def scaling_test(folder_name: str,
lattice_grid_shape: Tuple[int, int] = (420, 180),
plate_size: int = 40,
inlet_density: float = 1.0,
inlet_velocity: float = 0.1,
kinematic_viscosity: float = 0.04,
time_steps: int = 20000):
"""
Executes the scaling test. Measures the time for simulation and saves results.
Args:
folder_name: folder where to save results
lattice_grid_shape: lattice size
plate_size: size of plate
inlet_density: density into the domain
inlet_velocity: velocity into the domain
kinematic_viscosity: kinematic viscosity
time_steps: number of time steps for simulation
"""
# setup
lx, ly = lattice_grid_shape
omega = np.reciprocal(3 * kinematic_viscosity + 0.5)
size = MPI.COMM_WORLD.Get_size()
rank = MPI.COMM_WORLD.Get_rank()
comm = MPI.COMM_WORLD
x_size, y_size = get_xy_size(size)
cartesian2d = comm.Create_cart(dims=[x_size, y_size],
periods=[True, True],
reorder=False)
coords2d = cartesian2d.Get_coords(rank)
n_local_x, n_local_y = get_local_coords(coords2d, lx, ly, x_size, y_size)
density, velocity = density_1_velocity_x_u0_velocity_y_0_initial(
(n_local_x + 2, n_local_y + 2), inlet_velocity)
f = equilibrium_distr_func(density, velocity)
bound_func = parallel_von_karman_boundary_conditions(
coords2d, n_local_x, n_local_y, lx, ly, x_size, y_size, inlet_density,
inlet_velocity, plate_size)
communication_func = communication(cartesian2d)
# main loop
if rank == 0:
start = time.time_ns()
for i in range(time_steps):
f, density, velocity = lattice_boltzmann_step(f, density, velocity,
omega, bound_func,
communication_func)
if rank == 0:
end = time.time_ns()
runtime_ns = end - start
runtime = runtime_ns / 10e9
mlups = lx * ly * time_steps / runtime
np.save(
r'./figures/von_karman_vortex_shedding/' + folder_name + '/' +
str(int(lx)) + '_' + str(int(ly)) + '_' + str(int(size)) + '.npy',
np.array([mlups]))
def plot_evolution_of_density(lattice_grid_shape: Tuple[int, int] = (50, 50),
initial_p0: float = 0.5,
epsilon: float = 0.08,
omega: float = 1.0,
time_steps: int = 2500,
number_of_visualizations: int = 20):
"""
Executes the experiment for shear wave decay given a sinusoidal density and saves the results.
Args:
lattice_grid_shape: lattice size
initial_p0: shift of density
epsilon: amplitude of sine wave
omega: relaxation parameter
time_steps: number of time steps for simulation
number_of_visualizations: total number of visualization. Has to be divisible by 5.
"""
assert 0 < omega < 2
assert time_steps > 0
assert number_of_visualizations % 5 == 0
density, velocity = sinusoidal_density_x(lattice_grid_shape, initial_p0,
epsilon)
f = equilibrium_distr_func(density, velocity)
fig, ax = plt.subplots(int(number_of_visualizations / 5),
5,
sharex=True,
sharey=True)
ax[0, 0].plot(np.arange(0, lattice_grid_shape[0]),
density[:, int(lattice_grid_shape[0] / 2)])
ax[0, 0].set_title('initial')
row_index, col_index = 0, 1
for i in trange(time_steps):
f, density, velocity = lattice_boltzmann_step(f, density, velocity,
omega)
if (i + 1) % int(time_steps / number_of_visualizations) == 0:
ax[row_index,
col_index].plot(np.arange(0, lattice_grid_shape[-1]),
density[:, int(lattice_grid_shape[0] / 2)])
ax[row_index, col_index].set_title('step ' + str(i))
col_index += 1
if col_index == 5:
col_index = 0
row_index += 1
if row_index == 4:
break
fig.subplots_adjust(left=0.125,
right=0.9,
bottom=0.1,
top=0.9,
wspace=0.75,
hspace=0.5)
plt.savefig(r'./figures/shear_wave_decay/evolution_density_surface.pgf')
