzidi_velocity, wall_distance)
+    check_velocity(noslip_velocity, quadratic_bb_velocity, wall_distance)
+
+
+@pytest.mark.parametrize("zero_centered", [False, True])
+@pytest.mark.parametrize("wall_distance", [0.1, 0.5, 0.9])
+@pytest.mark.parametrize("compressible", [True, False])
+def test_couette_flow_short(zero_centered, wall_distance, compressible):
+    stencil = LBStencil(Stencil.D2Q9)
+    couette_flow(stencil, Method.SRT, zero_centered, wall_distance, compressible)
+
+
+@pytest.mark.parametrize("method_enum", [Method.MRT, Method.CENTRAL_MOMENT, Method.CUMULANT])
+@pytest.mark.parametrize("zero_centered", [False, True])
+@pytest.mark.parametrize("wall_distance", [0.1, 0.5, 0.9])
+@pytest.mark.parametrize("compressible", [True, False])
+@pytest.mark.longrun
+def test_couette_flow_long(method_enum, zero_centered, wall_distance, compressible):
+    if method_enum is Method.CUMULANT and compressible is False:
+        pytest.skip("incompressible cumulant is not supported")
+
+    stencil = LBStencil(Stencil.D2Q9)
+    couette_flow(stencil, method_enum, zero_centered, wall_distance, compressible)
+
+
+@pytest.mark.parametrize("method_enum", [Method.SRT, Method.MRT, Method.CENTRAL_MOMENT, Method.CUMULANT])
+@pytest.mark.parametrize("wall_distance", [0.1, 0.5, 0.9])
+@pytest.mark.parametrize("stencil", [Stencil.D3Q19, Stencil.D3Q27])
+@pytest.mark.longrun
+def test_couette_flow_d3d(method_enum, wall_distance, stencil):
+    stencil = LBStencil(stencil)
+    couette_flow(stencil, method_enum, True, wall_distance, True)
+
+

tests/test_json_serializer.py

+"""
+Test the lbmpy-specific JSON encoder and serializer as used in the Database class.
+"""
+
+import tempfile
+import pystencils as ps
+
+from lbmpy import Stencil, Method, ForceModel, SubgridScaleModel
+from lbmpy.advanced_streaming import Timestep
+from lbmpy.creationfunctions import LBMConfig, LBMOptimisation, LBStencil
+from lbmpy.fieldaccess import StreamPullTwoFieldsAccessor
+
+from pystencils.runhelper import Database
+from lbmpy.db import LbmpyJsonSerializer
+
+
+def test_json_serializer():
+
+    stencil = LBStencil(Stencil.D3Q27)
+    q = stencil.Q
+    pdfs, pdfs_tmp = ps.fields(f"pdfs({q}), pdfs_tmp({q}): double[3D]", layout='fzyx')
+    density = ps.fields(f"rho: double[3D]", layout='fzyx')
+
+    from lbmpy.non_newtonian_models import CassonsParameters
+    cassons_params = CassonsParameters(0.2)
+
+    # create dummy lbmpy config
+    lbm_config = LBMConfig(stencil=LBStencil(Stencil.D3Q27), method=Method.CUMULANT, force_model=ForceModel.GUO,
+                           compressible=True, relaxation_rate=1.999, subgrid_scale_model=SubgridScaleModel.SMAGORINSKY,
+                           galilean_correction=True, cassons=cassons_params, density_input=density,
+                           kernel_type=StreamPullTwoFieldsAccessor, timestep=Timestep.BOTH)
+
+    lbm_optimization = LBMOptimisation(cse_pdfs=False, cse_global=False, builtin_periodicity=(True, False, False),
+                                       symbolic_field=pdfs, symbolic_temporary_field=pdfs_tmp)
+
+    # create dummy database
+    temp_dir = tempfile.TemporaryDirectory()
+    db = Database(file=temp_dir.name, serializer_info=('lbmpy_serializer', LbmpyJsonSerializer))
+
+    db.save(params={'lbm_config': lbm_config, 'lbm_optimization': lbm_optimization}, result={'test': 'dummy'})

lbmpy_tests/test_lbstep.py → tests/test_lbstep.py

 import numpy as np
 import pytest
+from types import MappingProxyType
+from pystencils import Target, CreateKernelConfig
 
 from lbmpy.scenarios import create_fully_periodic_flow, create_lid_driven_cavity
+from lbmpy import SubgridScaleModel
 
 try:
-    import pycuda.driver
+    import cupy
     gpu_available = True
 except ImportError:
     gpu_available = False
@@ -30,18 +33,18 @@ def test_data_handling_3d():
         for gpu in [False, True] if gpu_available else [False]:
             if parallel and gpu and not hasattr(wLB, 'cuda'):
                 continue
-            print("Testing parallel: %s\tgpu: %s" % (parallel, gpu))
-            opt_params = {'target': 'gpu' if gpu else 'cpu',
-                          'gpu_indexing_params': {'block_size': (8, 4, 2)}}
+            print(f"Testing parallel: {parallel}\tgpu: {gpu}")
+            config = CreateKernelConfig(target=Target.GPU if gpu else Target.CPU,
+                                        gpu_indexing_params=MappingProxyType({'block_size': (8, 4, 2)}))
             if parallel:
                 from pystencils.datahandling import ParallelDataHandling
                 blocks = wLB.createUniformBlockGrid(blocks=(2, 3, 4), cellsPerBlock=(5, 5, 5),
                                                     oneBlockPerProcess=False)
                 dh = ParallelDataHandling(blocks, dim=3)
-                rho = ldc_setup(data_handling=dh, optimization=opt_params)
+                rho = ldc_setup(data_handling=dh, config=config)
                 results.append(rho)
             else:
-                rho = ldc_setup(domain_size=(10, 15, 20), parallel=False, optimization=opt_params)
+                rho = ldc_setup(domain_size=(10, 15, 20), parallel=False, config=config)
                 results.append(rho)
     for i, arr in enumerate(results[1:]):
         print("Testing equivalence version 0 with version %d" % (i + 1,))
@@ -56,26 +59,32 @@ def test_data_handling_2d():
             if parallel and gpu and not hasattr(wLB, 'cuda'):
                 continue
 
-            print("Testing parallel: %s\tgpu: %s" % (parallel, gpu))
-            opt_params = {'target': 'gpu' if gpu else 'cpu',
-                          'gpu_indexing_params': {'block_size': (8, 4, 2)}}
+            print(f"Testing parallel: {parallel}\tgpu: {gpu}")
+            config = CreateKernelConfig(target=Target.GPU if gpu else Target.CPU,
+                                        gpu_indexing_params=MappingProxyType({'block_size': (8, 4, 2)}))
             if parallel:
                 from pystencils.datahandling import ParallelDataHandling
                 blocks = wLB.createUniformBlockGrid(blocks=(2, 3, 1), cellsPerBlock=(5, 5, 1),
                                                     oneBlockPerProcess=False)
                 dh = ParallelDataHandling(blocks, dim=2)
-                rho = ldc_setup(data_handling=dh, optimization=opt_params)
+                rho = ldc_setup(data_handling=dh, config=config)
                 results.append(rho)
             else:
-                rho = ldc_setup(domain_size=(10, 15), parallel=False, optimization=opt_params)
+                rho = ldc_setup(domain_size=(10, 15), parallel=False, config=config)
                 results.append(rho)
     for i, arr in enumerate(results[1:]):
-        print("Testing equivalence version 0 with version %d" % (i + 1,))
+        print(f"Testing equivalence version 0 with version {i + 1}")
         np.testing.assert_almost_equal(results[0], arr)
 
 
 def test_smagorinsky_setup():
-    step = create_lid_driven_cavity((30, 30), smagorinsky=0.16, relaxation_rate=1.99)
+    step = create_lid_driven_cavity((30, 30), subgrid_scale_model=(SubgridScaleModel.SMAGORINSKY, 0.16),
+                                    relaxation_rate=1.99)
+    step.run(10)
+
+def test_qr_setup():
+    step = create_lid_driven_cavity((30, 30), subgrid_scale_model=(SubgridScaleModel.QR, 0.33),
+                                    relaxation_rate=1.99)
     step.run(10)
 
