def acoustic_scaling(self, dt):
"""Computes relaxation rate and lattice velocity from time step length.
Args:
dt: time step length
Returns:
relaxation_rate, lattice_velocity
"""
lattice_velocity = dt / self.dx * self.physical_velocity
lattice_viscosity = self.kinematic_viscosity * dt / (self.dx ** 2)
relaxation_rate = relaxation_rate_from_lattice_viscosity(lattice_viscosity)
ResultType = namedtuple("AcousticScalingResult", ['relaxation_rate', 'lattice_velocity'])
return ResultType(relaxation_rate, lattice_velocity)
def schaefer_turek_2d(cells_per_diameter,
u_max=0.3,
max_lattice_velocity=0.05,
**kwargs):
"""Creates a 2D Schaefer Turek Benchmark.
Args:
cells_per_diameter: how many lattice cells are used to resolve the obstacle diameter
u_max: called U_m in the paper: the maximum inflow velocity in physical units, for the first setup
it is 0.3, for the second setup 1.5
max_lattice_velocity: maximum lattice velocity, the lower the more accurate is the simulation
should not be larger than 0.1, if chosen too small the relaxation rate gets near 2 and
simulation might also get unstable
kwargs: parameters forwarded to the lattice boltzmann method
Returns:
scenario object
"""
dx = 0.1 / cells_per_diameter
viscosity = 1e-3
dt = compute_delta_t(max_lattice_velocity, u_max, dx)
lattice_viscosity = viscosity / dx / dx * dt
omega = relaxation_rate_from_lattice_viscosity(lattice_viscosity)
domain_size, geometry_callback, parameter_info = geometry_2d(dx)
cylinder_diameter_l = parameter_info['cylinder_diameter_l']
u_bar_l = 2 / 3 * max_lattice_velocity
re_lattice = u_bar_l * cylinder_diameter_l / lattice_viscosity
print(
"Schaefer-Turek 2D: U_m = %.2f m/s cells=%s, dx=%f, dt=%f, omega=%f, Re=%.1f"
% (u_max, domain_size, dx, dt, omega, re_lattice))
initial_velocity = get_pipe_velocity_field(domain_size,
max_lattice_velocity)
scenario = create_channel(domain_size=domain_size,
u_max=max_lattice_velocity,
relaxation_rate=omega,
initial_velocity=initial_velocity,
**kwargs)
scenario.boundary_handling.set_boundary(NoSlip('obstacle'),
mask_callback=geometry_callback)
parameter_info['u_bar_l'] = u_bar_l
parameter_info['dt'] = dt
scenario.parameterInfo = parameter_info
return scenario
def fixed_lattice_velocity_scaling(self, lattice_velocity=0.1):
"""Computes relaxation rate and time step length from lattice velocity.
Check the returned relaxation rate! If it is very close to 2, the simulation might get unstable.
In that case increase the resolution (more cells_per_length)
All physical quantities have to be passed in the same set of units.
Args:
lattice_velocity: Lattice velocity corresponding to physical_velocity.
Maximum velocity should not be larger than 0.1 i.e. the fluid should not move
faster than 0.1 cells per time step
Returns:
relaxation_rate, dt
"""
dt = lattice_velocity / self.physical_velocity * self.dx
lattice_viscosity = self.kinematic_viscosity * dt / (self.dx ** 2)
relaxation_rate = relaxation_rate_from_lattice_viscosity(lattice_viscosity)
ResultType = namedtuple("FixedLatticeVelocityScalingResult", ['relaxation_rate', 'dt'])
return ResultType(relaxation_rate, dt)
def relaxation_rate_from_reynolds_number(re, u_0, domain_size):
nu = u_0 * domain_size / re
return relaxation_rate_from_lattice_viscosity(nu)
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 _update_omega_from_viscosity_and_dt_dx(self):
if self.dx.value == 0:
return
lattice_viscosity = self.kinematic_viscosity.value * 1e-6 * self.dt.value / (self.dx.value ** 2)
self.omega.value = relaxation_rate_from_lattice_viscosity(lattice_viscosity)
def run(l, l_0, u_0, v_0, nu, y_size, periodicity_in_kernel, **kwargs):
inv_result = {
'viscosity_error': np.nan,
'phase_error': np.nan,
'mlups': np.nan,
}
if 'initial_velocity' in kwargs:
del kwargs['initial_velocity']
print("Running size l=%d nu=%f " % (l, nu), kwargs)
initial_vel_arr = get_initial_velocity_field(l, l_0, u_0, v_0, y_size)
omega = relaxation_rate_from_lattice_viscosity(nu)
kwargs['relaxation_rates'] = [
sp.sympify(r) for r in kwargs['relaxation_rates']
]
if 'entropic' not in kwargs or not kwargs['entropic']:
kwargs['relaxation_rates'] = [
r.subs(sp.Symbol("omega"), omega)
for r in kwargs['relaxation_rates']
]
scenario = create_fully_periodic_flow(
initial_vel_arr, periodicity_in_kernel=periodicity_in_kernel, **kwargs)
if 'entropic' in kwargs and kwargs['entropic']:
scenario.kernelParams['omega'] = kwargs['relaxation_rates'][0].subs(
sp.Symbol("omega"), omega)
total_time_steps = 20000 * (l // l_0)**2
