def create_falling_drop(
domain_size=(160, 200), omega=1.9, kappas=(0.001, 0.001, 0.0005),
**kwargs):
c = sp.symbols("c_:3")
free_energy = free_energy_functional_n_phases_penalty_term(c, 1, kappas)
gravity = -0.1e-5
if 'optimization' not in kwargs:
kwargs['optimization'] = {'openmp': 4}
sc = PhaseFieldStep(free_energy,
c,
domain_size=domain_size,
hydro_dynamic_relaxation_rate=omega,
order_parameter_force={
2: (0, gravity),
1: (0, 0),
0: (0, 0)
},
**kwargs)
sc.set_concentration(make_slice[:, 0.4:], [1, 0, 0])
sc.set_concentration(make_slice[:, :0.4], [0, 1, 0])
sc.set_concentration(make_slice[0.45:0.55, 0.8:0.9], [0, 0, 1])
sc.hydro_lbm_step.boundary_handling.set_boundary(NoSlip(), make_slice[:,
0])
sc.set_pdf_fields_from_macroscopic_values()
return sc
def test_boundary_2D():
with ManualCodeGenerationContext(openmp=True,
double_accuracy=True) as ctx:
lb_method = create_lb_method(stencil='D2Q9', method='srt')
generate_boundary(ctx,
'Boundary',
NoSlip(),
lb_method,
target='gpu')
def test_slice_mask_combination():
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=bool)
sc.boundary_handling.set_boundary(NoSlip(), make_slice[6:7, -1], callback)
def test_advanced_streaming_noslip_single_cell(stencil, streaming_pattern,
prev_timestep):
"""
Advanced Streaming NoSlip Test
"""
stencil = LBStencil(stencil)
pdf_field = ps.fields(f'pdfs({stencil.Q}): [{stencil.D}D]')
prev_pdf_access = AccessPdfValues(stencil, streaming_pattern,
prev_timestep, 'out')
next_pdf_access = AccessPdfValues(stencil, streaming_pattern,
prev_timestep.next(), 'in')
pdfs = np.zeros((3, ) * stencil.D + (stencil.Q, ))
pos = (1, ) * stencil.D
for d in range(stencil.Q):
prev_pdf_access.write_pdf(pdfs, pos, d, d)
lbm_config = LBMConfig(stencil=stencil, method=Method.SRT)
lb_method = create_lb_method(lbm_config=lbm_config)
noslip = NoSlip()
index_struct_dtype = numpy_data_type_for_boundary_object(noslip, stencil.D)
index_field = Field('indexVector',
FieldType.INDEXED,
index_struct_dtype,
layout=[0],
shape=(TypedSymbol("indexVectorSize",
create_type(np.int64)), 1),
strides=(1, 1))
index_vector = np.array([pos + (d, ) for d in range(stencil.Q)],
dtype=index_struct_dtype)
ast = create_lattice_boltzmann_boundary_kernel(
pdf_field,
index_field,
lb_method,
noslip,
prev_timestep=prev_timestep,
streaming_pattern=streaming_pattern)
flex_kernel = ast.compile()
flex_kernel(pdfs=pdfs,
indexVector=index_vector,
indexVectorSize=len(index_vector))
reflected_pdfs = [
next_pdf_access.read_pdf(pdfs, pos, d) for d in range(stencil.Q)
]
inverse_pdfs = [inverse_dir_index(stencil, d) for d in range(stencil.Q)]
assert reflected_pdfs == inverse_pdfs
def test_boundary_utility_functions():
stencil = LBStencil(Stencil.D2Q9)
method = create_lb_method(lbm_config=LBMConfig(stencil=stencil))
noslip = NoSlip("noslip")
assert noslip == NoSlip("noslip")
assert not noslip == NoSlip("test")
assert not noslip == UBB((0, 0), name="ubb")
assert noslip.name == "noslip"
noslip.name = "test name setter"
assert noslip.name == "test name setter"
ubb = UBB((0, 0), name="ubb")
assert ubb == UBB((0, 0), name="ubb")
assert not noslip == UBB((0, 0), name="test")
assert not ubb == NoSlip("noslip")
simple_extrapolation = SimpleExtrapolationOutflow(
normal_direction=stencil[4], stencil=stencil, name="simple")
assert simple_extrapolation == SimpleExtrapolationOutflow(
normal_direction=stencil[4], stencil=stencil, name="simple")
assert not simple_extrapolation == SimpleExtrapolationOutflow(
normal_direction=stencil[4], stencil=stencil, name="test")
assert not simple_extrapolation == NoSlip("noslip")
outflow = ExtrapolationOutflow(normal_direction=stencil[4],
lb_method=method,
name="outflow")
assert outflow == ExtrapolationOutflow(normal_direction=stencil[4],
lb_method=method,
name="outflow")
assert not outflow == ExtrapolationOutflow(
normal_direction=stencil[4], lb_method=method, name="test")
assert not outflow == simple_extrapolation
density = FixedDensity(density=1.0, name="fixedDensity")
assert density == FixedDensity(density=1.0, name="fixedDensity")
assert not density == FixedDensity(density=1.0, name="test")
assert not density == UBB((0, 0), name="ubb")
diffusion = DiffusionDirichlet(concentration=1.0, name="diffusion")
assert diffusion == DiffusionDirichlet(concentration=1.0, name="diffusion")
assert not diffusion == DiffusionDirichlet(concentration=1.0, name="test")
assert not diffusion == density
neumann = NeumannByCopy(name="Neumann")
assert neumann == NeumannByCopy(name="Neumann")
assert not neumann == NeumannByCopy(name="test")
assert not neumann == diffusion
stream = StreamInConstant(constant=1.0, name="stream")
assert stream == StreamInConstant(constant=1.0, name="stream")
assert not stream == StreamInConstant(constant=1.0, name="test")
assert not stream == noslip
def create_lid_driven_cavity(domain_size=None,
lid_velocity=0.005,
lbm_kernel=None,
parallel=False,
data_handling=None,
**kwargs):
"""Creates a lid driven cavity scenario.