 
@@ -89,7 +98,7 @@ def test_advanced_initialization():
     init_vel[:, height // 3: height // 3 * 2, 0] = -velocity_magnitude
     # small random y velocity component
     init_vel[:, :, 1] = 0.1 * velocity_magnitude * np.random.rand(width, height)
-    shear_flow_scenario = create_fully_periodic_flow(initial_velocity=init_vel, relaxation_rate=1.95)
+    shear_flow_scenario = create_fully_periodic_flow(initial_velocity=init_vel, relaxation_rate=1.99)
     with pytest.raises(ValueError) as e:
         shear_flow_scenario.run_iterative_initialization(max_steps=20000, check_residuum_after=500)
     assert 'did not converge' in str(e.value)

tests/test_lees_edwards.py

+from functools import partial
+
+import pystencils as ps
+from lbmpy._compat import get_loop_counter_symbol
+from pystencils.slicing import get_periodic_boundary_functor
+
+from lbmpy.creationfunctions import create_lb_update_rule, LBMConfig, LBMOptimisation
+from lbmpy.enums import Stencil, ForceModel
+from lbmpy.stencils import LBStencil
+from lbmpy.updatekernels import create_stream_pull_with_output_kernel
+from lbmpy.macroscopic_value_kernels import macroscopic_values_setter
+from lbmpy.relaxationrates import lattice_viscosity_from_relaxation_rate
+
+import sympy as sp
+import numpy as np
+
+
+def get_le_boundary_functor(neighbor_stencil, shear_offset, ghost_layers=1, thickness=None, n=64):
+    functor_2 = get_periodic_boundary_functor(neighbor_stencil, ghost_layers, thickness)
+
+    def functor(pdfs, **_):
+
+        functor_2(pdfs)
+        weight = np.fmod(shear_offset[0] + n, 1.)
+
+        # First, we interpolate the upper pdfs
+        for i in range(len(pdfs[:, ghost_layers, :])):
+            ind1 = int(np.floor(i - shear_offset[0]) % n)
+            ind2 = int(np.ceil(i - shear_offset[0]) % n)
+
+            res = (1 - weight) * pdfs[ind1, ghost_layers, :] + weight * pdfs[ind2, ghost_layers, :]
+            pdfs[i, -ghost_layers, :] = res
+
+        # Second, we interpolate the lower pdfs
+        for i in range(len(pdfs[:, -ghost_layers, :])):
+            ind1 = int(np.floor(i + shear_offset[0]) % n)
+            ind2 = int(np.ceil(i + shear_offset[0]) % n)
+
+            res = (1 - weight) * pdfs[ind1, -ghost_layers - 1, :] + weight * pdfs[ind2, -ghost_layers - 1, :]
+            pdfs[i, ghost_layers - 1, :] = res
+
+    return functor
+
+
+def get_solution_navier_stokes(x, t, viscosity, velocity=1.0, height=1.0, max_iterations=10):
+    w = x / height - 0.5
+    for k in np.arange(1, max_iterations + 1):
+        w += 1.0 / (np.pi * k) * np.exp(-4 * np.pi ** 2 * viscosity * k ** 2 / height ** 2 * t) * np.sin(
+            2 * np.pi / height * k * x)
+    return velocity * w
+
+
+def test_lees_edwards():
+
+    domain_size = (64, 64)
+    omega = 1.0  # relaxation rate of first component
+    shear_velocity = 0.1  # shear velocity
+    shear_dir = 0  # direction of shear flow
+    shear_dir_normal = 1  # direction normal to shear plane, for interpolation
+
+    stencil = LBStencil(Stencil.D2Q9)
+
+    dh = ps.create_data_handling(domain_size, periodicity=True, default_target=ps.Target.CPU)
+
+    src = dh.add_array('src', values_per_cell=stencil.Q)
+    dh.fill('src', 1.0, ghost_layers=True)
+
+    dst = dh.add_array_like('dst', 'src')
+    dh.fill('dst', 0.0, ghost_layers=True)
+
+    force = dh.add_array('force', values_per_cell=stencil.D)
+    dh.fill('force', 0.0, ghost_layers=True)
+
+    rho = dh.add_array('rho', values_per_cell=1)
+    dh.fill('rho', 1.0, ghost_layers=True)
+    u = dh.add_array('u', values_per_cell=stencil.D)
+    dh.fill('u', 0.0, ghost_layers=True)
+
+    counters = [get_loop_counter_symbol(i) for i in range(stencil.D)]
+    points_up = sp.Symbol('points_up')
+    points_down = sp.Symbol('points_down')
+
+    u_p = sp.Piecewise((1, sp.And(counters[1] <= 1, points_down)),
+                       (-1, sp.And(counters[1] >= src.shape[1] - 2, points_up)), (0, True)) * shear_velocity
+
+    lbm_config = LBMConfig(stencil=stencil, relaxation_rate=omega, compressible=True,
+                           velocity_input=u.center_vector + sp.Matrix([u_p, 0]), density_input=rho,
+                           force_model=ForceModel.LUO, force=force.center_vector,
+                           kernel_type='collide_only')
+    lbm_opt = LBMOptimisation(symbolic_field=src)
+    collision = create_lb_update_rule(lbm_config=lbm_config, lbm_optimisation=lbm_opt)
+
+    to_insert = [s.lhs for s in collision.subexpressions
+                 if collision.method.first_order_equilibrium_moment_symbols[shear_dir]
+                 in s.free_symbols]
+    for s in to_insert:
+        collision = collision.new_with_inserted_subexpression(s)
+    ma = []
+    for a, c in zip(collision.main_assignments, collision.method.stencil):
+        if c[shear_dir_normal] == -1:
+            b = (True, False)
+        elif c[shear_dir_normal] == 1:
+            b = (False, True)
+        else:
+            b = (False, False)
+        a = ps.Assignment(a.lhs, a.rhs.replace(points_down, b[0]))
+        a = ps.Assignment(a.lhs, a.rhs.replace(points_up, b[1]))
+        ma.append(a)
+    collision.main_assignments = ma
+
+    stream = create_stream_pull_with_output_kernel(collision.method, src, dst,
+                                                   {'density': rho, 'velocity': u})
+
+    config = ps.CreateKernelConfig(target=dh.default_target)
+    stream_kernel = ps.create_kernel(stream, config=config).compile()
+    collision_kernel = ps.create_kernel(collision, config=config).compile()
+
+    init = macroscopic_values_setter(collision.method, velocity=(0, 0),
+                                     pdfs=src.center_vector, density=rho.center)
+    init_kernel = ps.create_kernel(init, ghost_layers=0).compile()
+
+    offset = [0.0]
+
+    sync_pdfs = dh.synchronization_function([src.name],
+                                            functor=partial(get_le_boundary_functor, shear_offset=offset))
+
+    dh.run_kernel(init_kernel)
+
+    time = 500
+
+    dh.all_to_gpu()
+    for i in range(time):
+        dh.run_kernel(collision_kernel)
+
+        sync_pdfs()
+        dh.run_kernel(stream_kernel)
+
+        dh.swap(src.name, dst.name)
+        offset[0] += shear_velocity
+    dh.all_to_cpu()
+
+    nu = lattice_viscosity_from_relaxation_rate(omega)
+    h = domain_size[0]
+    k_max = 100
+
+    analytical_solution = get_solution_navier_stokes(np.linspace(0.5, h - 0.5, h), time, nu, shear_velocity, h, k_max)
+    np.testing.assert_array_almost_equal(analytical_solution, dh.gather_array(u.name)[0, :, 0], decimal=5)
+
+    dh.fill(rho.name, 1.0, ghost_layers=True)
+    dh.run_kernel(init_kernel)
+    dh.fill(u.name, 0.0, ghost_layers=True)
+    dh.fill('force', 0.0, ghost_layers=True)
+    dh.cpu_arrays[force.name][64 // 3, 1, :] = [1e-2, -1e-1]
+
+    offset[0] = 0
+
+    time = 20
+
+    dh.all_to_gpu()
+    for i in range(time):
+        dh.run_kernel(collision_kernel)
+
+        sync_pdfs()
+        dh.run_kernel(stream_kernel)
+
+        dh.swap(src.name, dst.name)
+    dh.all_to_cpu()
+
+    vel_unshifted = np.array(dh.gather_array(u.name)[:, -3:-1, :])
+
+    dh.fill(rho.name, 1.0, ghost_layers=True)
+    dh.run_kernel(init_kernel)
+    dh.fill(u.name, 0.0, ghost_layers=True)
+    dh.fill('force', 0.0, ghost_layers=True)
+    dh.cpu_arrays[force.name][64 // 3, 1, :] = [1e-2, -1e-1]
+
+    offset[0] = 10
+
+    time = 20
+
+    dh.all_to_gpu()
+    for i in range(time):
+        dh.run_kernel(collision_kernel)
+
+        sync_pdfs()
+        dh.run_kernel(stream_kernel)
+
+        dh.swap(src.name, dst.name)
+    dh.all_to_cpu()
+
+    vel_shifted = np.array(dh.gather_array(u.name)[:, -3:-1, :])
+
+    vel_rolled = np.roll(vel_shifted, -offset[0], axis=0)
+
+    np.testing.assert_array_almost_equal(vel_unshifted, vel_rolled)

