def test_initialize_fneq(Case, dtype_device):
dtype, device = dtype_device
lattice = Lattice(D2Q9, device, dtype)
if Case == TaylorGreenVortex3D:
lattice = Lattice(D3Q27, dtype=dtype, device=device)
flow = Case(resolution=16, reynolds_number=1000, mach_number=0.01, lattice=lattice)
collision = BGKCollision(lattice, tau=flow.units.relaxation_parameter_lu)
streaming = StandardStreaming(lattice)
simulation_neq = Simulation(flow=flow, lattice=lattice, collision=collision, streaming=streaming)
pre_rho = lattice.rho(simulation_neq.f)
pre_u = lattice.u(simulation_neq.f)
simulation_neq.initialize_f_neq()
post_rho = lattice.rho(simulation_neq.f)
post_u = lattice.u(simulation_neq.f)
assert(torch.allclose(pre_rho,post_rho,1e-6))
assert(torch.allclose(pre_u,post_u))
if Case == TaylorGreenVortex2D:
error_reporter_neq = ErrorReporter(lattice, flow, interval=1, out=None)
error_reporter_eq = ErrorReporter(lattice, flow, interval=1, out=None)
simulation_eq = Simulation(flow=flow, lattice=lattice, collision=collision, streaming=streaming)
simulation_neq.reporters.append(error_reporter_neq)
simulation_eq.reporters.append(error_reporter_eq)
simulation_neq.step(10)
simulation_eq.step(10)
error_u, error_p = np.mean(np.abs(error_reporter_neq.out), axis=0).tolist()
error_u_eq, error_p_eq = np.mean(np.abs(error_reporter_eq.out), axis=0).tolist()
assert(error_u < error_u_eq)
def test_energy_spectrum(tmpdir, Flow):
lattice = Lattice(D2Q9, device='cpu')
if Flow == TaylorGreenVortex3D or Flow == 'DecayingTurbulence3D':
lattice = Lattice(D3Q27, device='cpu')
if Flow == 'DecayingTurbulence2D' or Flow == 'DecayingTurbulence3D':
Flow = DecayingTurbulence
flow = Flow(resolution=20,
reynolds_number=1600,
mach_number=0.01,
lattice=lattice)
collision = BGKCollision(lattice, tau=flow.units.relaxation_parameter_lu)
streaming = StandardStreaming(lattice)
simulation = Simulation(flow=flow,
lattice=lattice,
collision=collision,
streaming=streaming)
spectrum = lattice.convert_to_numpy(
EnergySpectrum(lattice, flow)(simulation.f))
energy = IncompressibleKineticEnergy(lattice, flow)(simulation.f).item()
if Flow == DecayingTurbulence:
# check that the reported spectrum agrees with the spectrum used for initialization
ek_ref, _ = flow.energy_spectrum
assert (spectrum == pytest.approx(ek_ref, rel=0.0, abs=0.1))
if Flow == TaylorGreenVortex2D or Flow == TaylorGreenVortex3D:
# check that flow has only one mode
ek_max = sorted(spectrum, reverse=True)
assert ek_max[0] * 1e-5 > ek_max[1]
assert (energy == pytest.approx(np.sum(spectrum), rel=0.1, abs=0.0))
def test_grid_fine_to_coarse_3d():
lattice = Lattice(D3Q27, 'cpu', dtype=torch.double)
flow_f = TaylorGreenVortex3D(40, 1600, 0.15, lattice)
collision_f = BGKCollision(lattice,
tau=flow_f.units.relaxation_parameter_lu)
sim_f = Simulation(flow_f, lattice, collision_f, streaming=None)
flow_c = TaylorGreenVortex3D(20, 1600, 0.15, lattice)
collision_c = BGKCollision(lattice,
tau=flow_c.units.relaxation_parameter_lu)
sim_c = Simulation(flow_c, lattice, collision_c, streaming=None)
f_c = grid_fine_to_coarse(lattice, sim_f.f,
flow_f.units.relaxation_parameter_lu,