plt.savefig(r'./figures/shear_wave_decay/evolution_density_surface.svg')
def milestone_2_test_1():
lx, ly = 50, 50
time_steps = 70
omega = 0.5
density, velocity = milestone_2_test_1_initial_val((lx, ly))
f = equilibrium_distr_func(density, velocity, 9)
for i in trange(time_steps):
f, density, velocity = lattice_boltzmann_step(f, density, velocity,
omega)
visualize_density_surface_plot(density, (lx, ly))
def milestone_3_test_1():
lx, ly = 50, 50
initial_p0 = 0.5
epsilon = 0.01
omega = 1.95
time_steps = 2000
density, velocity = sinusoidal_density_x((lx, ly), initial_p0, epsilon)
f = equilibrium_distr_func(density, velocity)
# visualize_density_surface_plot(density, (lx, ly))
dens = []
for i in trange(time_steps):
f, density, velocity = lattice_boltzmann_step(f, density, velocity,
omega)
den_min = np.amin(density)
den_max = np.amax(density)
dens.append(
np.abs(den_min) - initial_p0 if np.abs(den_min) > np.abs(den_max)
else np.abs(den_max) - initial_p0)
# if i % 1000 == 0:
# visualize_density_surface_plot(density, (lx, ly))
x = np.arange(0, time_steps)
dens = np.array(dens)
from scipy.signal import argrelextrema
indizes = argrelextrema(np.array(dens), np.greater)
a = dens[indizes]
viscosity_sim = curve_fit(
lambda t, v: epsilon * np.exp(-v * np.power(2 * np.pi / lx, 2) * t),
np.array(indizes).squeeze(), a)[0][0]
plt.plot(np.array(indizes).squeeze(),
a,
label='Simulated (v=' + str(round(viscosity_sim, 3)) + ")")
plt.plot(np.arange(0, time_steps),
np.array(dens),
label='Simulated True (v=' + str(round(viscosity_sim, 3)) + ")")
viscosity = (1 / 3) * (1 / omega - 0.5)
plt.plot(x,
epsilon * np.exp(-viscosity * np.power(2 * np.pi / lx, 2) * x),
label='Analytical (v=' + str(viscosity) + ")")
plt.legend()
plt.xlabel('Time t')
plt.ylabel('Amplitude a(t)')
plt.show()
a = epsilon * np.exp(-viscosity_sim * np.power(2 * np.pi / lx, 2)) * x
b = epsilon * np.exp(-viscosity * np.power(2 * np.pi / lx, 2)) * x
print(viscosity * 0.8 <= viscosity_sim <= viscosity * 1.2)
print(np.divide(viscosity - viscosity_sim, viscosity))
def run_test():
lx, ly = 420, 180
d = 40
u0 = 0.1
density_in = 1.0
kinematic_viscosity = 0.04
omega = np.reciprocal(3 * kinematic_viscosity + 0.5)
time_steps = 11
p_coords = [3 * lx // 4, ly // 2]
size = MPI.COMM_WORLD.Get_size()
rank = MPI.COMM_WORLD.Get_rank()
comm = MPI.COMM_WORLD
x_size, y_size = get_xy_size(size)
cartesian2d = comm.Create_cart(dims=[x_size, y_size], periods=[True, True], reorder=False)
coords2d = cartesian2d.Get_coords(rank)
n_local_x, n_local_y = get_local_coords(coords2d, lx, ly, x_size, y_size)
density, velocity = density_1_velocity_x_u0_velocity_y_0_initial((n_local_x + 2, n_local_y + 2), u0)
f = equilibrium_distr_func(density, velocity)
process_coord, px, py = global_coord_to_local_coord(coords2d, p_coords[0], p_coords[1], lx, ly, x_size, y_size)
if process_coord is not None:
vel_at_p = [np.linalg.norm(velocity[px, py, ...])]
bound_func = parallel_von_karman_boundary_conditions(coords2d, n_local_x, n_local_y, lx, ly, x_size, y_size, density_in, u0, d)
communication_func = communication(cartesian2d)
if rank == 0:
pbar = tqdm(total=time_steps)
for i in range(time_steps):
if rank == 0:
pbar.update(1)
f, density, velocity = lattice_boltzmann_step(f, density, velocity, omega, bound_func, communication_func)
if process_coord is not None:
vel_at_p.append(np.linalg.norm(velocity[px, py, ...]))
