lbmpy/methods/__init__.py

-from lbmpy.methods.creationfunctions import (
-    create_mrt_orthogonal, create_mrt_raw, create_srt, create_trt, create_trt_kbc,
-    create_trt_with_magic_number, create_with_continuous_maxwellian_eq_moments,
-    create_with_discrete_maxwellian_eq_moments, mrt_orthogonal_modes_literature,
-    create_centered_cumulant_model, create_with_default_polynomial_cumulants)
-
-from lbmpy.methods.abstractlbmethod import AbstractLbMethod, RelaxationInfo
-from lbmpy.methods.conservedquantitycomputation import AbstractConservedQuantityComputation
-
-from .conservedquantitycomputation import DensityVelocityComputation
-
-__all__ = ['RelaxationInfo', 'AbstractLbMethod',
-           'AbstractConservedQuantityComputation', 'DensityVelocityComputation',
-           'create_srt', 'create_trt', 'create_trt_with_magic_number', 'create_trt_kbc',
-           'create_mrt_orthogonal', 'create_mrt_raw',
-           'create_with_continuous_maxwellian_eq_moments', 'create_with_discrete_maxwellian_eq_moments',
-           'mrt_orthogonal_modes_literature', 'create_centered_cumulant_model',
-           'create_with_default_polynomial_cumulants']

lbmpy/methods/centeredcumulant/__init__.py

-from .force_model import CenteredCumulantForceModel
-from .centeredcumulantmethod import CenteredCumulantBasedLbMethod
-
-__all__ = ["CenteredCumulantForceModel", "CenteredCumulantBasedLbMethod"]

lbmpy/methods/centeredcumulant/centered_cumulants.py

-from lbmpy.stencils import get_stencil
-import sympy as sp
-
-from pystencils.stencil import have_same_entries
-
-from lbmpy.moments import MOMENT_SYMBOLS, moment_sort_key, exponent_to_polynomial_representation
-
-
-def statistical_quantity_symbol(name, exponents):
-    return sp.Symbol(f'{name}_{"".join(str(i) for i in exponents)}')
-
-
-def exponent_tuple_sort_key(x):
-    return moment_sort_key(exponent_to_polynomial_representation(x))
-
-
-def get_default_polynomial_cumulants_for_stencil(stencil):
-    """
-    Returns default groups of cumulants to be relaxed with common relaxation rates as stated in literature.
-    Groups are ordered like this:
-     - First group is density
-     - Second group are the momentum modes
-     - Third group are the shear modes
-     - Fourth group is the bulk mode
-     - Remaining groups do not govern hydrodynamic properties
-    """
-    x, y, z = MOMENT_SYMBOLS
-    if have_same_entries(stencil, get_stencil("D2Q9")):
-        #   Cumulants of the D2Q9 stencil up to third order are equal to
-        #   the central moments; only the fourth-order cumulant x**2 * y**2
-        #   has a more complicated form. They can be arranged into groups
-        #   for the preservation of rotational invariance as described by
-        #   Martin Geier in his dissertation.
-        #
-        #   Reference: Martin Geier. Ab inito derivation of the cascaded Lattice Boltzmann
-        #   Automaton. Dissertation. University of Freiburg. 2006.
-        return [
-            [sp.sympify(1)],        # density is conserved
-            [x, y],                 # momentum is relaxed for cumulant forcing
-
-            [x * y, x**2 - y**2],   # shear
-
-            [x**2 + y**2],          # bulk
-
-            [x**2 * y, x * y**2],
-            [x**2 * y**2]
-        ]
-
-    elif have_same_entries(stencil, get_stencil("D3Q19")):
-        #   D3Q19 cumulants are obtained by pruning the D3Q27 cumulant set as
-        #   described by Coreixas, 2019.
-        return [
-            [sp.sympify(1)],                # density is conserved
-            [x, y, z],                      # momentum might be affected by forcing
-
-            [x * y,
-             x * z,
-             y * z,
-             x ** 2 - y ** 2,
-             x ** 2 - z ** 2],              # shear
-
-            [x ** 2 + y ** 2 + z ** 2],     # bulk
-
-            [x * y ** 2 + x * z ** 2,
-             x ** 2 * y + y * z ** 2,
-             x ** 2 * z + y ** 2 * z],
-
-            [x * y ** 2 - x * z ** 2,
-             x ** 2 * y - y * z ** 2,
-             x ** 2 * z - y ** 2 * z],
-
-            [x ** 2 * y ** 2 - 2 * x ** 2 * z ** 2 + y ** 2 * z ** 2,
-             x ** 2 * y ** 2 + x ** 2 * z ** 2 - 2 * y ** 2 * z ** 2],
-
-            [x ** 2 * y ** 2 + x ** 2 * z ** 2 + y ** 2 * z ** 2]
-        ]
-
-    elif have_same_entries(stencil, get_stencil("D3Q27")):
-        #   Cumulants grouped to preserve rotational invariance as described by Geier et al, 2015
-        return [
-            [sp.sympify(1)],                # density is conserved
-            [x, y, z],                      # momentum might be affected by forcing
-
-            [x * y,
-             x * z,
-             y * z,
-             x ** 2 - y ** 2,
-             x ** 2 - z ** 2],              # shear
-
-            [x ** 2 + y ** 2 + z ** 2],     # bulk
-
-            [x * y ** 2 + x * z ** 2,
-             x ** 2 * y + y * z ** 2,
-             x ** 2 * z + y ** 2 * z],
-
-            [x * y ** 2 - x * z ** 2,
-             x ** 2 * y - y * z ** 2,
-             x ** 2 * z - y ** 2 * z],
-
-            [x * y * z],
-
-            [x ** 2 * y ** 2 - 2 * x ** 2 * z ** 2 + y ** 2 * z ** 2,
-             x ** 2 * y ** 2 + x ** 2 * z ** 2 - 2 * y ** 2 * z ** 2],
-
-            [x ** 2 * y ** 2 + x ** 2 * z ** 2 + y ** 2 * z ** 2],
-
-            [x ** 2 * y * z,
-             x * y ** 2 * z,
-             x * y * z ** 2],
-
-            [x ** 2 * y ** 2 * z,
-             x ** 2 * y * z ** 2,
-             x * y ** 2 * z ** 2],
-
-            [x ** 2 * y ** 2 * z ** 2]
-        ]
-    else:
-        raise ValueError("No default set of cumulants is available for this stencil. "
-                         "Please specify your own set of polynomial cumulants.")

lbmpy/phasefield_allen_cahn/analytical.py

-
-def analytic_rising_speed(gravitational_acceleration, bubble_diameter, viscosity_gas):
-    r"""
-    Calculated the analytical rising speed of a bubble. This is the expected end rising speed.
-    Args:
-        gravitational_acceleration: the gravitational acceleration acting in the simulation scenario. Usually it gets
-                                    calculated based on dimensionless parameters which describe the scenario
-        bubble_diameter: the diameter of the bubble at the beginning of the simulation
-        viscosity_gas: the viscosity of the fluid inside the bubble
-    """
-    result = -(gravitational_acceleration * bubble_diameter * bubble_diameter) / (12.0 * viscosity_gas)
-    return result