tests/test_macroscopic_value_kernels.py

+import pytest
+import numpy as np
+import sympy as sp
+
+from lbmpy.creationfunctions import create_lb_method, LBMConfig
+from lbmpy.enums import Stencil, ForceModel, Method
+from lbmpy.macroscopic_value_kernels import (
+    compile_macroscopic_values_getter, compile_macroscopic_values_setter, strain_rate_tensor_getter)
+from lbmpy.advanced_streaming.utility import streaming_patterns, Timestep
+from lbmpy.stencils import LBStencil
+
+
+@pytest.mark.parametrize('stencil', [Stencil.D2Q9, Stencil.D3Q19])
+@pytest.mark.parametrize('force_model', [ForceModel.GUO, ForceModel.LUO, None])
+@pytest.mark.parametrize('compressible', [True, False])
+@pytest.mark.parametrize('zero_centered', [True, False])
+@pytest.mark.parametrize('streaming_pattern', streaming_patterns)
+@pytest.mark.parametrize('prev_timestep', [Timestep.EVEN, Timestep.ODD])
+def test_set_get_density_velocity_with_fields(stencil, force_model, compressible, zero_centered, streaming_pattern, prev_timestep):
+    force = (0.1, 0.12, -0.17)
+    stencil = LBStencil(stencil)
+
+    lbm_config = LBMConfig(stencil=stencil, force_model=force_model, method=Method.TRT,
+                           compressible=compressible, zero_centered=zero_centered, force=force)
+
+    method = create_lb_method(lbm_config=lbm_config)
+    ghost_layers = 1
+    inner_size = (3, 7, 4)[:method.dim]
+    total_size = tuple(s + 2 * ghost_layers for s in inner_size)
+    pdf_arr = np.zeros(total_size + (len(method.stencil),))
+
+    inner_slice = (slice(ghost_layers, -ghost_layers, 1), ) * method.dim
+    density_input_field = np.zeros(total_size)
+    velocity_input_field = np.zeros(total_size + (method.dim, ))
+    density_input_field[inner_slice] = 1 + 0.2 * (np.random.random_sample(inner_size) - 0.5)
+    velocity_input_field[inner_slice] = 0.1 * \
+        (np.random.random_sample(inner_size + (method.dim, )) - 0.5)
+
+    quantities_to_set = {'density': density_input_field, 'velocity': velocity_input_field}
+
+    setter = compile_macroscopic_values_setter(method, pdf_arr=pdf_arr, quantities_to_set=quantities_to_set,
+                                               ghost_layers=ghost_layers, streaming_pattern=streaming_pattern, previous_timestep=prev_timestep)
+    setter(pdf_arr)
+
+    getter = compile_macroscopic_values_getter(method, ['density', 'density_deviation', 'velocity'], pdf_arr=pdf_arr, 
+                                               ghost_layers=ghost_layers, streaming_pattern=streaming_pattern, previous_timestep=prev_timestep)
+
+    inner_part = (slice(ghost_layers, -ghost_layers), ) * stencil.D
+
+    density_output_field = np.zeros_like(density_input_field)
+    density_deviation_output_field = np.zeros_like(density_input_field)
+    velocity_output_field = np.zeros_like(velocity_input_field)
+    getter(pdfs=pdf_arr, density=density_output_field, density_deviation=density_deviation_output_field, velocity=velocity_output_field)
+    np.testing.assert_almost_equal(density_input_field, density_output_field)
+    np.testing.assert_almost_equal(density_input_field[inner_part] - 1.0, density_deviation_output_field[inner_part])
+    np.testing.assert_almost_equal(velocity_input_field, velocity_output_field)
+
+
+@pytest.mark.parametrize('stencil', [Stencil.D2Q9, Stencil.D3Q19])
+@pytest.mark.parametrize('force_model', [ForceModel.GUO, ForceModel.LUO, None])
+@pytest.mark.parametrize('compressible', [True, False])
+def test_set_get_constant_velocity(stencil, force_model, compressible):
+    ref_velocity = [0.01, -0.2, 0.1]
+
+    force = (0.1, 0.12, -0.17)
+
+    stencil = LBStencil(stencil)
+    lbm_config = LBMConfig(stencil=stencil, force_model=force_model, method=Method.TRT,
+                           compressible=compressible, force=force)
+
+    method = create_lb_method(lbm_config=lbm_config)
+    size = (1, 1, 1)[:method.dim]
+    pdf_arr = np.zeros(size + (len(method.stencil),))
+    setter = compile_macroscopic_values_setter(method, pdf_arr=pdf_arr, ghost_layers=0,
+                                               quantities_to_set={'velocity': ref_velocity[:method.dim]}, )
+    setter(pdf_arr)
+
+    getter = compile_macroscopic_values_getter(method, ['velocity'], pdf_arr=pdf_arr, ghost_layers=0)
+    velocity_output_field = np.zeros(size + (method.dim, ))
+    getter(pdfs=pdf_arr, velocity=velocity_output_field)
+    if method.dim == 2:
+        computed_velocity = velocity_output_field[0, 0, :]
+    else:
+        computed_velocity = velocity_output_field[0, 0, 0, :]
+
+    np.testing.assert_almost_equal(np.array(ref_velocity[:method.dim]), computed_velocity)
+
+
+@pytest.mark.parametrize('stencil', [Stencil.D2Q9, Stencil.D3Q19])
+@pytest.mark.parametrize("method_enum", [Method.SRT, Method.TRT, Method.MRT, Method.CUMULANT])
+def test_get_strain_rate_tensor(stencil, method_enum):
+    stencil = LBStencil(stencil)
+    lbm_config = LBMConfig(stencil=stencil, method=method_enum, compressible=True)
+    method = create_lb_method(lbm_config=lbm_config)
+
+    pdfs = sp.symbols(f"f_:{stencil.Q}")
+    strain_rate_tensor = sp.symbols(f"strain_rate_tensor_:{method.dim * method.dim}")
+
+    getter_assignments = strain_rate_tensor_getter(method, strain_rate_tensor, pdfs)
+
+    assert len(getter_assignments) == method.dim * method.dim