flow_c.units.relaxation_parameter_lu)
p_c_init, u_c_init = flow_c.initial_solution(flow_c.grid)
rho_c_init = flow_c.units.convert_pressure_pu_to_density_lu(p_c_init)
u_c_init = flow_c.units.convert_velocity_to_lu(u_c_init)
shear_c_init = lattice.shear_tensor(sim_c.f)
shear_c = lattice.shear_tensor(f_c)
assert np.isclose(lattice.u(f_c).cpu().numpy(), u_c_init).all()
assert np.isclose(lattice.rho(f_c).cpu().numpy(), rho_c_init).all()
assert torch.isclose(f_c, sim_c.f).all()
assert torch.isclose(shear_c_init, shear_c).all()
def test_torch_gradient_3d(order):
lattice = Lattice(
D3Q27,
device='cpu',
)
flow = TaylorGreenVortex3D(resolution=100,
reynolds_number=1,
mach_number=0.05,
lattice=lattice)
grid = flow.grid
p, u = flow.initial_solution(grid)
dx = flow.units.convert_length_to_pu(1.0)
u0_grad = torch_gradient(lattice.convert_to_tensor(u[0]),
dx=dx,
order=order).numpy()
u0_grad_np = np.array(np.gradient(u[0], dx))
u0_grad_analytic = np.array([
np.cos(grid[0]) * np.cos(grid[1]) * np.cos(grid[2]),
np.sin(grid[0]) * np.sin(grid[1]) * (-np.cos(grid[2])),
np.sin(grid[0]) * (-np.cos(grid[1])) * np.sin(grid[2])
])
assert np.allclose(u0_grad_analytic, u0_grad, rtol=0.0, atol=1e-3)
assert np.allclose(u0_grad_np[:, 2:-2, 2:-2, 2:-2],
u0_grad[:, 2:-2, 2:-2, 2:-2],
rtol=0.0,
atol=1e-3)
def test_HDF5Reporter(tmpdir):
lattice = Lattice(D2Q9, "cpu")
flow = TaylorGreenVortex2D(resolution=16,
reynolds_number=10,
mach_number=0.05,
lattice=lattice)
collision = BGKCollision(lattice=lattice,
tau=flow.units.relaxation_parameter_lu)
streaming = StandardStreaming(lattice=lattice)
simulation = Simulation(flow=flow,
lattice=lattice,
collision=collision,
streaming=streaming)
hdf5_reporter = HDF5Reporter(flow=flow,
collision=collision,
interval=1,
filebase=tmpdir / "output")
simulation.reporters.append(hdf5_reporter)
simulation.step(3)
assert os.path.isfile(tmpdir / "output.h5")
dataset_train = LettuceDataset(filebase=tmpdir / "output.h5", target=True)
train_loader = torch.utils.data.DataLoader(dataset_train, shuffle=False)
print(dataset_train)
for (f, target, idx) in train_loader:
assert idx in (0, 1, 2)
assert f.shape == (1, 9, 16, 16)
assert target.shape == (1, 9, 16, 16)
def test_obstacle(stencil, dtype_device):
dtype, device = dtype_device
lattice = Lattice(stencil, dtype=dtype, device=device)
if stencil is D2Q9:
mask = np.zeros([20, 10])
mask[3:6, 3:6] = 1
flow = Obstacle2D(20, 10, 100, 0.1, lattice=lattice, char_length_lu=3)
if stencil is D3Q27:
mask = np.zeros([20, 10, 5])
mask[3:6, 3:6, :] = 1
flow = Obstacle3D(20,
10,
5,
100,
0.1,
lattice=lattice,
char_length_lu=3)
collision = BGKCollision(lattice, tau=flow.units.relaxation_parameter_lu)
flow.mask = mask != 0
streaming = StandardStreaming(lattice)
simulation = Simulation(flow=flow,
lattice=lattice,
collision=collision,
streaming=streaming)
simulation.step(2)
def test_divergence(stencil, dtype_device):
dtype, device = dtype_device
lattice = Lattice(stencil, dtype=dtype, device=device)
flow = DecayingTurbulence(50, 1, 0.05, lattice=lattice, ic_energy=0.5)
collision = BGKCollision(lattice, tau=flow.units.relaxation_parameter_lu)