vel_at_p_test = np.load(r'./tests/von_karman_vortex_shedding/vel_at_p.npy')
assert vel_at_p[-1] == vel_at_p_test[i + 1]
for j in range(9):
save_mpiio(cartesian2d, r'./tests/tmp/f_' + str(j) + '.npy', f[1:-1, 1:-1, j])
if rank == 0:
f_gather = [np.load(r'./tests/tmp/f_' + str(j) + '.npy') for j in range(9)]
f_gather = np.stack(f_gather, axis=-1)
f_test = np.load(r'./tests/von_karman_vortex_shedding/f_' + str(i) + '.npy')
assert f_gather.shape == f_test.shape
assert np.allclose(f_gather, f_test)
def milestone_3_test_2():
lx, ly = 50, 200
epsilon = 0.08
omega = 1.5
time_steps = 2000
density, velocity = sinusoidal_velocity_x((lx, ly), epsilon)
f = equilibrium_distr_func(density, velocity)
# visualize_density_surface_plot(velocity[..., 1], (lx, ly))
vels = []
for i in trange(time_steps):
f, density, velocity = lattice_boltzmann_step(f, density, velocity,
omega)
# if i % 100 == 0:
# visualize_density_surface_plot(velocity[..., 0], (lx, ly))
# visualize_velocity_field(velocity, (50, 50))
vel_min = np.amin(velocity)
vel_max = np.amax(velocity)
vels.append(
np.abs(vel_min) if np.abs(vel_min) > np.abs(vel_max) else np.
abs(vel_max))
x = t = np.arange(0, time_steps)
vels = np.array(vels)
viscosity_sim = curve_fit(
lambda t, v: epsilon * np.exp(-v * np.power(2 * np.pi / ly, 2) * t), x,
vels)[0][0]
plt.plot(np.arange(0, time_steps),
np.array(vels),
label='Simulated (v=' + str(round(viscosity_sim, 3)) + ")")
viscosity = (1 / 3) * (1 / omega - 0.5)
plt.plot(t,
epsilon * np.exp(-viscosity * np.power(2 * np.pi / ly, 2) * t),
label='Analytical (v=' + str(round(viscosity, 3)) + ")")
plt.legend()
plt.xlabel('Time t')
plt.ylabel('Amplitude a(t)')
plt.show()
def plot_measured_viscosity_vs_omega(lattice_grid_shape: Tuple[int,
int] = (50, 50),
initial_p0: float = 0.5,
epsilon_p: float = 0.08,
epsilon_v: float = 0.08,
time_steps: int = 2500,
omega_discretization: int = 50):
"""
Executes the experiment to study the relationship between theoretical kinematic viscosity and relaxation parameter
omega and saves the results.
Args:
lattice_grid_shape: lattice size
initial_p0: shift of density
epsilon_p: amplitude of density sine wave
epsilon_v: amplitude of velocity sine wave
time_steps: number of time steps
omega_discretization: number of how many omegas should be discretized
"""
fig, ax = plt.subplots(1, 2, sharex=True, sharey=True)
omega = np.linspace(0.01, 1.99, omega_discretization)
initial_distr_funcs = [
sinusoidal_density_x(lattice_grid_shape, initial_p0, epsilon_p),
sinusoidal_velocity_x(lattice_grid_shape, epsilon_v)
]
for i, initial in enumerate(tqdm(initial_distr_funcs)):
viscosity_sim = []
viscosity_true = []
for om in tqdm(omega):
density, velocity = initial
f = equilibrium_distr_func(density, velocity)
vels = []
dens = []
for _ in trange(time_steps):
f, density, velocity = lattice_boltzmann_step(
f, density, velocity, om)
if i == 0:
den_min = np.amin(density)
den_max = np.amax(density)
dens.append(
np.abs(den_min) -
initial_p0 if np.abs(den_min) > np.abs(den_max) else
np.abs(den_max) - initial_p0)
elif i == 1:
vel_min = np.amin(velocity)
vel_max = np.amax(velocity)
vels.append(
np.abs(vel_min) if np.abs(vel_min) > np.abs(vel_max)
else np.abs(vel_max))
x = np.arange(0, time_steps)
if i == 0:
dens = np.array(dens)
indizes = argrelextrema(dens, np.greater)
a = dens[indizes]
viscosity_sim.append(
curve_fit(
lambda t, v: epsilon_p * np.exp(-v * np.power(
2 * np.pi / lattice_grid_shape[0], 2) * t),
np.array(indizes).squeeze(), a)[0][0])
elif i == 1:
vels = np.array(vels)
viscosity_sim.append(
curve_fit(
lambda t, v: epsilon_v * np.exp(-v * np.power(
2 * np.pi / lattice_grid_shape[-1], 2) * t), x,
vels)[0][0])
viscosity_true.append((1 / 3) * (1 / om - 0.5))
viscosity_sim = np.array(viscosity_sim)
ax[i].plot(omega, viscosity_sim, label='Simul. visc.')