tests/test_maxwellian_equilibrium.py

+import pytest
+
+from lbmpy.cumulants import raw_moment_as_function_of_cumulants
+from lbmpy.enums import Stencil
+from lbmpy.maxwellian_equilibrium import *
+from lbmpy.moments import (
+    MOMENT_SYMBOLS, exponents_to_polynomial_representations, moment_matrix,
+    moments_up_to_component_order, moments_up_to_order)
+from lbmpy.stencils import LBStencil
+from pystencils.sympyextensions import remove_higher_order_terms
+
+
+def test_maxwellian_moments():
+    """Check moments of continuous Maxwellian"""
+    rho = sp.Symbol("rho")
+    u = sp.symbols("u_0 u_1 u_2")
+    c_s = sp.Symbol("c_s")
+    eq_moments = get_equilibrium_values_of_maxwell_boltzmann_function(((0, 0, 0), (0, 0, 1)),
+                                                                      dim=3, rho=rho, u=u, c_s_sq=c_s ** 2,
+                                                                      space="moment")
+    assert eq_moments[0] == rho
+    assert eq_moments[1] == rho * u[2]
+
+    x, y, z = MOMENT_SYMBOLS
+    one = sp.Rational(1, 1)
+    eq_moments = get_equilibrium_values_of_maxwell_boltzmann_function((one, x, x ** 2, x * y),
+                                                                      dim=2, rho=rho, u=u[:2], c_s_sq=c_s ** 2,
+                                                                      space="moment")
+    assert eq_moments[0] == rho
+    assert eq_moments[1] == rho * u[0]
+    assert eq_moments[2] == rho * (c_s ** 2 + u[0] ** 2)
+    assert eq_moments[3] == rho * u[0] * u[1]
+
+
+@pytest.mark.parametrize('stencil', [Stencil.D2Q9, Stencil.D3Q15, Stencil.D3Q19, Stencil.D3Q27])
+def test_continuous_discrete_moment_equivalence(stencil):
+    """Check that moments up to order 3 agree with moments of the continuous Maxwellian"""
+    stencil = LBStencil(stencil)
+    c_s_sq = sp.Rational(1, 3)
+    moments = tuple(moments_up_to_order(3, dim=stencil.D, include_permutations=False))
+    cm = sp.Matrix(get_equilibrium_values_of_maxwell_boltzmann_function(moments, order=2, dim=stencil.D,
+                                                                        c_s_sq=c_s_sq, space="moment"))
+    dm = sp.Matrix(get_moments_of_discrete_maxwellian_equilibrium(stencil, moments, order=2,
+                                                                  compressible=True, c_s_sq=c_s_sq))
+
+    diff = sp.simplify(cm - dm)
+    for d in diff:
+        assert d == 0
+
+
+@pytest.mark.parametrize('stencil', [Stencil.D2Q9, Stencil.D3Q27])
+def test_moment_cumulant_continuous_equivalence(stencil):
+    """Test that discrete equilibrium is the same up to order 3 when obtained with following methods
+
+    * eq1: take moments of continuous Maxwellian and transform back to pdf space
+    * eq2: take cumulants of continuous Maxwellian, transform to moments then transform to pdf space
+    * eq3: take discrete equilibrium from LBM literature
+    * eq4: same as eq1 but with built-in function
+    """
+    stencil = LBStencil(stencil)
+    u = sp.symbols(f"u_:{stencil.D}")
+    indices = tuple(moments_up_to_component_order(2, dim=stencil.D))
+    c_s_sq = sp.Rational(1, 3)
+    eq_moments1 = get_equilibrium_values_of_maxwell_boltzmann_function(indices, dim=stencil.D, u=u, c_s_sq=c_s_sq,
+                                                                       space="moment")
+    eq_cumulants = get_equilibrium_values_of_maxwell_boltzmann_function(indices, dim=stencil.D, u=u, c_s_sq=c_s_sq,
+                                                                        space="cumulant")
+    eq_cumulants = {idx: c for idx, c in zip(indices, eq_cumulants)}
+    eq_moments2 = [raw_moment_as_function_of_cumulants(idx, eq_cumulants) for idx in indices]
+    pdfs_to_moments = moment_matrix(indices, stencil)
+
+    def normalize(expressions):
+        return [remove_higher_order_terms(e.expand(), symbols=u, order=3) for e in expressions]
+
+    eq1 = normalize(pdfs_to_moments.inv() * sp.Matrix(eq_moments1))
+    eq2 = normalize(pdfs_to_moments.inv() * sp.Matrix(eq_moments2))
+    eq3 = normalize(discrete_maxwellian_equilibrium(stencil, order=3, c_s_sq=c_s_sq, compressible=True))
+    eq4 = normalize(generate_equilibrium_by_matching_moments(stencil, indices, c_s_sq=c_s_sq))
+
+    assert eq1 == eq2
+    assert eq2 == eq3
+    assert eq3 == eq4
+
+
+@pytest.mark.parametrize('stencil', [Stencil.D2Q9, Stencil.D3Q27])
+def test_moment_cumulant_continuous_equivalence_polynomial_formulation(stencil):
+    """Same as test above, but instead of index tuples, the polynomial formulation is used."""
+    stencil = LBStencil(stencil)
+    u = sp.symbols(f"u_:{stencil.D}")
+    index_tuples = tuple(moments_up_to_component_order(2, dim=stencil.D))
+    indices = exponents_to_polynomial_representations(index_tuples)
+    c_s_sq = sp.Rational(1, 3)
+    eq_moments1 = get_equilibrium_values_of_maxwell_boltzmann_function(indices, dim=stencil.D,
+                                                                       u=u, c_s_sq=c_s_sq, space="moment")
+    eq_cumulants = get_equilibrium_values_of_maxwell_boltzmann_function(indices, dim=stencil.D,
+                                                                        u=u, c_s_sq=c_s_sq, space="cumulant")
+    eq_cumulants = {idx: c for idx, c in zip(index_tuples, eq_cumulants)}
+    eq_moments2 = [raw_moment_as_function_of_cumulants(idx, eq_cumulants) for idx in index_tuples]
+    pdfs_to_moments = moment_matrix(indices, stencil)
+
+    def normalize(expressions):
+        return [remove_higher_order_terms(e.expand(), symbols=u, order=3) for e in expressions]
+
+    eq1 = normalize(pdfs_to_moments.inv() * sp.Matrix(eq_moments1))
+    eq2 = normalize(pdfs_to_moments.inv() * sp.Matrix(eq_moments2))
+    eq3 = normalize(discrete_maxwellian_equilibrium(stencil, order=3, c_s_sq=c_s_sq, compressible=True))
+    eq4 = normalize(generate_equilibrium_by_matching_moments(stencil, indices, c_s_sq=c_s_sq))
+
+    assert eq1 == eq2
+    assert eq2 == eq3
+    assert eq3 == eq4

tests/test_moment_transform_api.py

+import pytest
+import sympy as sp
+
+from lbmpy.enums import Stencil
+from lbmpy.stencils import LBStencil
+from lbmpy.moments import get_default_moment_set_for_stencil
+
+from lbmpy.moment_transforms import (
+    PdfsToMomentsByMatrixTransform, PdfsToMomentsByChimeraTransform,
+    PdfsToCentralMomentsByShiftMatrix, PdfsToCentralMomentsByMatrix, FastCentralMomentTransform
+)
+
+transforms = [
+    PdfsToMomentsByMatrixTransform, PdfsToMomentsByChimeraTransform,
+    PdfsToCentralMomentsByShiftMatrix, PdfsToCentralMomentsByMatrix, FastCentralMomentTransform
+]
+
+
+@pytest.mark.parametrize('transform_class', transforms)
+def test_monomial_equations(transform_class):
+    stencil = LBStencil(Stencil.D2Q9)
+    rho = sp.symbols("rho")
+    u = sp.symbols(f"u_:{stencil.D}")
+    moment_polynomials = get_default_moment_set_for_stencil(stencil)
+    transform = transform_class(stencil, moment_polynomials, rho, u)
+    pdfs = sp.symbols(f"f_:{stencil.Q}")
+    fw_eqs = transform.forward_transform(pdfs, return_monomials=True)
+    bw_eqs = transform.backward_transform(pdfs, start_from_monomials=True)
+
+    mono_symbols_pre = set(transform.pre_collision_monomial_symbols)
+    mono_symbols_post = set(transform.post_collision_monomial_symbols)
+
+    assert mono_symbols_pre <= set(fw_eqs.defined_symbols)
+    assert mono_symbols_post <= set(bw_eqs.free_symbols)
+
+    symbols_pre = set(transform.pre_collision_symbols)
+    symbols_post = set(transform.post_collision_symbols)
+
+    assert symbols_pre.isdisjoint(set(fw_eqs.atoms(sp.Symbol)))
+    assert symbols_post.isdisjoint(set(bw_eqs.atoms(sp.Symbol)))