streaming = StandardStreaming(lattice)
simulation = Simulation(flow=flow,
lattice=lattice,
collision=collision,
streaming=streaming)
ekin = flow.units.convert_incompressible_energy_to_pu(
torch.sum(lattice.incompressible_energy(
simulation.f))) * flow.units.convert_length_to_pu(1.0)**lattice.D
u0 = flow.units.convert_velocity_to_pu(lattice.u(simulation.f)[0])
u1 = flow.units.convert_velocity_to_pu(lattice.u(simulation.f)[1])
dx = flow.units.convert_length_to_pu(1.0)
grad_u0 = torch_gradient(u0, dx=dx, order=6).cpu().numpy()
grad_u1 = torch_gradient(u1, dx=dx, order=6).cpu().numpy()
divergence = np.sum(grad_u0[0] + grad_u1[1])
if lattice.D == 3:
u2 = flow.units.convert_velocity_to_pu(lattice.u(simulation.f)[2])
grad_u2 = torch_gradient(u2, dx=dx, order=6).cpu().numpy()
divergence += np.sum(grad_u2[2])
assert (flow.ic_energy == pytest.approx(lattice.convert_to_numpy(ekin),
rel=1))
assert (0 == pytest.approx(divergence, abs=2e-3))
def test_initialization(dtype_device, use_jacobi):
dtype, device = dtype_device
lattice = Lattice(D2Q9, device, dtype)
flow = TaylorGreenVortex2D(resolution=24,
reynolds_number=10,
mach_number=0.05,
lattice=lattice)
collision = BGKCollision(lattice, tau=flow.units.relaxation_parameter_lu)
streaming = StandardStreaming(lattice)
simulation = Simulation(flow=flow,
lattice=lattice,
collision=collision,
streaming=streaming)
# set initial pressure to 0 everywhere
p, u = flow.initial_solution(flow.grid)
u0 = lattice.convert_to_tensor(flow.units.convert_velocity_to_lu(u))
rho0 = lattice.convert_to_tensor(np.ones_like(u0[0, ...].cpu()))
simulation.f = lattice.equilibrium(rho0, u0)
if use_jacobi:
simulation.initialize_pressure(1000, 1e-6)
num_iterations = 0
else:
num_iterations = simulation.initialize(500, 1e-3)
piter = lattice.convert_to_numpy(
flow.units.convert_density_lu_to_pressure_pu(lattice.rho(
simulation.f)))
# assert that pressure is converged up to 0.05 (max p
assert piter == pytest.approx(p, rel=0.0, abs=5e-2)
assert num_iterations < 500
def test_force_guo(ForceType, device):
dtype = torch.double
lattice = Lattice(D2Q9, dtype=dtype, device=device)
flow = PoiseuilleFlow2D(resolution=10,
reynolds_number=1,
mach_number=0.02,
lattice=lattice,
initialize_with_zeros=True)
force = ForceType(lattice,
tau=flow.units.relaxation_parameter_lu,
acceleration=flow.units.convert_acceleration_to_lu(
flow.acceleration))
collision = BGKCollision(lattice,
tau=flow.units.relaxation_parameter_lu,
force=force)
streaming = StandardStreaming(lattice)
simulation = Simulation(flow=flow,
lattice=lattice,
collision=collision,
streaming=streaming)
simulation.step(500)
# compare with reference solution
u_sim = flow.units.convert_velocity_to_pu(
lattice.convert_to_numpy(lattice.u(simulation.f)))
_, u_ref = flow.analytic_solution(flow.grid)
fluidnodes = np.where(np.logical_not(flow.boundaries[0].mask.cpu()))
assert u_ref[0].max() == pytest.approx(u_sim[0].max(), rel=0.005)
assert u_ref[0][fluidnodes] == pytest.approx(u_sim[0][fluidnodes],
rel=None,
abs=0.005 * u_ref[0].max())
def test_readme():
"""Whenever you have to change this test, the example in README.rst has to change, too.