viscosity_true = np.array(viscosity_true)
ax[i].plot(omega, viscosity_true, label='Analyt. visc.')
ax[i].legend()
ax[i].set_yscale('log')
ax[i].set_title("Sinusoidal Density" if i ==
0 else "Sinusoidal Velocity")
ax[i].set_xlabel(r'relaxation parameter $\omega$')
ax[i].set_ylabel(r'viscosity $\nu$ [$\frac{lu²}{s}$]')
plt.savefig(r'./figures/shear_wave_decay/meas_visc_vs_omega.svg')
plt.savefig(r'./figures/shear_wave_decay/meas_visc_vs_omega.pgf')
def plot_couette_flow_vel_vectors(lattice_grid_shape: Tuple[int,
int] = (20, 30),
omega: float = 1.0,
U: float = 0.05,
time_steps: int = 5000):
"""
Executes the couette flow experiment and save results. Results contain comparision with analytical solution,
absolute error, linear regression of simulation results
Args:
lattice_grid_shape: lattice size
omega: relaxation parameter
U: velocity of moving wall
time_steps: number of time steps for simulation
"""
assert U <= 1 / np.sqrt(3)
lx, ly = lattice_grid_shape
density, velocity = density_1_velocity_0_initial((lx, ly))
f = equilibrium_distr_func(density, velocity)
boundary_func = couette_flow_boundary_conditions(lx, ly, U,
np.mean(density))
for _ in trange(time_steps):
f, density, velocity = lattice_boltzmann_step(f, density, velocity,
omega, boundary_func)
vx = velocity[..., 0]
for vec, y_coord in zip(vx[int(lx / 2), :], np.arange(0, ly)):
origin = [0, y_coord]
plt.quiver(*origin,
*[vec, 0.0],
color='blue',
scale_units='xy',
scale=1,
headwidth=3,
width=0.0025)
plt.plot(vx[int(lx / 2), :],
np.arange(0, ly),
label='Simul. sol.',
linewidth=1,
c='blue',
linestyle=':')
plt.plot(U * (ly - np.arange(0, ly + 1)) / ly,
np.arange(0, ly + 1) - 0.5,
label='Analyt. sol.',
c='red',
linestyle='--')
plt.plot(np.linspace(0, U, 100),
np.ones_like(np.linspace(0, U, 100)) * (ly - 1) + 0.5,
label='Rigid wall',
linewidth=1.5,
c='orange',
linestyle='-.')