tests/test_momentbased_equivalences.py

+import pytest
+import sympy as sp
+from dataclasses import replace
+
+from lbmpy.enums import CollisionSpace
+from lbmpy.methods import CollisionSpaceInfo
+from lbmpy.creationfunctions import create_lb_method, create_lb_collision_rule, LBMConfig, LBMOptimisation
+from lbmpy.enums import Method, ForceModel, Stencil
+from lbmpy.moments import (
+    extract_monomials, get_default_moment_set_for_stencil, non_aliased_polynomial_raw_moments,
+    exponent_tuple_sort_key)
+from lbmpy.stencils import LBStencil
+
+from lbmpy.methods.creationfunctions import create_srt
+from lbmpy.methods.default_moment_sets import mrt_orthogonal_modes_literature
+from lbmpy.maxwellian_equilibrium import get_weights
+
+from lbmpy.moment_transforms import (
+    PdfsToMomentsByMatrixTransform, PdfsToMomentsByChimeraTransform
+)
+
+
+@pytest.mark.parametrize('stencil', [Stencil.D2Q9, Stencil.D3Q15, Stencil.D3Q19, Stencil.D3Q27])
+@pytest.mark.parametrize('monomials', [False, True])
+def test_moment_transform_equivalences(stencil, monomials):
+    stencil = LBStencil(stencil)
+
+    pdfs = sp.symbols(f"f_:{stencil.Q}")
+    rho = sp.Symbol('rho')
+    u = sp.symbols(f"u_:{stencil.D}")
+
+    moment_polynomials = get_default_moment_set_for_stencil(stencil)
+    if monomials:
+        polys_nonaliased = non_aliased_polynomial_raw_moments(moment_polynomials, stencil)
+        moment_exponents = sorted(extract_monomials(polys_nonaliased), key=exponent_tuple_sort_key)
+        moment_polynomials = None
+    else:
+        moment_exponents = None
+
+    matrix_transform = PdfsToMomentsByMatrixTransform(stencil, moment_polynomials, rho, u,
+                                                      moment_exponents=moment_exponents)
+    chimera_transform = PdfsToMomentsByChimeraTransform(stencil, moment_polynomials, rho, u,
+                                                        moment_exponents=moment_exponents)
+
+    f_to_m_matrix = matrix_transform.forward_transform(pdfs, return_monomials=monomials)
+    f_to_m_matrix = f_to_m_matrix.new_without_subexpressions().main_assignments_dict
+
+    f_to_m_chimera = chimera_transform.forward_transform(pdfs, return_monomials=monomials)
+    f_to_m_chimera = f_to_m_chimera.new_without_subexpressions().main_assignments_dict
+
+    m_to_f_matrix = matrix_transform.backward_transform(pdfs, start_from_monomials=monomials)
+    m_to_f_matrix = m_to_f_matrix.new_without_subexpressions().main_assignments_dict
+
+    m_to_f_chimera = chimera_transform.backward_transform(pdfs, start_from_monomials=monomials)
+    m_to_f_chimera = m_to_f_chimera.new_without_subexpressions().main_assignments_dict
+
+    m_pre_matrix = matrix_transform.pre_collision_monomial_symbols if monomials else matrix_transform.pre_collision_symbols
+    m_pre_chimera = chimera_transform.pre_collision_monomial_symbols if monomials else chimera_transform.pre_collision_symbols
+
+    for m1, m2 in zip(m_pre_matrix, m_pre_chimera):
+        rhs_matrix = f_to_m_matrix[m1]
+        rhs_chimera = f_to_m_chimera[m2]
+        diff = (rhs_matrix - rhs_chimera).expand()
+        assert diff == 0, f"Mismatch between matrix and chimera forward transform at {m1}, {m2}."
+
+    for f in pdfs:
+        rhs_matrix = m_to_f_matrix[f]
+        rhs_chimera = m_to_f_chimera[f]
+        diff = (rhs_matrix - rhs_chimera).expand()
+        assert diff == 0, f"Mismatch between matrix and chimera backward transform at {f}"
+
+
+d3q15_literature = mrt_orthogonal_modes_literature(LBStencil(Stencil.D3Q15), True)
+d3q19_literature = mrt_orthogonal_modes_literature(LBStencil(Stencil.D3Q19), True)
+
+setups = [
+    (Stencil.D2Q9, Method.SRT, None, ForceModel.GUO),
+    (Stencil.D2Q9, Method.MRT, None, ForceModel.SIMPLE),
+    (Stencil.D3Q15, Method.MRT, None, ForceModel.SIMPLE),
+    (Stencil.D3Q15, Method.MRT, d3q15_literature, ForceModel.SIMPLE),
+    (Stencil.D3Q19, Method.TRT, None, ForceModel.SIMPLE),
+    (Stencil.D3Q19, Method.MRT, d3q19_literature, ForceModel.GUO),
+    (Stencil.D3Q27, Method.SRT, None, ForceModel.GUO)
+]
+
+
+@pytest.mark.parametrize('setup', setups)
+def test_population_and_moment_space_equivalence(setup: tuple):
+    stencil = LBStencil(setup[0])
+    method = setup[1]
+    nested_moments = setup[2]
+    fmodel = setup[3]
+    force = sp.symbols(f'F_:{stencil.D}')
+    conserved_moments = 1 + stencil.D
+
+    rr = [*[0] * conserved_moments, *sp.symbols(f'omega_:{stencil.Q - conserved_moments}')]
+    lbm_config = LBMConfig(stencil=stencil, method=method, relaxation_rates=rr,
+                           nested_moments=nested_moments, force_model=fmodel, force=force,
+                           weighted=True, compressible=True, collision_space_info=CollisionSpaceInfo(CollisionSpace.RAW_MOMENTS))
+
+    lbm_opt = LBMOptimisation(cse_global=False, cse_pdfs=False, pre_simplification=True, simplification=False)
+
+    lb_method_moment_space = create_lb_method(lbm_config=lbm_config)
+
+    lbm_config = replace(lbm_config, collision_space_info=CollisionSpaceInfo(CollisionSpace.POPULATIONS))
+    lb_method_pdf_space = create_lb_method(lbm_config=lbm_config)
+
+    rho = lb_method_moment_space.zeroth_order_equilibrium_moment_symbol
+    u = lb_method_moment_space.first_order_equilibrium_moment_symbols
+    keep = set((rho,) + u)
+    cr_moment_space = create_lb_collision_rule(lb_method=lb_method_moment_space, lbm_optimisation=lbm_opt)
+    cr_moment_space = cr_moment_space.new_without_subexpressions(subexpressions_to_keep=keep)
+
+    lbm_opt = replace(lbm_opt, simplification='auto')
+    cr_pdf_space = create_lb_collision_rule(lb_method=lb_method_pdf_space, lbm_optimisation=lbm_opt)
+    cr_pdf_space = cr_pdf_space.new_without_subexpressions(subexpressions_to_keep=keep)
+
+    for a, b in zip(cr_moment_space.main_assignments, cr_pdf_space.main_assignments):
+        diff = (a.rhs - b.rhs).expand()
+        assert diff == 0, f"Mismatch between population- and moment-space equations in PDFs {a.lhs}, {b.lhs}"
+
+
+@pytest.mark.parametrize('stencil', [Stencil.D2Q9, Stencil.D3Q19])
+@pytest.mark.parametrize('compressible', [True, False])
+def test_full_and_delta_equilibrium_equivalence(stencil, compressible):
+    stencil = LBStencil(stencil)
+    zero_centered = True
+    omega = sp.Symbol('omega')
+
+    rho = sp.Symbol("rho")
+    rho_background = sp.Integer(1)
+    delta_rho = sp.Symbol("delta_rho")
+    
+    subs = { delta_rho : rho - rho_background }
+    eqs = []
+
+    for delta_eq in [False, True]:
+        method = create_srt(stencil, omega, continuous_equilibrium=True, compressible=compressible,
+                            zero_centered=zero_centered, delta_equilibrium=delta_eq, equilibrium_order=None,
+                            collision_space_info=CollisionSpaceInfo(CollisionSpace.RAW_MOMENTS))
+        eq = method.get_equilibrium_terms()
+        eqs.append(eq.subs(subs))
+
+    assert (eqs[0] - eqs[1]).expand() == sp.Matrix((0,) * stencil.Q)
+
+
+@pytest.mark.parametrize('stencil', [Stencil.D2Q9, Stencil.D3Q19])
+@pytest.mark.parametrize('compressible', [True, False])
+@pytest.mark.longrun
+def test_full_and_delta_population_space_equivalence(stencil, compressible):
+    stencil = LBStencil(stencil)
+    zero_centered = True
+    omega = sp.Symbol('omega')
+
+    rho = sp.Symbol("rho")
+    rho_background = sp.Integer(1)
+    delta_rho = sp.Symbol("delta_rho")
+    
+    subs = { delta_rho : rho - rho_background }
+    eqs = []
+
+    for delta_eq in [False, True]:
+        method = create_srt(stencil, omega, continuous_equilibrium=True, compressible=compressible,
+                            zero_centered=zero_centered, delta_equilibrium=delta_eq, equilibrium_order=None,
+                            collision_space_info=CollisionSpaceInfo(CollisionSpace.RAW_MOMENTS))
+        eq = method.get_collision_rule().new_without_subexpressions()
+        eq = sp.Matrix([a.rhs for a in eq])
+        eqs.append(eq.subs(subs))
+
+    assert (eqs[0] - eqs[1]).expand() == sp.Matrix((0,) * stencil.Q)
+
+
+@pytest.mark.parametrize('stencil', [Stencil.D2Q9, Stencil.D3Q19])
+@pytest.mark.parametrize('compressible', [True, False])
+@pytest.mark.parametrize('delta_eq', [True, False])
+def test_zero_centering_equilibrium_equivalence(stencil, compressible, delta_eq):
+    stencil = LBStencil(stencil)
+    omega = sp.Symbol('omega')
+
+    weights = sp.Matrix(get_weights(stencil))
+
+    rho = sp.Symbol("rho")
+    rho_background = sp.Integer(1)
+    delta_rho = sp.Symbol("delta_rho")
+    
+    subs = { delta_rho : rho - rho_background }
+    eqs = []
+
+    for zero_centered in [False, True]:
+        method = create_srt(stencil, omega, continuous_equilibrium=True, compressible=compressible,
+                            zero_centered=zero_centered, delta_equilibrium=delta_eq and zero_centered,
+                            equilibrium_order=None, 
+                            collision_space_info=CollisionSpaceInfo(CollisionSpace.RAW_MOMENTS))
+        eq = method.get_equilibrium_terms()
+        eqs.append(eq.subs(subs))
+
+    assert (eqs[0] - eqs[1]).expand() == weights
+
+
+@pytest.mark.parametrize('stencil', [Stencil.D2Q9, Stencil.D3Q19])
+@pytest.mark.parametrize('compressible', [True, False])
+@pytest.mark.parametrize('delta_eq', [True, False])
+@pytest.mark.longrun
+def test_zero_centering_population_space_equivalence(stencil, compressible, delta_eq):
+    stencil = LBStencil(stencil)
+    omega = sp.Symbol('omega')
+
+    weights = sp.Matrix(get_weights(stencil))
+
+    rho = sp.Symbol("rho")
+    rho_background = sp.Integer(1)
+    delta_rho = sp.Symbol("delta_rho")
+
+    delta_f = sp.symbols(f"delta_f_:{stencil.Q}")
+    
+    subs = { delta_rho : rho - rho_background }
+    eqs = []
+
+    for zero_centered in [False, True]:
+        method = create_srt(stencil, omega, continuous_equilibrium=True, compressible=compressible,
+                            zero_centered=zero_centered, delta_equilibrium=delta_eq and zero_centered,
+                            equilibrium_order=None,
+                            collision_space_info=CollisionSpaceInfo(CollisionSpace.RAW_MOMENTS))
+        eq = method.get_collision_rule().new_without_subexpressions()
+        eq = sp.Matrix([a.rhs for a in eq])
+
+        if zero_centered:
+            eq = eq.subs({f : df for f, df in zip(method.pre_collision_pdf_symbols, delta_f)})
+        else:
+            eq = eq.subs({f : w + df for f, df, w in zip(method.pre_collision_pdf_symbols, delta_f, weights)})
+
+        eqs.append(eq.subs(subs))
+
+    assert (eqs[0] - eqs[1]).expand() == weights