Note differences in the device + number of steps.
"""
import torch
from lettuce import BGKCollision, StandardStreaming, Lattice, D2Q9, TaylorGreenVortex2D, Simulation
device = "cpu"
dtype = torch.float32
lattice = Lattice(D2Q9, device, dtype)
flow = TaylorGreenVortex2D(resolution=256,
reynolds_number=10,
mach_number=0.05,
lattice=lattice)
collision = BGKCollision(lattice, tau=flow.units.relaxation_parameter_lu)
streaming = StandardStreaming(lattice)
simulation = Simulation(flow=flow,
lattice=lattice,
collision=collision,
streaming=streaming)
mlups = simulation.step(num_steps=1)
print("Performance in MLUPS:", mlups)
def test_flow_3d(IncompressibleFlow, dtype_device):
dtype, device = dtype_device
lattice = Lattice(D3Q27, dtype=dtype, device=device)
flow = IncompressibleFlow(16, 1, 0.05, lattice=lattice)
collision = BGKCollision(lattice, tau=flow.units.relaxation_parameter_lu)
streaming = StandardStreaming(lattice)
simulation = Simulation(flow=flow, lattice=lattice, collision=collision, streaming=streaming)
simulation.step(1)
def test_generic_reporters(Reporter, Case, dtype_device):
dtype, device = dtype_device
lattice = Lattice(D2Q9, dtype=dtype, device=device)
flow = Case(64, 10000, 0.05, lattice=lattice)
if Case == TaylorGreenVortex3D:
lattice = Lattice(D3Q27, dtype=dtype, device=device)
collision = BGKCollision(lattice, tau=flow.units.relaxation_parameter_lu)
streaming = StandardStreaming(lattice)
simulation = Simulation(flow=flow,
lattice=lattice,
collision=collision,
streaming=streaming)
kinE_reporter = Reporter(lattice, flow, interval=1, out=None)
simulation.reporters.append(kinE_reporter)
simulation.step(2)
assert (np.asarray(kinE_reporter.out)[1, 1] == pytest.approx(np.asarray(
kinE_reporter.out)[0, 1],
rel=0.05))
def test_write_vtk(tmpdir):
lattice = Lattice(D2Q9, "cpu")
flow = TaylorGreenVortex2D(resolution=16,
reynolds_number=10,
mach_number=0.05,
lattice=lattice)
p, u = flow.initial_solution(flow.grid)
point_dict = {"p": p[0, ..., None]}
write_vtk(point_dict, id=1, filename_base=tmpdir / "output")
assert os.path.isfile(tmpdir / "output_00000001.vtr")
def test_masks(dtype_device):
"""test if masks are applied from boundary conditions"""
dtype, device = dtype_device
lattice = Lattice(D2Q9, dtype=dtype, device=device)
flow = Obstacle((10, 5), 100, 0.1, lattice, 2)
flow.mask[1, 1] = 1
streaming = StandardStreaming(lattice)
simulation = Simulation(flow, lattice, None, streaming)
assert simulation.streaming.no_stream_mask.any()
assert simulation.no_collision_mask.any()
def test_write_image(tmpdir):
pytest.skip("matplotlib not working")
lattice = Lattice(D2Q9, "cpu")
flow = TaylorGreenVortex2D(resolution=16,
reynolds_number=10,
mach_number=0.05,
lattice=lattice)
p, u = flow.initial_solution(flow.grid)
write_image(tmpdir / "p.png", p[0])
print(tmpdir / "p.png")
assert os.path.isfile(tmpdir / "p.png")
def test_save_and_load(dtype_device, tmpdir):
dtype, device = dtype_device
lattice = Lattice(D2Q9, device, dtype)