plt.plot(np.linspace(0, U, 100),
np.zeros_like(np.linspace(0, U, 100)) - 0.5,
label='Moving wall',
linewidth=1.5,
c='green',
linestyle='-')
plt.ylabel('y position [lu]')
plt.xlabel(r'velocity in x-direction $\mathbf{u}_x$ [$\frac{lu}{s}$]')
plt.legend()
plt.savefig(r'./figures/couette_flow/vel_vectors.svg', bbox_inches='tight')
plt.savefig(r'./figures/couette_flow/vel_vectors.pgf', bbox_inches='tight')
plt.close()
simulated = vx[int(lx / 2)]
slope, intercept, rvalue, pvalue, stderr = linregress(
np.arange(ly), simulated)
with open('./figures/couette_flow/linregress.csv', 'w',
newline='') as csvfile:
fieldnames = ['slope', 'intercept', 'rvalue', 'pvalue', 'stderr']
writer = csv.DictWriter(csvfile, fieldnames=fieldnames)
writer.writeheader()
writer.writerow({
'slope': slope,
'intercept': intercept,
'rvalue': rvalue,
'pvalue': pvalue,
'stderr': stderr
})
analytical_points = [
intercept + slope * (x + 0.5) for x in np.arange(0, ly)
]
simulated_points = vx[int(lx / 2), :]
abs_error = np.abs(simulated_points - analytical_points)
abs_error = np.where(abs_error < 10e-4, 0, abs_error)
plt.plot(np.arange(0, ly), abs_error)
plt.xlabel(r'y position [lu]')
plt.ylabel(r'absolute error [\%]')
plt.savefig(r'./figures/couette_flow/absolute_error.svg',
bbox_inches='tight')
plt.savefig(r'./figures/couette_flow/absolute_error.pgf',
bbox_inches='tight')
def plot_poiseuille_flow_vel_vectors(lattice_grid_shape: Tuple[int,
int] = (200,
60),
omega: float = 1.5,
delta_p: float = 0.001,
time_steps: int = 40000):
"""
Executes the poiseuille flow experiment. Results contain qualitative comparison to analytical solution,
difference of area under curve at the inlet and middle channel, pressure along the centerline and the
absolute error.
Args:
lattice_grid_shape: lattice size
omega: relaxation parameter
delta_p: pressure difference
time_steps: number of time steps of the simulation
"""
lx, ly = lattice_grid_shape
rho_0 = 1
delta_rho = delta_p * 3
rho_inlet = rho_0 + (delta_rho / 2)
rho_outlet = rho_0 - (delta_rho / 2)
p_in = rho_inlet / 3
p_out = rho_outlet / 3
boundary_func = poiseuille_flow_boundary_conditions(lx, ly, p_in, p_out)
density, velocity = density_1_velocity_0_initial((lx, ly))
f = equilibrium_distr_func(density, velocity)
for _ in trange(time_steps):
f, density, velocity = lattice_boltzmann_step(f, density, velocity,
omega, boundary_func)
vx = velocity[..., 0]
x_coords = [1, lx // 2]
centerline = ly // 2
areas = []
colors = ['cyan', 'blue']
linestyle = [':', '-.']
for c, ls, x_coord in zip(colors, linestyle, x_coords):
for vec, y_coord in zip(vx[x_coord, :], np.arange(0, ly)):
origin = [0, y_coord]
plt.quiver(*origin,
*[vec, 0.0],
color=c,
scale_units='xy',
scale=1,
headwidth=3,
width=0.0025)
plt.plot(vx[x_coord, :],
np.arange(0, ly),
label='Sim. sol. channel ' + str(x_coord),
linewidth=1,
c=c,
linestyle=ls)
areas.append(np.trapz(vx[x_coord, :], np.arange(0, ly)))
viscosity = (1 / 3) * (1 / omega - 0.5)
dynamic_viscosity = viscosity * np.mean(density[x_coord, :])
h = ly
y = np.arange(0, ly + 1)
dp_dx = np.divide(p_out - p_in, lx)
uy = -np.reciprocal(2 * dynamic_viscosity) * dp_dx * y * (h - y)
plt.plot(uy, y - 0.5, label='Analyt. sol.', c='red', linestyle='--')