Args:
domain_size: tuple specifying the number of cells in each dimension
lid_velocity: x velocity of lid in lattice coordinates.
lbm_kernel: a LBM function, which would otherwise automatically created
kwargs: other parameters are passed on to the method, see :mod:`lbmpy.creationfunctions`
parallel: True for distributed memory parallelization with walberla
data_handling: see documentation of :func:`create_fully_periodic_flow`
Returns:
instance of :class:`Scenario`
"""
assert domain_size is not None or data_handling is not None
if data_handling is None:
optimization = kwargs.get('optimization', None)
target = optimization.get('target', None) if optimization else None
data_handling = create_data_handling(domain_size,
periodicity=False,
default_ghost_layers=1,
parallel=parallel,
default_target=target)
step = LatticeBoltzmannStep(data_handling=data_handling,
lbm_kernel=lbm_kernel,
name="ldc",
**kwargs)
my_ubb = UBB(velocity=[lid_velocity, 0, 0][:step.method.dim])
step.boundary_handling.set_boundary(my_ubb,
slice_from_direction('N', step.dim))
for direction in ('W', 'E', 'S') if step.dim == 2 else ('W', 'E', 'S', 'T',
'B'):
step.boundary_handling.set_boundary(
NoSlip(), slice_from_direction(direction, step.dim))
return step
def test_force_on_boundary():
results = []
domain_size = (80, 30)
boundaries = [
NoSlip('obstacle_noslip'),
UBB((0, ) * len(domain_size), name='obstacle_UBB')
]
for parallel in (False, True) if wLB else (False, ):
for boundary_obj in boundaries:
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(f" -> force = {force}")
results.append(force)
for res in results[1:]:
np.testing.assert_almost_equal(results[0], res)
def test_lattice_model():
with ManualCodeGenerationContext() as ctx:
force_field = ps.fields("force(3): [3D]", layout='fzyx')
omega = sp.Symbol("omega")
cr = create_lb_collision_rule(stencil='D3Q19',
method='srt',
relaxation_rates=[omega],
compressible=True,
force_model='guo',
force=force_field.center_vector)
scaling = RefinementScaling()
scaling.add_standard_relaxation_rate_scaling(omega)
scaling.add_force_scaling(force_field)
generate_lattice_model(ctx,
'SrtWithForceFieldModel',
cr,
refinement_scaling=scaling)
generate_boundary(ctx, 'MyUBB', UBB([0.05, 0, 0]), cr.method)
generate_boundary(ctx, 'MyNoSlip', NoSlip(), cr.method)
assert 'static const bool compressible = true;' in ctx.files[
'SrtWithForceFieldModel.h']
lb_method,
update_rule_params=options_without_opt)
# gpu LB sweep & boundaries
generate_sweep(ctx,
'UniformGridGPU_LbKernel',
update_rule,
field_swaps=[('pdfs', 'pdfs_tmp')],
inner_outer_split=True,
target='gpu',
gpu_indexing_params=sweep_params,
varying_parameters=vp)
generate_boundary(ctx,
'UniformGridGPU_NoSlip',
NoSlip(),
lb_method,
target='gpu')
generate_boundary(ctx,
'UniformGridGPU_UBB',
UBB([0.05, 0, 0]),
lb_method,
target='gpu')
# getter & setter
setter_assignments = macroscopic_values_setter(
lb_method,
velocity=velocity_field.center_vector,
pdfs=pdfs.center_vector,
density=1)
getter_assignments = macroscopic_values_getter(
def create_channel(domain_size=None,
force=None,
pressure_difference=None,
u_max=None,
diameter_callback=None,
duct=False,
wall_boundary=NoSlip(),
parallel=False,
data_handling=None,
**kwargs):
"""Create a channel scenario (2D or 3D).