tests/test_momentbased_methods_equilibrium.py

+"""
+Moment-based methods are created by specifying moments and their equilibrium value.
+This test checks if the equilibrium formula obtained by this method is the same as the explicitly
+given discrete_maxwellian_equilibrium
+"""
+import pytest
+import sympy as sp
+
+from lbmpy.creationfunctions import create_lb_method, LBMConfig
+from lbmpy.enums import Stencil, Method
+from lbmpy.maxwellian_equilibrium import discrete_maxwellian_equilibrium
+from lbmpy.methods import create_mrt_orthogonal, create_srt, create_trt, mrt_orthogonal_modes_literature
+from lbmpy.moments import is_bulk_moment, is_shear_moment
+from lbmpy.relaxationrates import get_shear_relaxation_rate
+from lbmpy.stencils import LBStencil
+
+
+def check_for_matching_equilibrium(method_name, stencil, compressibility):
+    omega = sp.Symbol("omega")
+    if method_name == Method.SRT:
+        method = create_srt(stencil, omega, compressible=compressibility,
+                            continuous_equilibrium=False, equilibrium_order=2)
+    elif method_name == Method.TRT:
+        method = create_trt(stencil, omega, omega, compressible=compressibility,
+                            continuous_equilibrium=False, equilibrium_order=2)
+    elif method_name == Method.MRT:
+        method = create_mrt_orthogonal(stencil, [omega] * stencil.Q, continuous_equilibrium=False,
+                                       weighted=False, compressible=compressibility, equilibrium_order=2)
+    else:
+        raise ValueError("Unknown method")
+
+    reference_equilibrium = discrete_maxwellian_equilibrium(stencil, order=2,
+                                                            c_s_sq=sp.Rational(1, 3), compressible=compressibility)
+    equilibrium = method.get_equilibrium()
+    equilibrium = equilibrium.new_without_subexpressions(subexpressions_to_keep=sp.symbols("rho u_0 u_1 u_2"))
+
+    diff = sp.Matrix(reference_equilibrium) - sp.Matrix([eq.rhs for eq in equilibrium.main_assignments])
+    diff = sp.simplify(diff)
+    assert sum(diff).is_zero
+
+
+@pytest.mark.parametrize('stencil', [Stencil.D2Q9, Stencil.D3Q15, Stencil.D3Q19, Stencil.D3Q27])
+@pytest.mark.parametrize('method', [Method.SRT, Method.TRT, Method.MRT])
+def test_for_matching_equilibrium_for_stencil(stencil, method):
+    stencil = LBStencil(stencil)
+    check_for_matching_equilibrium(method, stencil, True)
+    check_for_matching_equilibrium(method, stencil, False)
+
+
+def test_relaxation_rate_setter():
+    o1, o2, o3 = sp.symbols("o1 o2 o3")
+
+    lbm_config_1 = LBMConfig(method=Method.SRT, stencil=LBStencil(Stencil.D2Q9), relaxation_rates=[o3])
+    lbm_config_2 = LBMConfig(method=Method.MRT, stencil=LBStencil(Stencil.D2Q9), relaxation_rates=[o3, o3, o3, o3])
+    lbm_config_3 = LBMConfig(method=Method.MRT, stencil=LBStencil(Stencil.D2Q9), zero_centered=False,
+                             relaxation_rates=[o3] * 9, entropic=True)
+
+    method = create_lb_method(lbm_config=lbm_config_1)
+    method2 = create_lb_method(lbm_config=lbm_config_2)
+    method3 = create_lb_method(lbm_config=lbm_config_3)
+    method.set_zeroth_moment_relaxation_rate(o1)
+    method.set_first_moment_relaxation_rate(o2)
+    assert get_shear_relaxation_rate(method) == o3
+    method.set_zeroth_moment_relaxation_rate(o3)
+    method.set_first_moment_relaxation_rate(o3)
+    method2.set_conserved_moments_relaxation_rate(o3)
+    assert method.collision_matrix == method2.collision_matrix == method3.collision_matrix
+
+
+def test_mrt_orthogonal():
+    m_ref = {}
+
+    moments = mrt_orthogonal_modes_literature(LBStencil(Stencil.D2Q9), True)
+    lbm_config = LBMConfig(method=Method.MRT, stencil=LBStencil(Stencil.D2Q9), continuous_equilibrium=True,
+                           nested_moments=moments)
+    m = create_lb_method(lbm_config=lbm_config)
+    assert m.is_weighted_orthogonal
+    m_ref[(Stencil.D2Q9, True)] = m
+
+    moments = mrt_orthogonal_modes_literature(LBStencil(Stencil.D3Q15), True)
+    lbm_config = LBMConfig(method=Method.MRT, stencil=LBStencil(Stencil.D3Q15), continuous_equilibrium=True,
+                           nested_moments=moments)
+    m = create_lb_method(lbm_config=lbm_config)
+    assert m.is_weighted_orthogonal
+    m_ref[(Stencil.D3Q15, True)] = m
+
+    moments = mrt_orthogonal_modes_literature(LBStencil(Stencil.D3Q19), True)
+    lbm_config = LBMConfig(method=Method.MRT, stencil=LBStencil(Stencil.D3Q19), continuous_equilibrium=True,
+                           nested_moments=moments)
+    m = create_lb_method(lbm_config=lbm_config)
+    assert m.is_weighted_orthogonal
+    m_ref[(Stencil.D3Q19, True)] = m
+
+    moments = mrt_orthogonal_modes_literature(LBStencil(Stencil.D3Q27), False)
+    lbm_config = LBMConfig(method=Method.MRT, stencil=LBStencil(Stencil.D3Q27), continuous_equilibrium=True,
+                           nested_moments=moments)
+    m = create_lb_method(lbm_config=lbm_config)
+    assert m.is_orthogonal
+    m_ref[(Stencil.D3Q27, False)] = m
+
+    for weighted in [True, False]:
+        for stencil in [Stencil.D2Q9, Stencil.D3Q15, Stencil.D3Q19, Stencil.D3Q27]:
+            lbm_config = LBMConfig(method=Method.MRT, stencil=LBStencil(stencil), continuous_equilibrium=True,
+                                   weighted=weighted)
+            m = create_lb_method(lbm_config=lbm_config)
+            if weighted:
+                assert m.is_weighted_orthogonal
+            else:
+                assert m.is_orthogonal
+            bulk_moments = set([mom for mom in m.moments if is_bulk_moment(mom, m.dim)])
+            shear_moments = set([mom for mom in m.moments if is_shear_moment(mom, m.dim)])
+            assert len(bulk_moments) == 1
+            assert len(shear_moments) == 1 + (m.dim - 2) + m.dim * (m.dim - 1) / 2
+
+            if (stencil, weighted) in m_ref:
+                ref = m_ref[(stencil, weighted)]
+                bulk_moments_lit = set([mom for mom in ref.moments if is_bulk_moment(mom, ref.dim)])
+                shear_moments_lit = set([mom for mom in ref.moments if is_shear_moment(mom, ref.dim)])
+
+                if stencil != Stencil.D3Q27:  # this one uses a different linear combination in literature
+                    assert shear_moments == shear_moments_lit
+                assert bulk_moments == bulk_moments_lit

lbmpy_tests/test_moments.py → tests/test_moments.py

 from lbmpy.moments import *
-from lbmpy.stencils import get_stencil
+from lbmpy.enums import Stencil
+from lbmpy.stencils import LBStencil
 
 
 def test_moment_permutation_multiplicity():
@@ -69,7 +70,34 @@ def test_gram_schmidt_orthogonalization():
     moments = moments_up_to_component_order(2, 2)
     assert len(moments) == 9
 