plt.plot(np.linspace(0,
np.amax(vx) * 1.05, 100),
np.zeros_like(np.linspace(0,
np.amax(vx) * 1.05, 100)) - 0.5,
label='Rigid wall',
linewidth=1.5,
c='green',
linestyle='-')
plt.plot(np.linspace(0,
np.amax(vx) * 1.05, 100),
np.ones_like(np.linspace(0,
np.amax(vx) * 1.05, 100)) *
(ly - 1) + 0.5,
label='Rigid wall',
linewidth=1.5,
c='green',
linestyle='-')
plt.ylabel('y position [lu]')
plt.xlabel(r'velocity in x-direction $\mathbf{u}_x$ [$\frac{lu}{s}$]')
handles, labels = plt.gca().get_legend_handles_labels()
by_label = OrderedDict(zip(labels, handles))
plt.legend(by_label.values(), by_label.keys())
plt.legend(by_label.values(), by_label.keys(), loc='lower right')
plt.savefig(r'./figures/poiseuille_flow/vel_vectors.svg',
bbox_inches='tight')
plt.savefig(r'./figures/poiseuille_flow/vel_vectors.pgf',
bbox_inches='tight')
plt.close()
areas.append(areas[0] / areas[1])
areas = np.array(areas)
with open('./figures/poiseuille_flow/areas.csv', 'w',
newline='') as csvfile:
fieldnames = ['inlet', 'middle', 'relative_difference']
writer = csv.DictWriter(csvfile, fieldnames=fieldnames)
writer.writeheader()
writer.writerow({
'inlet': areas[0],
'middle': areas[1],
'relative_difference': areas[2]
})
plt.plot(np.arange(0, lx - 2),
density[1:-1, centerline] / 3,
label='Pressure along centerline')
plt.plot(np.arange(0, lx - 2),
np.ones_like(np.arange(0, lx - 2)) * p_out,
label='Outgoing pressure')
plt.plot(np.arange(0, lx - 2),
np.ones_like(np.arange(0, lx - 2)) * p_in,
label='Ingoing pressure')
plt.xlabel('x position [lu]')
plt.ylabel(r'pressure along centerline $p$ [$Pa$]')
plt.legend()
plt.savefig(r'./figures/poiseuille_flow/density_along_centerline.svg',
bbox_inches='tight')
plt.savefig(r'./figures/poiseuille_flow/density_along_centerline.pgf',
bbox_inches='tight')
plt.close()
popt, pcov = curve_fit(lambda y, a, b, c: a * (y**2) + b * y + c,
np.arange(0, ly), vx[x_coord, :])
with open('./figures/poiseuille_flow/curve_fit.csv', 'w',
newline='') as csvfile:
fieldnames = ['popt', 'pcov']
writer = csv.DictWriter(csvfile, fieldnames=fieldnames)
writer.writeheader()
writer.writerow({'popt': popt, 'pcov': pcov})
a, b, c = popt
analytical_points = [
a * ((x + 0.5)**2) + b * (x + 0.5) + c for x in np.arange(0, ly)
]
simulated_points = vx[int(lx // 2), :]
abs_error = np.abs(simulated_points - analytical_points)
abs_error = np.where(abs_error < 10e-4, 0, abs_error)
plt.plot(np.arange(0, ly), abs_error)
plt.xlabel(r'y position [lu]')
plt.ylabel(r'absolute error [\%]')
plt.savefig(r'./figures/poiseuille_flow/absolute_error.svg',
bbox_inches='tight')
plt.savefig(r'./figures/poiseuille_flow/absolute_error.pgf',
bbox_inches='tight')
def milestone_7():
lx, ly = 420, 180
d = 40
u0 = 0.1
density_in = 1.0
kinematic_viscosity = 0.04
omega = np.reciprocal(3 * kinematic_viscosity + 0.5)
time_steps = 100000
p_coords = [3 * lx // 4, ly // 2]
size = MPI.COMM_WORLD.Get_size()
rank = MPI.COMM_WORLD.Get_rank()
comm = MPI.COMM_WORLD
x_size, y_size = get_xy_size(size)
cartesian2d = comm.Create_cart(dims=[x_size, y_size],
periods=[True, True],
reorder=False)
coords2d = cartesian2d.Get_coords(rank)
n_local_x, n_local_y = get_local_coords(coords2d, lx, ly, x_size, y_size)
def boundary(coord2d, n_local_x, n_local_y):