The channel can be driven either by force, velocity inflow or pressure difference. Choose one and pass
exactly one of the parameters 'force', 'pressure_difference' or 'u_max'.
Args:
domain_size: size of the simulation domain. First coordinate is the flow direction.
force: Periodic channel, driven by a body force. Pass force in flow direction in lattice units here.
pressure_difference: Inflow and outflow are fixed pressure conditions, with the given pressure difference.
u_max: Parabolic velocity profile prescribed at inflow, pressure boundary =1.0 at outflow.
diameter_callback: optional callback for channel with varying diameters. Only valid if duct=False.
The callback receives x coordinate array and domain_size and returns a
an array of diameters of the same shape
duct: if true the channel has rectangular instead of circular cross section
wall_boundary: instance of boundary class that should be set at the channel walls
parallel: True for distributed memory parallelization with walberla
data_handling: see documentation of :func:`create_fully_periodic_flow`
kwargs: all other keyword parameters are passed directly to scenario class.
"""
assert domain_size is not None or data_handling is not None
if [bool(p) for p in (force, pressure_difference, u_max)].count(True) != 1:
raise ValueError(
"Please specify exactly one of the parameters 'force', 'pressure_difference' or 'u_max'"
)
periodicity = (True, False, False) if force else (False, False, False)
if data_handling is None:
dim = len(domain_size)
assert dim in (2, 3)
data_handling = create_data_handling(domain_size,
periodicity=periodicity[:dim],
default_ghost_layers=1,
parallel=parallel)
dim = data_handling.dim
if force:
kwargs['force'] = tuple([force, 0, 0][:dim])
assert data_handling.periodicity[0]
step = LatticeBoltzmannStep(data_handling=data_handling,
name="force_driven_channel",
**kwargs)
elif pressure_difference:
inflow = FixedDensity(1.0 + pressure_difference)
outflow = FixedDensity(1.0)
step = LatticeBoltzmannStep(data_handling=data_handling,
name="pressure_driven_channel",
**kwargs)
step.boundary_handling.set_boundary(inflow,
slice_from_direction('W', dim))
step.boundary_handling.set_boundary(outflow,
slice_from_direction('E', dim))
elif u_max:
if duct:
raise NotImplementedError(
"Velocity inflow for duct flows not yet implemented")
step = LatticeBoltzmannStep(data_handling=data_handling,
name="velocity_driven_channel",
**kwargs)
diameter = diameter_callback(np.array([
0
]), domain_size)[0] if diameter_callback else min(domain_size[1:])
add_pipe_inflow_boundary(step.boundary_handling,
u_max,
slice_from_direction('W', dim),
flow_direction=0,
diameter=diameter)
outflow = FixedDensity(1.0)
step.boundary_handling.set_boundary(outflow,
slice_from_direction('E', dim))
else:
assert False
directions = ('N', 'S', 'T', 'B') if dim == 3 else ('N', 'S')
for direction in directions:
step.boundary_handling.set_boundary(
wall_boundary, slice_from_direction(direction, dim))
if duct and diameter_callback is not None:
raise ValueError(
"For duct flows, passing a diameter callback does not make sense.")
if not duct:
diameter = min(step.boundary_handling.shape[1:])
add_pipe_walls(step.boundary_handling,
diameter_callback if diameter_callback else diameter,
wall_boundary)
return step
import sympy as sp
import pystencils as ps
from lbmpy.creationfunctions import create_lb_method
from lbmpy.boundaries import NoSlip, UBB
from pystencils_walberla import CodeGeneration
from lbmpy_walberla import generate_lattice_model, RefinementScaling, generate_boundary
with CodeGeneration() as ctx:
omega = sp.Symbol("omega")
force_field = ps.fields("force(3): [3D]", layout='fzyx')
# lattice Boltzmann method
lb_method = create_lb_method(stencil='D3Q19',
method='srt',
relaxation_rates=[omega],
force_model='guo',
force=force_field.center_vector)
scaling = RefinementScaling()
scaling.add_standard_relaxation_rate_scaling(omega)
scaling.add_force_scaling(force_field)
# generate components
generate_lattice_model(ctx,
'SrtWithForceFieldModel',
lb_method,
refinement_scaling=scaling)
generate_boundary(ctx, 'MyUBB', UBB([0.05, 0, 0]), lb_method)
generate_boundary(ctx, 'MyNoSlip', NoSlip(), lb_method)
def genNoSlip():
boundary = NoSlip(name='MyNoSlip')
method = create_lb_method(stencil='D3Q19', method='srt')
return create_boundary_class(boundary, method)
method='mrt3',
relaxation_rates=[omega, omega, omega_free],
entropic=
True, # entropic method where second omega is chosen s.t. entropy condition
omega_output_field=
omega_out, # scalar field where automatically chosen omega of entropic or Smagorinsky method is written to
force=force_field.