flow = TaylorGreenVortex2D(resolution=16, reynolds_number=10, mach_number=0.05, lattice=lattice)
collision = BGKCollision(lattice, tau=flow.units.relaxation_parameter_lu)
streaming = StandardStreaming(lattice)
simulation = Simulation(flow=flow, lattice=lattice, collision=collision, streaming=streaming)
simulation.step(10)
simulation.save_checkpoint(tmpdir / "checkpoint.pic")
simulation2 = Simulation(flow=flow, lattice=lattice, collision=collision, streaming=streaming)
simulation2.load_checkpoint(tmpdir / "checkpoint.pic")
assert lattice.convert_to_numpy(simulation2.f) == pytest.approx(lattice.convert_to_numpy(simulation.f))
def test_pressure_poisson(dtype_device, Stencil):
dtype, device = dtype_device
lattice = Lattice(Stencil(), device, dtype)
flow_class = TaylorGreenVortex2D if Stencil is D2Q9 else TaylorGreenVortex3D
flow = flow_class(resolution=32, reynolds_number=100, mach_number=0.05, lattice=lattice)
p0, u = flow.initial_solution(flow.grid)
u = flow.units.convert_velocity_to_lu(lattice.convert_to_tensor(u))
rho0 = flow.units.convert_pressure_pu_to_density_lu(lattice.convert_to_tensor(p0))
rho = pressure_poisson(flow.units, u, torch.ones_like(rho0))
pfinal = flow.units.convert_density_lu_to_pressure_pu(rho).cpu().numpy()
print(p0.max(), p0.min(), p0.mean(), pfinal.max(), pfinal.min(), pfinal.mean())
print((p0 - pfinal).max(), (p0 - pfinal).min())
assert p0 == pytest.approx(pfinal, rel=0.0, abs=0.05)
def test_torch_gradient_2d(order):
lattice = Lattice(D2Q9, device='cpu', )
flow = TaylorGreenVortex2D(resolution=100, reynolds_number=1, mach_number=0.05, lattice=lattice)
grid = flow.grid
p, u = flow.initial_solution(grid)
dx = flow.units.convert_length_to_pu(1.0)
u0_grad = torch_gradient(lattice.convert_to_tensor(u[0]), dx=dx, order=order).numpy()
u0_grad_np = np.array(np.gradient(u[0], dx))
u0_grad_analytic = np.array([
-np.sin(grid[0]) * np.sin(grid[1]),
np.cos(grid[0]) * np.cos(grid[1]),
])
assert (u0_grad_analytic == pytest.approx(u0_grad, rel=0.0, abs=1e-3))
assert (u0_grad_np[:, 2:-2, 2:-2] == pytest.approx(u0_grad[:, 2:-2, 2:-2], rel=0.0, abs=1e-3))
def test_generic_reporters(Observable, Case, dtype_device):
dtype, device = dtype_device
lattice = Lattice(D2Q9, dtype=dtype, device=device)
flow = Case(32, 10000, 0.05, lattice=lattice)
if Case == TaylorGreenVortex3D:
lattice = Lattice(D3Q27, dtype=dtype, device=device)
collision = BGKCollision(lattice, tau=flow.units.relaxation_parameter_lu)
streaming = StandardStreaming(lattice)
simulation = Simulation(flow=flow,
lattice=lattice,
collision=collision,
streaming=streaming)
reporter = ObservableReporter(Observable(lattice, flow),
interval=1,
out=None)
simulation.reporters.append(reporter)
simulation.step(2)
values = np.asarray(reporter.out)
if Observable is EnergySpectrum:
assert values[1, 2:] == pytest.approx(values[0, 2:],
rel=0.0,
abs=values[0, 2:].sum() / 10)
else:
assert values[1, 2] == pytest.approx(values[0, 2], rel=0.05)
def convergence(ctx, init_f_neq):
"""Use Taylor Green 2D for convergence test in diffusive scaling."""