def bc(f_pre_streaming,
f_post_streaming,
density=None,
velocity=None,
f_previous=None):
# inlet
if x_in_process(coord2d, 0, lx, x_size):
f_post_streaming[1:-1, 1:-1, :] = inlet(
(n_local_x, n_local_y), density_in,
u0)(f_post_streaming.copy()[1:-1, 1:-1, :])
# outlet
if x_in_process(coord2d, lx - 1, lx, x_size) and x_in_process(
coord2d, lx - 2, lx, x_size):
f_post_streaming[1:-1,
1:-1, :] = outlet()(
f_previous.copy()[1:-1, 1:-1, :],
f_post_streaming.copy()[1:-1, 1:-1, :])
elif x_in_process(coord2d, lx - 1, lx, x_size) or x_in_process(
coord2d, lx - 2, lx, x_size):
# TODO communicate f_previous
raise NotImplementedError
# plate boundary condition
y_min, y_max = ly // 2 - d // 2 + 1, ly // 2 + d // 2 - 1
if x_in_process(coord2d, lx // 4, lx, x_size): # left side
local_x = global_to_local_direction(coord2d[0], lx // 4, lx,
x_size)
for y in range(y_min, y_max):
if y_in_process(coord2d, y, ly, y_size):
local_y = global_to_local_direction(
coord2d[1], y, ly, y_size)
f_post_streaming[local_x, local_y,
[3, 7, 6]] = f_pre_streaming[
local_x, local_y, [1, 5, 8]]
if y_in_process(coord2d, ly // 2 + d // 2 - 1, ly,
y_size): # left side upper corner
local_y = global_to_local_direction(
coord2d[1], ly // 2 + d // 2 - 1, ly, y_size)
f_post_streaming[local_x, local_y,
[3, 6]] = f_pre_streaming[local_x,
local_y, [1, 8]]
if y_in_process(coord2d, ly // 2 - d // 2, ly,
y_size): # left side lower corner
local_y = global_to_local_direction(
coord2d[1], ly // 2 - d // 2, ly, y_size)
f_post_streaming[local_x, local_y,
[3, 7]] = f_pre_streaming[local_x,
local_y, [1, 5]]
if x_in_process(coord2d, lx // 4 + 1, lx, x_size): # right side
local_x = global_to_local_direction(coord2d[0], lx // 4 + 1,
lx, x_size)
for y in range(y_min, y_max):
if y_in_process(coord2d, y, ly, y_size):
local_y = global_to_local_direction(
coord2d[1], y, ly, y_size)
f_post_streaming[local_x, local_y,
[1, 5, 8]] = f_pre_streaming[
local_x, local_y, [3, 7, 6]]
if y_in_process(coord2d, ly // 2 + d // 2 - 1, ly,
y_size): # right side upper corner
local_y = global_to_local_direction(
coord2d[1], ly // 2 + d // 2 - 1, ly, y_size)
f_post_streaming[local_x, local_y,
[1, 5]] = f_pre_streaming[local_x,
local_y, [3, 7]]
if y_in_process(coord2d, ly // 2 - d // 2, ly,
y_size): # right side lower corner
local_y = global_to_local_direction(
coord2d[1], ly // 2 - d // 2, ly, y_size)
f_post_streaming[local_x, local_y,
[1, 8]] = f_pre_streaming[local_x,
local_y, [3, 6]]
return f_post_streaming
return bc
density, velocity = density_1_velocity_x_u0_velocity_y_0_initial(
(n_local_x + 2, n_local_y + 2), u0)
f = equilibrium_distr_func(density, velocity)
process_coord, px, py = global_coord_to_local_coord(
coords2d, p_coords[0], p_coords[1], lx, ly, x_size, y_size)
if process_coord is not None:
vel_at_p = [np.linalg.norm(velocity[px, py, ...])]
bound_func = boundary(coords2d, n_local_x, n_local_y)
communication_func = communication(cartesian2d)
if rank == 0:
pbar = tqdm(total=time_steps)
for i in range(time_steps):
if rank == 0:
pbar.update(1)
f, density, velocity = lattice_boltzmann_step(f, density, velocity,
omega, bound_func,
communication_func)
if process_coord is not None:
vel_at_p.append(np.linalg.norm(velocity[px, py, ...]))