center_vector, # read forces for each lattice cell from an external force field
# that is initialized and changed in C++ app
output={'velocity': vel_field
}, # write macroscopic velocity to field in every time step
# useful for coupling multiple LB methods, e.g. hydrodynamic to advection/diffusion LBM
optimization={'cse_global': True})
# the refinement scaling object describes how certain parameters are scaled across grid scales
# there are two default scaling behaviors available for relaxation rates and forces:
scaling = RefinementScaling()
scaling.add_standard_relaxation_rate_scaling(omega)
scaling.add_force_scaling(force_field)
# generate lattice model and (optionally) boundary conditions
# for CPU simulations waLBerla's internal boundary handling can be used as well
generate_lattice_model(ctx,
'LbCodeGenerationExample_LatticeModel',
collision_rule,
refinement_scaling=scaling)
generate_boundary(ctx, 'LbCodeGenerationExample_UBB', UBB([0.05, 0, 0]),
collision_rule.method)
generate_boundary(ctx, 'LbCodeGenerationExample_NoSlip', NoSlip(),
collision_rule.method)
def __init__(self, stencil, streaming_pattern, wall_boundary=None, target=Target.CPU):
if wall_boundary is None:
wall_boundary = NoSlip()
self.target = target
self.gpu = target in [Target.GPU]
# Stencil
self.stencil = stencil
self.q = stencil.Q
self.dim = stencil.D
# Streaming
self.streaming_pattern = streaming_pattern
self.inplace = is_inplace(self.streaming_pattern)
self.timesteps = get_timesteps(streaming_pattern)
self.zeroth_timestep = self.timesteps[0]
# Domain, Data Handling and PDF fields
self.pipe_length = 60
self.pipe_radius = 15
self.domain_size = (self.pipe_length, ) + (2 * self.pipe_radius,) * (self.dim - 1)
self.periodicity = (True, ) + (False, ) * (self.dim - 1)
self.force = (0.0001, ) + (0.0,) * (self.dim - 1)
self.dh = create_data_handling(domain_size=self.domain_size,
periodicity=self.periodicity, default_target=self.target)
self.pdfs = self.dh.add_array('pdfs', self.q)
if not self.inplace:
self.pdfs_tmp = self.dh.add_array_like('pdfs_tmp', self.pdfs.name)
# LBM Streaming and Collision
lbm_config = LBMConfig(stencil=stencil, method=Method.SRT, relaxation_rate=1.0,
force_model=ForceModel.GUO, force=self.force, streaming_pattern=streaming_pattern)
lbm_opt = LBMOptimisation(symbolic_field=self.pdfs)
config = CreateKernelConfig(target=self.target)
if not self.inplace:
lbm_opt = replace(lbm_opt, symbolic_temporary_field=self.pdfs_tmp)
self.lb_collision = create_lb_collision_rule(lbm_config=lbm_config, lbm_optimisation=lbm_opt)
self.lb_method = self.lb_collision.method
self.lb_kernels = []
for t in self.timesteps:
lbm_config = replace(lbm_config, timestep=t)
self.lb_kernels.append(create_lb_function(collision_rule=self.lb_collision,
lbm_config=lbm_config,
lbm_optimisation=lbm_opt,
config=config))
# Macroscopic Values
self.density = 1.0
self.density_field = self.dh.add_array('rho', 1)
u_x = 0.0
self.velocity = (u_x,) * self.dim
self.velocity_field = self.dh.add_array('u', self.dim)
setter = macroscopic_values_setter(
self.lb_method, self.density, self.velocity, self.pdfs,
streaming_pattern=self.streaming_pattern, previous_timestep=self.zeroth_timestep)
self.init_kernel = create_kernel(setter,
config=CreateKernelConfig(target=target, ghost_layers=1)).compile()
self.getter_kernels = []
for t in self.timesteps:
getter = macroscopic_values_getter(
self.lb_method, self.density_field, self.velocity_field, self.pdfs,
streaming_pattern=self.streaming_pattern, previous_timestep=t)
self.getter_kernels.append(create_kernel(getter,
config=CreateKernelConfig(target=target, ghost_layers=1)).compile())
# Periodicity
self.periodicity_handler = LBMPeriodicityHandling(
self.stencil, self.dh, self.pdfs.name, streaming_pattern=self.streaming_pattern)
# Boundary Handling
self.wall = wall_boundary
self.bh = LatticeBoltzmannBoundaryHandling(
self.lb_method, self.dh, self.pdfs.name,
streaming_pattern=self.streaming_pattern, target=self.target)
self.bh.set_boundary(boundary_obj=self.wall, mask_callback=self.mask_callback)
self.current_timestep = self.zeroth_timestep
def genNoSlip():
boundary = NoSlip(name='MyNoSlip')
method = createLatticeBoltzmannMethod(stencil='D3Q19', method='srt')
return createBoundaryClass(boundary, method)
from pystencils_walberla import CodeGeneration, generate_sweep
with CodeGeneration() as ctx:
# LB options
options = {
'method': 'srt',
'stencil': 'D3Q19',
'relaxation_rate': sp.Symbol("omega"),
'field_name': 'pdfs',
'compressible': False,
'temporary_field_name': 'pdfs_tmp',
'optimization': {'cse_global': True,
'cse_pdfs': True,
'gpu_indexing_params': {'block_size': (128, 1, 1)}}
}
lb_method = create_lb_method(**options)
update_rule = create_lb_update_rule(lb_method=lb_method, **options)