device, dtype = ctx.obj['device'], ctx.obj['dtype']
lattice = Lattice(D2Q9, device, dtype)
error_u_old = None
error_p_old = None
print(("{:>15} " * 5).format("resolution", "error (u)", "order (u)",
"error (p)", "order (p)"))
for i in range(4, 9):
resolution = 2**i
mach_number = 8 / resolution
# Simulation
flow = TaylorGreenVortex2D(resolution=resolution,
reynolds_number=10000,
mach_number=mach_number,
lattice=lattice)
collision = BGKCollision(lattice,
tau=flow.units.relaxation_parameter_lu)
streaming = StandardStreaming(lattice)
simulation = Simulation(flow=flow,
lattice=lattice,
collision=collision,
streaming=streaming)
if (init_f_neq):
simulation.initialize_f_neq()
error_reporter = ErrorReporter(lattice, flow, interval=1, out=None)
simulation.reporters.append(error_reporter)
for _ in range(10 * resolution):
simulation.step(1)
error_u, error_p = np.mean(np.abs(error_reporter.out), axis=0).tolist()
factor_u = 0 if error_u_old is None else error_u_old / error_u
factor_p = 0 if error_p_old is None else error_p_old / error_p
error_u_old = error_u
error_p_old = error_p
print("{:15} {:15.2e} {:15.1f} {:15.2e} {:15.1f}".format(
resolution, error_u, factor_u / 2, error_p, factor_p / 2))
if factor_u / 2 < 1.9:
print("Velocity convergence order < 2.")
if factor_p / 2 < 0.9:
print("Velocity convergence order < 1.")
if factor_u / 2 < 1.9 or factor_p / 2 < 0.9:
sys.exit(1)
else:
return 0
def benchmark(ctx, steps, resolution, profile_out, flow, vtk_out):
"""Run a short simulation and print performance in MLUPS.
"""
# start profiling
if profile_out:
profile = cProfile.Profile()
profile.enable()
# setup and run simulation
device, dtype = ctx.obj['device'], ctx.obj['dtype']
flow_class, stencil = flow_by_name[flow]
lattice = Lattice(stencil, device, dtype)
flow = flow_class(resolution=resolution,
reynolds_number=1,
mach_number=0.05,
lattice=lattice)
force = Guo(lattice,
tau=flow.units.relaxation_parameter_lu,
acceleration=flow.units.convert_acceleration_to_lu(
flow.force)) if hasattr(flow, "acceleration") else None
collision = BGKCollision(lattice,
tau=flow.units.relaxation_parameter_lu,
force=force)
streaming = StandardStreaming(lattice)
simulation = Simulation(flow=flow,
lattice=lattice,
collision=collision,
streaming=streaming)
if vtk_out:
simulation.reporters.append(VTKReporter(lattice, flow, interval=10))
mlups = simulation.step(num_steps=steps)
# write profiling output
if profile_out:
profile.disable()
stats = pstats.Stats(profile)
stats.sort_stats('cumulative')
stats.print_stats()
profile.dump_stats(profile_out)
click.echo(f"Saved profiling information to {profile_out}.")