initial_time_steps = 11000 * (l // l_0)**2
eval_interval = 1000 * (l // l_0)**2
scenario.run(initial_time_steps)
if np.isnan(scenario.velocity_slice()).any():
return inv_result
magnitudes = []
phases = []
mlups = []
while scenario.time_steps_run < total_time_steps:
mlup_current_run = scenario.benchmark_run(eval_interval)
if np.isnan(scenario.velocity_slice()).any():
return inv_result
magnitude, phase = get_amplitude_and_phase(
scenario.velocity[:, y_size // 2, :, 1])
magnitudes.append(magnitude)
phases.append(abs(phase))
mlups.append(mlup_current_run)
assert scenario.time_steps_run == total_time_steps
estimated_viscosity = get_viscosity(magnitudes, eval_interval, l)
viscosity_error = abs(estimated_viscosity -
nu) / nu # called ER_\nu in the paper
result = {
'viscosity_error': viscosity_error,
'phaseError': get_phase_error(phases, eval_interval),
'mlups': max(mlups),
}
print(" Result", result)
return result
def test_shear_flow(target, stencil_name):
# Cuda
if target == ps.Target.GPU:
pytest.importorskip("pycuda")
# LB parameters
stencil = LBStencil(stencil_name)
if stencil.D == 2:
L = (4, width)
elif stencil.D == 3:
L = (4, width, 4)
else:
raise Exception()
periodicity = [True, False] + [True] * (stencil.D - 2)
omega = 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=stencil.Q)
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=stencil.D)
p = dh.add_array('p', values_per_cell=stencil.D**2)
# LB Setup
lbm_config = LBMConfig(stencil=stencil, relaxation_rate=omega, method=Method.TRT,
compressible=True, 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)
# Second moment test setup
cqc = collision.method.conserved_quantity_computation
getter_eqs = cqc.output_equations_from_pdfs(src.center_vector,
{'moment2': p})
kernel_compute_p = ps.create_kernel(getter_eqs, config=config).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()
vel_vec = sp.Matrix([0.5 * shear_velocity] + [0] * (stencil.D - 1))
if stencil.D == 2:
lbbh.set_boundary(UBB(velocity=vel_vec), ps.make_slice[:, :wall_thickness])
lbbh.set_boundary(UBB(velocity=-vel_vec), ps.make_slice[:, -wall_thickness:])
elif stencil.D == 3:
lbbh.set_boundary(UBB(velocity=vel_vec), ps.make_slice[:, :wall_thickness, :])
lbbh.set_boundary(UBB(velocity=-vel_vec), ps.make_slice[:, -wall_thickness:, :])
else:
raise Exception()
for bh in lbbh, :
assert len(bh._boundary_object_to_boundary_info) == 2, "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)
sync_pdfs = dh.synchronization_function([src.name])
# Time loop
def time_loop(steps):
dh.all_to_gpu()
for i in range(steps):
dh.run_kernel(collision_kernel)
sync_pdfs()
lbbh()
dh.run_kernel(stream_kernel)
dh.run_kernel(kernel_compute_p)
dh.swap(src.name, dst.name)
if u.name in dh.gpu_arrays:
dh.to_cpu(u.name)
uu = dh.gather_array(u.name)
# average periodic directions
if stencil.D == 3: # dont' swap order
uu = np.average(uu, axis=2)
uu = np.average(uu, axis=0)
if p.name in dh.gpu_arrays:
dh.to_cpu(p.name)
pp = dh.gather_array(p.name)
# average periodic directions
if stencil.D == 3: # dont' swap order
pp = np.average(pp, axis=2)
pp = np.average(pp, axis=0)
# cut off wall regions
uu = uu[wall_thickness:-wall_thickness]
pp = pp[wall_thickness:-wall_thickness]
if stencil.D == 2:
pp = pp.reshape((len(pp), 2, 2))
if stencil.D == 3:
pp = pp.reshape((len(pp), 3, 3))
return uu, pp
init()
# Simulation
profile, pressure_profile = time_loop(t_max)
expected = shear_flow(x=(np.arange(0, actual_width) + .5),
t=t_max,
nu=eta / rho_0,
v=shear_velocity,
h=actual_width,
k_max=100)
if stencil.D == 2:
shear_direction = np.array((1, 0), dtype=float)
shear_plane_normal = np.array((0, 1), dtype=float)
if stencil.D == 3:
shear_direction = np.array((1, 0, 0), dtype=float)
shear_plane_normal = np.array((0, 1, 0), dtype=float)
shear_rate = shear_velocity / actual_width
dynamic_viscosity = eta * rho_0
correction_factor = eta / (eta - 1. / 6.)
p_expected = rho_0 * np.identity(dh.dim) / 3.0 + dynamic_viscosity * shear_rate / correction_factor * (
np.outer(shear_plane_normal, shear_direction) + np.transpose(np.outer(shear_plane_normal, shear_direction)))
# Sustract the tensorproduct of the velosity to get the pressure
pressure_profile[:, 0, 0] -= rho_0 * profile[:, 0]**2
np.testing.assert_allclose(profile[:, 0], expected[1:-1], atol=1E-9)
for i in range(actual_width - 2):
np.testing.assert_allclose(pressure_profile[i], p_expected, atol=1E-9, rtol=1E-3)
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()