# CPU lattice model - required for macroscopic value computation, VTK output etc.
generate_lattice_model(ctx, 'UniformGridGPU_LatticeModel', lb_method)
# gpu LB sweep & boundaries
generate_sweep(ctx, 'UniformGridGPU_LbKernel', update_rule, field_swaps=[('pdfs', 'pdfs_tmp')],
inner_outer_split=True, target='gpu')
generate_boundary(ctx, 'UniformGridGPU_NoSlip', NoSlip(), lb_method, target='gpu')
generate_boundary(ctx, 'UniformGridGPU_UBB', UBB([0.05, 0, 0]), lb_method, target='gpu')
# communication
generate_pack_info_from_kernel(ctx, 'UniformGridGPU_PackInfo', update_rule, target='gpu')
def poiseuille_channel(target, stencil_name):
# physical parameters
rho_0 = 1.2 # density
eta = 0.2 # kinematic viscosity
width = 41 # of box
actual_width = width - 2 # subtract boundary layer from box width
ext_force_density = 0.2 / actual_width ** 2 # scale by width to keep stable
# LB parameters
lb_stencil = LBStencil(stencil_name)
if lb_stencil.D == 2:
L = (4, width)
elif lb_stencil.D == 3:
L = (4, width, 4)
else:
raise Exception()
periodicity = [True, False] + [True] * (lb_stencil.D - 2)
omega = lbmpy.relaxationrates.relaxation_rate_from_lattice_viscosity(eta)
# ## Data structures
dh = ps.create_data_handling(L, periodicity=periodicity, default_target=target)
src = dh.add_array('src', values_per_cell=len(lb_stencil))
dst = dh.add_array_like('dst', 'src')
ρ = dh.add_array('rho', latex_name='\\rho', values_per_cell=1)
u = dh.add_array('u', values_per_cell=dh.dim)
# LB Setup
lbm_config = LBMConfig(stencil=lb_stencil, relaxation_rate=omega, method=Method.TRT,
compressible=True, force_model=ForceModel.GUO,
force=tuple([ext_force_density] + [0] * (lb_stencil.D - 1)),
kernel_type='collide_only')
lbm_opt = LBMOptimisation(symbolic_field=src)
collision = create_lb_update_rule(lbm_config=lbm_config, lbm_optimisation=lbm_opt)
stream = create_stream_pull_with_output_kernel(collision.method, src, dst, {'velocity': u})
config = ps.CreateKernelConfig(cpu_openmp=False, target=dh.default_target)
stream_kernel = ps.create_kernel(stream, config=config).compile()
collision_kernel = ps.create_kernel(collision, config=config).compile()
# Boundaries
lbbh = LatticeBoltzmannBoundaryHandling(collision.method, dh, src.name, target=dh.default_target)
# ## 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()
noslip = NoSlip()
wall_thickness = 2
if lb_stencil.D == 2:
lbbh.set_boundary(noslip, ps.make_slice[:, :wall_thickness])
lbbh.set_boundary(noslip, ps.make_slice[:, -wall_thickness:])
elif lb_stencil.D == 3:
lbbh.set_boundary(noslip, ps.make_slice[:, :wall_thickness, :])
lbbh.set_boundary(noslip, ps.make_slice[:, -wall_thickness:, :])
else:
raise Exception()
for bh in lbbh, :
assert len(bh._boundary_object_to_boundary_info) == 1, "Restart kernel to clear boundaries"
def init():
dh.fill(ρ.name, rho_0)
dh.fill(u.name, np.nan, ghost_layers=True, inner_ghost_layers=True)
dh.fill(u.name, 0)
dh.run_kernel(init_kernel)
# In[6]:
sync_pdfs = dh.synchronization_function([src.name])
# Time loop
def time_loop(steps):
dh.all_to_gpu()
i = -1
last_max_vel = -1
for i in range(steps):
dh.run_kernel(collision_kernel)
sync_pdfs()
lbbh()
dh.run_kernel(stream_kernel)
dh.swap(src.name, dst.name)
# Consider early termination
if i % 100 == 0:
if u.name in dh.gpu_arrays:
dh.to_cpu(u.name)
uu = dh.gather_array(u.name)
# average periodic directions
if lb_stencil.D == 3: # dont' swap order