-    stencil = get_stencil("D2Q9")
+    stencil = LBStencil(Stencil.D2Q9)
     orthogonal_moments = gram_schmidt(moments, stencil)
     pdfs_to_moments = moment_matrix(orthogonal_moments, stencil)
     assert (pdfs_to_moments * pdfs_to_moments.T).is_diagonal()
+
+
+def test_is_bulk_moment():
+    x, y, z = MOMENT_SYMBOLS
+    assert not is_bulk_moment(x, 2)
+    assert not is_bulk_moment(x ** 3, 2)
+    assert not is_bulk_moment(x * y, 2)
+    assert not is_bulk_moment(x ** 2, 2)
+    assert not is_bulk_moment(x ** 2 + y ** 2, 3)
+    assert is_bulk_moment(x ** 2 + y ** 2, 2)
+    assert is_bulk_moment(x ** 2 + y ** 2 + z ** 2, 3)
+    assert is_bulk_moment(x ** 2 + y ** 2 + x, 2)
+    assert is_bulk_moment(x ** 2 + y ** 2 + 1, 2)
+
+
+def test_is_shear_moment():
+    x, y, z = MOMENT_SYMBOLS
+    assert not is_shear_moment(x ** 3, 2)
+    assert not is_shear_moment(x, 2)
+    assert not is_shear_moment(x ** 2 + y ** 2, 2)
+    assert not is_shear_moment(x ** 2 + y ** 2 + z ** 2, 3)
+    assert is_shear_moment(x ** 2, 2)
+    assert is_shear_moment(x ** 2 - 1, 2)
+    assert is_shear_moment(x ** 2 - x, 2)
+    assert is_shear_moment(x * y, 2)
+    assert is_shear_moment(x * y - 1, 2)
+    assert is_shear_moment(x * y - x, 2)

tests/test_mrt_simplifications.py

+import pytest
+
+import sympy as sp
+
+from pystencils.sympyextensions import is_constant
+
+from lbmpy import Stencil, LBStencil, Method, create_lb_collision_rule, LBMConfig, LBMOptimisation
+
+@pytest.mark.parametrize('method', [Method.MRT, Method.CENTRAL_MOMENT, Method.CUMULANT])
+def test_mrt_simplifications(method: Method):
+    stencil = Stencil.D3Q19
+    lbm_config = LBMConfig(stencil=stencil, method=method, compressible=True)
+    lbm_opt = LBMOptimisation(simplification='auto')
+
+    cr = create_lb_collision_rule(lbm_config=lbm_config, lbm_optimisation=lbm_opt)
+
+    
+    for subexp in cr.subexpressions:
+        rhs = subexp.rhs
+        #   Check for aliases
+        assert not isinstance(rhs, sp.Symbol)
+
+        #   Check for logarithms
+        assert not rhs.atoms(sp.log)
+
+        #   Check for nonextracted constant summands or factors
+        exprs = rhs.atoms(sp.Add, sp.Mul)
+        for expr in exprs:
+            for arg in expr.args:
+                if isinstance(arg, sp.Number):
+                    if arg not in {sp.Number(1), sp.Number(-1), sp.Float(1), sp.Float(-1)}:
+                        breakpoint()
+                    
+        #   Check for divisions
+        if not (isinstance(rhs, sp.Pow) and rhs.args[1] < 0):
+            powers = rhs.atoms(sp.Pow)
+            for p in powers:
+                assert p.args[1] > 0

