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_grid_fine_to_coarse_2d():
lattice = Lattice(D2Q9, 'cpu', dtype=torch.double)
# streaming = StandardStreaming(lattice)
flow_f = TaylorGreenVortex2D(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 = TaylorGreenVortex2D(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_init, u_init = flow_c.initial_solution(flow_c.grid)
rho_init = lattice.convert_to_tensor(
flow_c.units.convert_pressure_pu_to_density_lu(p_init))
u_init = lattice.convert_to_tensor(
flow_c.units.convert_velocity_to_lu(u_init))
shear_c_init = lattice.shear_tensor(sim_c.f)
shear_c = lattice.shear_tensor(f_c)
assert torch.isclose(lattice.u(f_c), u_init).all()
assert torch.isclose(lattice.rho(f_c), rho_init).all()
assert torch.isclose(f_c, sim_c.f).all()
assert torch.isclose(shear_c_init, shear_c).all()
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_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_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_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))