uu = np.average(uu, axis=2)
uu = np.average(uu, axis=0)
max_vel = np.nanmax(uu)
if np.abs(max_vel / last_max_vel - 1) < 5E-6:
break
last_max_vel = max_vel
# cut off wall regions
uu = uu[wall_thickness:-wall_thickness]
# correct for f/2 term
uu -= np.array([ext_force_density / 2 / rho_0] + [0] * (lb_stencil.D - 1))
return uu
init()
# Simulation
profile = time_loop(5000)
# compare against analytical solution
# The profile is of shape (n,3). Force is in x-direction
y = np.arange(len(profile[:, 0]))
mid = (y[-1] - y[0]) / 2 # Mid point of channel
expected = poiseuille_flow((y - mid), actual_width, ext_force_density, rho_0 * eta)
np.testing.assert_allclose(profile[:, 0], expected, rtol=0.006)
# Test zero vel in other directions
np.testing.assert_allclose(profile[:, 1:], np.zeros_like(profile[:, 1:]), atol=1E-9)
def rod_simulation(stencil_name,
diameter,
parallel=False,
entropic=False,
re=150,
time_to_simulate=17.0,
eval_interval=0.5,
write_vtk=True,
write_numpy=True):
if stencil_name == 'D3Q19_new':
stencil = Stencil.D3Q19
maxwellian_moments = True
elif stencil_name == 'D3Q19_old':
stencil = Stencil.D3Q19
maxwellian_moments = False
elif stencil_name == 'D3Q27':
stencil = Stencil.D3Q27
maxwellian_moments = False
else:
raise ValueError("Unknown stencil name " + stencil_name)
d = diameter
length = 16 * d
u_max_at_throat = 0.07
u_max_at_inflow = 0.07 / (3**2)
# Geometry parameters
inflow_area = int(1.5 * d)
constriction_length = int(1.8904 * d)
throat_length = int(10 / 3 * d)
constriction_diameter = int(d / 3)
u_mean_at_throat = u_max_at_throat / 2
lattice_viscosity = u_mean_at_throat * constriction_diameter / re
omega = relaxation_rate_from_lattice_viscosity(lattice_viscosity)
lbm_config = LBMConfig(stencil=LBStencil(stencil),
compressible=True,
method=Method.SRT,
relaxation_rate=omega,
entropic=entropic,
maxwellian_moments=maxwellian_moments)
kernel_params = {}
print("ω=", omega)
dh = create_data_handling(domain_size=(length, d, d), parallel=parallel)
sc = LatticeBoltzmannStep(data_handling=dh,
kernel_params=kernel_params,
name=stencil_name,
lbm_config=lbm_config)
# ----------------- Boundary Setup --------------------------------
def pipe_geometry(x, *_):
# initialize with full diameter everywhere
result = np.ones_like(x) * d
# constriction
constriction_begin = inflow_area
constriction_end = constriction_begin + constriction_length
c_x = np.linspace(0, 1, constriction_length)
result[constriction_begin:constriction_end] = d * (
1 - c_x) + constriction_diameter * c_x
# throat
throat_start = constriction_end
throat_end = throat_start + throat_length
result[throat_start:throat_end] = constriction_diameter
return result
bh = sc.boundary_handling
add_pipe_inflow_boundary(bh, u_max_at_inflow, make_slice[0, :, :])
outflow = FixedDensity(1.0)
bh.set_boundary(outflow, slice_from_direction('E', 3))
wall = NoSlip()
add_pipe_walls(bh, pipe_geometry, wall)
# ----------------- Run --------------------------------------------
scenario_name = stencil_name
if not os.path.exists(scenario_name):
os.mkdir(scenario_name)
def to_time_steps(non_dimensional_time):
return int(diameter / (u_max_at_inflow / 2) * non_dimensional_time)
time_steps = to_time_steps(time_to_simulate)
eval_interval = to_time_steps(eval_interval)
print("Total number of time steps", time_steps)
for i in range(time_steps // eval_interval):
sc.run(eval_interval)
if write_vtk:
sc.write_vtk()
vel = sc.velocity[:, :, :, :]
max_vel = np.max(vel)
print("Time steps:", sc.time_steps_run, "/", time_steps,
"Max velocity: ", max_vel)
if np.isnan(max_vel):
raise ValueError("Simulation went unstable")
if write_numpy:
np.save(scenario_name + f'/velocity_{sc.time_steps_run}',
sc.velocity_slice().filled(0.0))
def test_simple(target):
if target == Target.GPU:
import pytest
pytest.importorskip('pycuda')
dh = create_data_handling((4, 4), parallel=False, default_target=target)
dh.add_array('pdfs', values_per_cell=9, cpu=True, gpu=target != Target.CPU)
for i in range(9):
dh.fill("pdfs", i, value_idx=i, ghost_layers=True)
if target == Target.GPU:
dh.all_to_gpu()
lbm_config = LBMConfig(stencil=LBStencil(Stencil.D2Q9),
compressible=False,
relaxation_rate=1.8)
config = CreateKernelConfig(target=target)
lb_func = create_lb_function(lbm_config=lbm_config, config=config)
bh = LatticeBoltzmannBoundaryHandling(lb_func.method,
dh,
'pdfs',
target=target)
wall = NoSlip()
moving_wall = UBB((1, 0))
bh.set_boundary(wall, make_slice[0, :])
bh.set_boundary(wall, make_slice[-1, :])
bh.set_boundary(wall, make_slice[:, 0])
bh.set_boundary(moving_wall, make_slice[:, -1])
bh.prepare()
bh()
if target == Target.GPU:
dh.all_to_cpu()
# left lower corner
assert (dh.cpu_arrays['pdfs'][0, 0, 6] == 7)
assert (dh.cpu_arrays['pdfs'][0, 1, 4] == 3)
assert (dh.cpu_arrays['pdfs'][0, 1, 6] == 7)
assert (dh.cpu_arrays['pdfs'][1, 0, 1] == 2)
assert (dh.cpu_arrays['pdfs'][1, 0, 6] == 7)
# left side
assert (all(dh.cpu_arrays['pdfs'][0, 2:4, 4] == 3))
assert (all(dh.cpu_arrays['pdfs'][0, 2:4, 6] == 7))
assert (all(dh.cpu_arrays['pdfs'][0, 2:4, 5] == 5))
# left upper corner
assert (dh.cpu_arrays['pdfs'][0, 4, 4] == 3)
assert (dh.cpu_arrays['pdfs'][0, 4, 8] == 5)
assert (dh.cpu_arrays['pdfs'][0, 5, 8] == 5 + 6 / 36)
assert (dh.cpu_arrays['pdfs'][1, 5, 8] == 5 + 6 / 36)
assert (dh.cpu_arrays['pdfs'][1, 5, 2] == 1)
# top side
assert (all(dh.cpu_arrays['pdfs'][2:4, 5, 2] == 1))
assert (all(dh.cpu_arrays['pdfs'][2:4, 5, 7] == 6 - 6 / 36))
assert (all(dh.cpu_arrays['pdfs'][2:4, 5, 8] == 5 + 6 / 36))
# right upper corner
assert (dh.cpu_arrays['pdfs'][4, 5, 2] == 1)
assert (dh.cpu_arrays['pdfs'][4, 5, 7] == 6 - 6 / 36)
assert (dh.cpu_arrays['pdfs'][5, 5, 7] == 6 - 6 / 36)
assert (dh.cpu_arrays['pdfs'][5, 4, 3] == 4)
assert (dh.cpu_arrays['pdfs'][5, 4, 7] == 6)
# right side
assert (all(dh.cpu_arrays['pdfs'][5, 2:4, 3] == 4))
assert (all(dh.cpu_arrays['pdfs'][5, 2:4, 5] == 8))
assert (all(dh.cpu_arrays['pdfs'][5, 2:4, 7] == 6))
# right lower corner
assert (dh.cpu_arrays['pdfs'][5, 1, 3] == 4)
assert (dh.cpu_arrays['pdfs'][5, 1, 5] == 8)
assert (dh.cpu_arrays['pdfs'][5, 0, 5] == 8)
assert (dh.cpu_arrays['pdfs'][4, 0, 1] == 2)
assert (dh.cpu_arrays['pdfs'][4, 0, 5] == 8)
# lower side
assert (all(dh.cpu_arrays['pdfs'][0, 2:4, 4] == 3))
assert (all(dh.cpu_arrays['pdfs'][0, 2:4, 6] == 7))
assert (all(dh.cpu_arrays['pdfs'][0, 2:4, 8] == 5))
def flow_around_sphere(stencil, galilean_correction, L_LU, total_steps):
if galilean_correction and stencil.Q != 27:
return True
target = Target.GPU
streaming_pattern = 'aa'
timesteps = get_timesteps(streaming_pattern)
u_max = 0.05
Re = 500000
kinematic_viscosity = (L_LU * u_max) / Re
initial_velocity = (u_max, ) + (0, ) * (stencil.D - 1)
omega_v = relaxation_rate_from_lattice_viscosity(kinematic_viscosity)