tests/test_oldroydb.py

+from lbmpy.updatekernels import create_stream_pull_with_output_kernel
+from lbmpy import create_lb_update_rule, relaxation_rate_from_lattice_viscosity, ForceModel, Method, LBStencil
+from lbmpy.macroscopic_value_kernels import macroscopic_values_setter
+from pystencils.boundaries.boundaryhandling import BoundaryHandling
+from pystencils.boundaries.boundaryconditions import Neumann, Dirichlet
+from lbmpy.boundaries.boundaryhandling import LatticeBoltzmannBoundaryHandling
+from lbmpy.boundaries import NoSlip
+
+from lbmpy._compat import IS_PYSTENCILS_2
+from lbmpy.oldroydb import *
+import pytest
+
+# # Lattice Boltzmann with Finite-Volume Oldroyd-B
+# # taken from the electronic supplement of https://doi.org/10.1140/epje/s10189-020-00005-6,
+# # available at https://doi.org/10.24416/UU01-2AFZSW
+
+pytest.importorskip('scipy.optimize')
+
+
+@pytest.mark.xfail(IS_PYSTENCILS_2, reason="Staggered kernels are unavailable")
+def test_oldroydb():
+    import scipy.optimize
+
+    # ## Definitions
+
+    L = (34, 34)
+    lambda_p = sp.Symbol("lambda_p")
+    eta_p = sp.Symbol("eta_p")
+
+    lb_stencil = LBStencil("D2Q9")
+    fv_stencil = LBStencil("D2Q9")
+    eta = 1 - eta_p
+    omega = relaxation_rate_from_lattice_viscosity(eta)
+
+    f_pre = 0.00001
+
+    # ## Data structures
+
+    dh = ps.create_data_handling(L, periodicity=(True, False), default_target=ps.Target.CPU)
+
+    opts = {'cpu_openmp': False,
+            'cpu_vectorize_info': None,
+            'target': dh.default_target}
+
+    src = dh.add_array('src', values_per_cell=len(lb_stencil), layout='c')
+    dst = dh.add_array_like('dst', 'src')
+    ρ = dh.add_array('rho', layout='c', latex_name='\\rho')
+    u = dh.add_array('u', values_per_cell=dh.dim, layout='c')
+    tauface = dh.add_array('tau_face', values_per_cell=(len(fv_stencil) // 2, dh.dim, dh.dim), latex_name='\\tau_f',
+                           field_type=ps.FieldType.STAGGERED, layout='c')
+
+    tau = dh.add_array('tau', values_per_cell=(dh.dim, dh.dim), layout='c', latex_name='\\tau')
+    tauflux = dh.add_array('j_tau', values_per_cell=(len(fv_stencil) // 2, dh.dim, dh.dim), latex_name='j_\\tau',
+                           field_type=ps.FieldType.STAGGERED_FLUX, layout='c')
+    F = dh.add_array('F', values_per_cell=dh.dim, layout='c')
+
+    fluxbh = BoundaryHandling(dh, tauflux.name, fv_stencil, name="flux_boundary_handling",
+                              openmp=opts['cpu_openmp'], target=dh.default_target)
+    ubh = BoundaryHandling(dh, u.name, lb_stencil, name="velocity_boundary_handling",
+                           openmp=opts['cpu_openmp'], target=dh.default_target)
+    taufacebh = BoundaryHandling(dh, tauface.name, fv_stencil, name="tauface_boundary_handling",
+                                 openmp=opts['cpu_openmp'], target=dh.default_target)
+
+    # ## Solver
+
+    collision = create_lb_update_rule(stencil=lb_stencil,
+                                      method=Method.TRT,
+                                      relaxation_rate=omega,
+                                      compressible=True,
+                                      force_model=ForceModel.GUO,
+                                      force=F.center_vector + sp.Matrix([f_pre, 0]),
+                                      kernel_type='collide_only',
+                                      optimization={'symbolic_field': src})
+
+    stream = create_stream_pull_with_output_kernel(collision.method, src, dst, {'density': ρ, 'velocity': u})
+
+    lbbh = LatticeBoltzmannBoundaryHandling(collision.method, dh, src.name,
+                                            openmp=opts['cpu_openmp'], target=dh.default_target)
+
+    stream_kernel = ps.create_kernel(stream, **opts).compile()
+    collision_kernel = ps.create_kernel(collision, **opts).compile()
+
+    ob = OldroydB(dh.dim, u, tau, F, tauflux, tauface, lambda_p, eta_p)
+    flux_kernel = ps.create_staggered_kernel(ob.flux(), **opts).compile()
+    tauface_kernel = ps.create_staggered_kernel(ob.tauface(), **opts).compile()
+    continuity_kernel = ps.create_kernel(ob.continuity(), **opts).compile()
+    force_kernel = ps.create_kernel(ob.force(), **opts).compile()
+
+    # ## Set up the simulation
+
+    init = macroscopic_values_setter(collision.method, velocity=(0,) * dh.dim,
+                                     pdfs=src.center_vector, density=ρ.center)
+    init_kernel = ps.create_kernel(init, ghost_layers=0).compile()
+
+    # no-slip for the fluid, no-flux for the stress
+    noslip = NoSlip()
+    noflux = Flux(fv_stencil)
+    nostressdiff = Flux(fv_stencil, tau.center_vector)
+
+    # put some good values into the boundaries so we can take derivatives
+    noforce = Neumann()  # put the same stress into the boundary cells that is in the nearest fluid cell
+    noflow = Dirichlet((0,) * dh.dim)  # put zero velocity into the boundary cells
+
+    lbbh.set_boundary(noslip, ps.make_slice[:, :4])
+    lbbh.set_boundary(noslip, ps.make_slice[:, -4:])
+    fluxbh.set_boundary(noflux, ps.make_slice[:, :4])
+    fluxbh.set_boundary(noflux, ps.make_slice[:, -4:])
+    ubh.set_boundary(noflow, ps.make_slice[:, :4])
+    ubh.set_boundary(noflow, ps.make_slice[:, -4:])
+    taufacebh.set_boundary(nostressdiff, ps.make_slice[:, :4])
+    taufacebh.set_boundary(nostressdiff, ps.make_slice[:, -4:])
+
+    for bh in lbbh, fluxbh, ubh, taufacebh:
+        assert len(bh._boundary_object_to_boundary_info) == 1, "Restart kernel to clear boundaries"
+
+    def init():
+        dh.fill(ρ.name, np.nan, ghost_layers=True, inner_ghost_layers=True)
+        dh.fill(ρ.name, 1)
+        dh.fill(u.name, np.nan, ghost_layers=True, inner_ghost_layers=True)
+        dh.fill(u.name, 0)
+        dh.fill(tau.name, np.nan, ghost_layers=True, inner_ghost_layers=True)
+        dh.fill(tau.name, 0)
+        dh.fill(tauflux.name, np.nan, ghost_layers=True, inner_ghost_layers=True)
+        dh.fill(tauface.name, np.nan, ghost_layers=True, inner_ghost_layers=True)
+        dh.fill(F.name, np.nan, ghost_layers=True, inner_ghost_layers=True)
+        dh.fill(F.name, 0)  # needed for LB initialization
+
+        sync_tau()  # force calculation inside the initialization needs neighbor taus
+        dh.run_kernel(init_kernel)
+        dh.fill(F.name, np.nan)
+
+    sync_pdfs = dh.synchronization_function([src.name])  # needed before stream, but after collision
+    sync_u = dh.synchronization_function([u.name])  # needed before continuity, but after stream
+    sync_tau = dh.synchronization_function([tau.name])  # needed before flux and tauface, but after continuity
+
+    def time_loop(steps, lambda_p_val, eta_p_val):
+        dh.all_to_gpu()
+        vmid = np.empty((2, steps // 10 + 1))
+        sync_tau()
+        sync_u()
+        ubh()
+        i = -1
+        for i in range(steps):
+            dh.run_kernel(flux_kernel)
+            fluxbh()  # zero the fluxes into/out of boundaries
+            dh.run_kernel(continuity_kernel, **{lambda_p.name: lambda_p_val, eta_p.name: eta_p_val})
+
+            sync_tau()
+            dh.run_kernel(tauface_kernel)  # needed for force
+            taufacebh()
+            dh.run_kernel(force_kernel)
+
+            dh.run_kernel(collision_kernel, **{eta_p.name: eta_p_val})
+            sync_pdfs()
+            lbbh()  # bounce-back populations into boundaries
+            dh.run_kernel(stream_kernel)
+            sync_u()
+            ubh()  # need neighboring us for flux and continuity
+
+            dh.swap(src.name, dst.name)
+
+            if i % 10 == 0:
+                if u.name in dh.gpu_arrays:
+                    dh.to_cpu(u.name)
+                uu = dh.gather_array(u.name)
+                uu = uu[L[0] // 2 - 1:L[0] // 2 + 1, L[1] // 2 - 1:L[1] // 2 + 1, 0].mean()
+                if np.isnan(uu):
+                    raise Exception(f"NaN encountered after {i} steps")
+                vmid[:, i // 10] = [i, uu]
+        sync_u()
+        dh.all_to_cpu()
+
+        return vmid[:, :i // 10 + 1]
+
+    # ## Analytical solution
+    # 
+    # comes from Waters and King, Unsteady flow of an elastico-viscous liquid, Rheologica Acta 9, 345–355 (1970).
+
+    def N(n):
+        return (2 * n - 1) * np.pi
+
+    def Alpha_n(N, El, eta_p):
+        return 1 + (1 - eta_p) * El * N * N / 4
+
+    def Beta_n(alpha_n, N, El):
+        return np.sqrt(np.abs(alpha_n * alpha_n - El * N * N))
+
+    def Gamma_n(N, El, eta_p):
+        return 1 - (1 + eta_p) * El * N * N / 4
+
+    def G(alpha_n, beta_n, gamma_n, flag, T):
+        if (flag):
+            return ((1.0 - gamma_n / beta_n) * np.exp(-(alpha_n + beta_n) * T / 2) +
+                    (1.0 + gamma_n / beta_n) * np.exp((beta_n - alpha_n) * T / 2))
+        else:
+            return 2 * np.exp(-alpha_n * T / 2) * (np.cos(beta_n * T / 2) + (gamma_n / beta_n) * np.sin(beta_n * T / 2))
+
+    def W(T, El, eta_p):
+        W_ = 1.5
+        for n in range(1, 1000):
+            N_ = N(n)
+            alpha_n = Alpha_n(N_, El, eta_p)
+
+            if alpha_n * alpha_n - El * N_ * N_ < 0:
+                flag_ = False
+            else:
+                flag_ = True
+
+            beta_n = Beta_n(alpha_n, N_, El)
+            gamma_n = Gamma_n(N_, El, eta_p)
+            G_ = G(alpha_n, beta_n, gamma_n, flag_, T)
+
+            W_ -= 24 * (np.sin(N_ / 2) / (N_ * N_ * N_)) * G_
+
+        return W_
+
+    # ## Run the simulation
+
+    lambda_p_val = 3000
+    eta_p_val = 0.9
+
+    init()
+    vmid = time_loop(lambda_p_val * 4, lambda_p_val, eta_p_val)
+
+    actual_width = sum(dh.gather_array(lbbh.flag_array_name)[L[0] // 2, :] == 1)
+    uref = float(f_pre * actual_width ** 2 / (8 * (eta + eta_p)))
+
+    Wi = lambda_p_val * uref / (actual_width / 2)
+    Re = uref * (actual_width / 2) / (eta + eta_p)
+    El = float(Wi / Re)
+
+    pref = 1 / W(vmid[0, -1] / lambda_p_val, El, eta_p_val)
+
+    El_measured, pref_measured = scipy.optimize.curve_fit(lambda a, b, c: W(a, b, eta_p_val) * c,
+                                                          vmid[0, :] / lambda_p_val, vmid[1, :] / vmid[1, -1],
+                                                          p0=(El, pref))[0]
+    measured_width = np.sqrt(4 * lambda_p_val * float(eta + eta_p) / El_measured)
+
+    print(f"El={El}, El_measured={El_measured}")
+    print(f"L={actual_width}, L_measured={measured_width}")
+
+    assert abs(measured_width - actual_width) < 1, "effective channel width differs significantly from defined width"
+
+    an = W(vmid[0, :] / lambda_p_val, El, eta_p_val) * pref
+    an_measured = W(vmid[0, :] / lambda_p_val, El_measured, eta_p_val) * pref_measured
+
+    diff = abs(vmid[1, :] / vmid[1, -1] - an_measured) / an_measured
+    assert diff[lambda_p_val // 5:].max() < 0.03, "maximum velocity deviation is too large"
+
+#    from pystencils import plot as plt
+#
+#     plt.xlabel("$t$")
+#     plt.ylabel(r"$u_{max}/u_{max}^{Newtonian}$")
+#     plt.plot(vmid[0,:], vmid[1,:]/vmid[1,-1] if vmid[1,-1] != 0 else 0, label='FVM')
+#     plt.plot(vmid[0,:], np.ones_like(vmid[0,:]), 'k--', label='Newtonian')
+#
+#     plt.plot(vmid[0,:], an, label="analytic")
+#     plt.plot(vmid[0,:], an_measured, label="analytic, fit width")
+#     plt.legend()
+#
+#     if eta_p_val == 0.1:
+#         plt.ylim(0.9, 1.15)
+#     elif lambda_p_val == 9000:
+#         plt.ylim(0.8, 1.5)
+#     elif eta_p_val == 0.3:
+#         plt.ylim(0.8, 1.4)
+#     plt.show()

lbmpy_tests/test_plot.py → tests/test_plot.py

 import os
 from tempfile import TemporaryDirectory
+import shutil
+
+import pytest
 
 import numpy as np
 
@@ -7,6 +10,7 @@ import lbmpy.plot as plt
 from lbmpy.scenarios import create_lid_driven_cavity
 
 
+@pytest.mark.skipif(shutil.which('ffmpeg') is None, reason="ffmpeg not available")
 def test_animation():
 
     ldc = create_lid_driven_cavity((10, 10), relaxation_rate=1.8)

tests/test_poisuille_channel.py

+"""
+Test Poiseuille flow against analytical solution
+"""
+
+import pytest
+
+from lbmpy.enums import Stencil, CollisionSpace
+
+import pystencils as ps
+from . import poiseuille
+
+
+@pytest.mark.parametrize('target', (ps.Target.CPU, ps.Target.GPU))
+@pytest.mark.parametrize('stencil_name', (Stencil.D2Q9, Stencil.D3Q19))
+@pytest.mark.parametrize('zero_centered', (False, True))
+@pytest.mark.parametrize('moment_space_collision', (False, True))
+def test_poiseuille_channel(target, stencil_name, zero_centered, moment_space_collision):
+    # Cuda
+    if target == ps.Target.GPU:
+        import pytest
+        pytest.importorskip("cupy")
+
+    cspace_info = CollisionSpace.RAW_MOMENTS if moment_space_collision else CollisionSpace.POPULATIONS
+    poiseuille.poiseuille_channel(target=target,
+                                  stencil_name=stencil_name,
+                                  zero_centered=zero_centered,
+                                  collision_space_info=cspace_info)