click.echo("Finished {} steps in {} bit precision. MLUPS: {:10.2f}".format(
steps,
str(dtype).replace("torch.float", ""), mlups))
return 0
def test_vtk_reporter_no_mask(tmpdir):
lattice = Lattice(D2Q9, "cpu")
flow = TaylorGreenVortex2D(resolution=16,
reynolds_number=10,
mach_number=0.05,
lattice=lattice)
collision = BGKCollision(lattice, tau=flow.units.relaxation_parameter_lu)
streaming = StandardStreaming(lattice)
simulation = Simulation(flow=flow,
lattice=lattice,
collision=collision,
streaming=streaming)
vtk_reporter = VTKReporter(lattice,
flow,
interval=1,
filename_base=tmpdir / "output")
simulation.reporters.append(vtk_reporter)
simulation.step(2)
assert os.path.isfile(tmpdir / "output_00000000.vtr")
assert os.path.isfile(tmpdir / "output_00000001.vtr")
def test_equilibrium_pressure_outlet(dtype_device):
dtype, device = dtype_device
lattice = Lattice(D2Q9, dtype=dtype, device=device)
class MyObstacle(Obstacle2D):
@property
def boundaries(self, *args):
x, y = self.grid
return [
EquilibriumBoundaryPU(
np.abs(x) < 1e-6, self.units.lattice, self.units,
np.array([self.units.characteristic_velocity_pu, 0])),
EquilibriumOutletP(self.units.lattice, [0, -1]),
EquilibriumOutletP(self.units.lattice, [0, 1]),
EquilibriumOutletP(self.units.lattice, [1, 0]),
BounceBackBoundary(self.mask, self.units.lattice)
]
flow = MyObstacle(30,
30,
reynolds_number=10,
mach_number=0.1,
lattice=lattice,
char_length_lu=10)
mask = np.zeros_like(flow.grid[0], dtype=np.bool)
mask[10:20, 10:20] = 1
flow.mask = mask
simulation = Simulation(
flow, lattice,
RegularizedCollision(lattice, flow.units.relaxation_parameter_lu),
StandardStreaming(lattice))
simulation.step(20)
rho = lattice.rho(simulation.f)
u = lattice.u(simulation.f)
feq = lattice.equilibrium(torch.ones_like(rho), u)
p = flow.units.convert_density_lu_to_pressure_pu(rho)
zeros = torch.zeros_like(p[0, -1, :])
assert torch.allclose(zeros, p[:, -1, :], rtol=0, atol=1e-4)
assert torch.allclose(zeros, p[:, :, 0], rtol=0, atol=1e-4)
assert torch.allclose(zeros, p[:, :, -1], rtol=0, atol=1e-4)
assert torch.allclose(feq[:, -1, 1:-1], feq[:, -2, 1:-1])
def test_torch_gradient_2d(order):
lattice = Lattice(
D2Q9,
device='cpu',
)
flow = TaylorGreenVortex2D(resolution=100,
reynolds_number=1,
mach_number=0.05,
lattice=lattice)
grid = flow.grid
p, u = flow.initial_solution(grid)
dx = grid[0][0][1] - grid[0][0][0]
u0_grad = torch_gradient(lattice.convert_to_tensor(u[0]),
dx=dx,
order=order).numpy()
u0_grad_analytic = np.array([
-np.sin(grid[0]) * np.sin(grid[1]),
np.cos(grid[0]) * np.cos(grid[1]),
])
assert (u0_grad_analytic[0, 1, :] == pytest.approx(u0_grad[0, 1, :],
rel=2))
def grid(self):
grid = [
np.linspace(0, 2 * np.pi, num=self.resolution, endpoint=False)
for _ in range(self.units.lattice.D)
]
return np.meshgrid(*grid)
@property
def boundaries(self):
return []
print('Generates reference data on fine grid')
torch.cuda.empty_cache()
lattice = Lattice(D2Q9, device=device, dtype=torch.double)
flow_fine = flowclass(
resolution=2 * resolution,
reynolds_number=reynolds,
mach_number=mach,
lattice=lattice,
)
tau_fine = flow_fine.units.relaxation_parameter_lu
flow_coarse = flowclass(
resolution=resolution,
reynolds_number=reynolds,
mach_number=mach,
lattice=lattice,
)
collision = BGKCollision(lattice, tau=tau_fine)
def lattice(request, dtype_device):
"""Run a test for all lattices (all stencils, devices and data types available on the device.)"""
dtype, device = dtype_device
return Lattice(request.param, device=device, dtype=dtype)