channel_size = (10 * L_LU, ) + (5 * L_LU, ) * (stencil.D - 1)
sphere_position = (channel_size[0] //
3, ) + (channel_size[1] // 2, ) * (stencil.D - 1)
sphere_radius = L_LU // 2
lbm_config = LBMConfig(stencil=stencil,
method=Method.CUMULANT,
relaxation_rate=omega_v,
galilean_correction=galilean_correction)
lbm_opt = LBMOptimisation(pre_simplification=True)
config = CreateKernelConfig(target=target)
lb_method = create_lb_method(lbm_config=lbm_config)
def get_extrapolation_kernel(timestep):
boundary_assignments = []
indexing = BetweenTimestepsIndexing(
pdf_field,
stencil,
streaming_pattern=streaming_pattern,
prev_timestep=timestep)
f_out, _ = indexing.proxy_fields
for i, d in enumerate(stencil):
if d[0] == -1:
asm = Assignment(f_out.neighbor(0, 1)(i), f_out.center(i))
boundary_assignments.append(asm)
boundary_assignments = indexing.substitute_proxies(
boundary_assignments)
iter_slice = get_slice_before_ghost_layer((1, ) + (0, ) *
(stencil.D - 1))
extrapolation_ast = create_kernel(boundary_assignments,
config=CreateKernelConfig(
iteration_slice=iter_slice,
ghost_layers=1,
target=target))
return extrapolation_ast.compile()
dh = create_data_handling(channel_size,
periodicity=False,
default_layout='fzyx',
default_target=target)
u_field = dh.add_array('u', stencil.D)
rho_field = dh.add_array('rho', 1)
pdf_field = dh.add_array('pdfs', stencil.Q)
dh.fill(u_field.name, 0.0, ghost_layers=True)
dh.fill(rho_field.name, 0.0, ghost_layers=True)
dh.to_gpu(u_field.name)
dh.to_gpu(rho_field.name)
lbm_opt = replace(lbm_opt, symbolic_field=pdf_field)
bh = LatticeBoltzmannBoundaryHandling(lb_method,
dh,
pdf_field.name,
streaming_pattern=streaming_pattern,
target=target)
wall = NoSlip()
inflow = UBB(initial_velocity)
bh.set_boundary(inflow, slice_from_direction('W', stencil.D))
directions = ('N', 'S', 'T', 'B') if stencil.D == 3 else ('N', 'S')
for direction in directions:
bh.set_boundary(wall, slice_from_direction(direction, stencil.D))
outflow_kernels = [
get_extrapolation_kernel(Timestep.EVEN),
get_extrapolation_kernel(Timestep.ODD)
]
def sphere_boundary_callback(x, y, z=None):
x = x - sphere_position[0]
y = y - sphere_position[1]
z = z - sphere_position[2] if z is not None else 0
return np.sqrt(x**2 + y**2 + z**2) <= sphere_radius
bh.set_boundary(wall, mask_callback=sphere_boundary_callback)
init_eqs = pdf_initialization_assignments(
lb_method,
1.0,
initial_velocity,
pdf_field,
streaming_pattern=streaming_pattern,
previous_timestep=timesteps[0])
init_kernel = create_kernel(init_eqs, config=config).compile()
output = {'density': rho_field, 'velocity': u_field}
lbm_config = replace(lbm_config, output=output)
lb_collision_rule = create_lb_collision_rule(lb_method=lb_method,
lbm_config=lbm_config,
lbm_optimisation=lbm_opt)
lb_kernels = []
for t in timesteps:
lbm_config = replace(lbm_config, timestep=t)
lbm_config = replace(lbm_config, streaming_pattern=streaming_pattern)
lb_kernels.append(
create_lb_function(collision_rule=lb_collision_rule,
lbm_config=lbm_config,
lbm_optimisation=lbm_opt,
config=config))
timestep = timesteps[0]
dh.run_kernel(init_kernel)
stability_check_frequency = 1000
for i in range(total_steps):
bh(prev_timestep=timestep)
dh.run_kernel(outflow_kernels[timestep.idx])
timestep = timestep.next()
dh.run_kernel(lb_kernels[timestep.idx])
if i % stability_check_frequency == 0:
dh.to_cpu(u_field.name)
assert np.isfinite(dh.cpu_arrays[u_field.name]).all()