if i % 100 == 0:
abs_vel = np.linalg.norm(velocity[1:-1, 1:-1, :], axis=-1)
assert abs_vel.shape == (n_local_x, n_local_y)
save_mpiio(
cartesian2d,
r'./figures/von_karman_vortex_shedding/all_png_parallel/vel_norm.npy',
abs_vel)
if rank == 0:
abs_vel = np.load(
r'./figures/von_karman_vortex_shedding/all_png_parallel/vel_norm.npy'
)
normalized_vel = abs_vel / np.amax(abs_vel)
from PIL import Image
from matplotlib import cm
img = Image.fromarray(
np.uint8(cm.viridis(normalized_vel.T) * 255))
img.save(
r'./figures/von_karman_vortex_shedding/all_png_parallel/' +
str(i) + '.png')
os.remove(
r'./figures/von_karman_vortex_shedding/all_png_parallel/vel_norm.npy'
)
np.save(r'../figures/von_karman_vortex_shedding/vel_at_p.py', vel_at_p)
vel_at_p = np.load(
r'../figures/von_karman_vortex_shedding/vel_at_p.py.npy')
np.save(r'../figures/von_karman_vortex_shedding/velocity.py', velocity)
velocity = np.load(
r'../figures/von_karman_vortex_shedding/velocity.py.npy')
np.save(r'../figures/von_karman_vortex_shedding/density.py', density)
density = np.load(r'../figures/von_karman_vortex_shedding/density.py.npy')
absolute_velocity = np.linalg.norm(velocity, axis=-1)
normalized_abs_velocity = absolute_velocity / np.amax(absolute_velocity)
plt.imshow(normalized_abs_velocity.T)
plt.colorbar()
plt.show()
plt.plot(np.arange(0, time_steps + 1), vel_at_p, linewidth=0.3)
plt.show()
vel_at_p = vel_at_p[70000:]
plt.plot(vel_at_p)
plt.show()
yf = np.fft.fft(vel_at_p)
freq = np.fft.fftfreq(len(vel_at_p), 1)
plt.plot(freq, np.abs(yf.imag))
plt.show()
vortex_frequency = np.abs(freq[np.argmax(yf.imag)])
print(vortex_frequency)
strouhal = strouhal_number(vortex_frequency, d, u0)
print(strouhal)
reynolds = reynolds_number(d, u0, kinematic_viscosity)
print(reynolds)
def milestone_6():
lx, ly = 420, 180
d = 40
u0 = 0.1
density_in = 1.0
kinematic_viscosity = 0.04
omega = np.reciprocal(3 * kinematic_viscosity + 0.5)
time_steps = 100000
p_coords = [3 * lx // 4, ly // 2]
def boundary(f_pre_streaming,
f_post_streaming,
density=None,
velocity=None,
f_previous=None):
f_post_streaming = inlet((lx, ly), density_in, u0)(f_post_streaming)
f_post_streaming = outlet()(f_previous, f_post_streaming)
plate_boundary = np.zeros((lx, ly))
plate_boundary[lx // 4, ly // 2 - d // 2:ly // 2 + d // 2] = 1
f_post_streaming = rigid_object(plate_boundary.astype(np.bool))(
f_pre_streaming, f_post_streaming)
return f_post_streaming
density, velocity = density_1_velocity_x_u0_velocity_y_0_initial((lx, ly),
u0)
f = equilibrium_distr_func(density, velocity)
vel_at_p = [np.linalg.norm(velocity[p_coords[0], p_coords[1], ...])]
for i in trange(time_steps):
f, density, velocity = lattice_boltzmann_step(f, density, velocity,
omega, boundary)
vel_at_p.append(np.linalg.norm(velocity[p_coords[0], p_coords[1],
...]))
np.save(r'../tests/von_karman_vortex_shedding/f_' + str(i) + '.npy', f)
# np.save(r'../tests/von_karman_vortex_shedding/density_' + str(i), density)
# np.save(r'../tests/von_karman_vortex_shedding/velocity_' + str(i), velocity)
if i == 10:
np.save(r'../tests/von_karman_vortex_shedding/vel_at_p', vel_at_p)
raise Exception('Stop here')
if i % 100 == 0:
absolute_velocity = np.linalg.norm(velocity, axis=-1)
normalized_abs_velocity = absolute_velocity / np.amax(
absolute_velocity)
from PIL import Image
from matplotlib import cm
img = Image.fromarray(
np.uint8(cm.viridis(normalized_abs_velocity.T) * 255))
img.save(r'../figures/von_karman_vortex_shedding/all_png/' +
str(i) + '.png')
np.save(r'../figures/von_karman_vortex_shedding/vel_at_p.py', vel_at_p)
vel_at_p = np.load(
r'../figures/von_karman_vortex_shedding/vel_at_p.py.npy')
np.save(r'../figures/von_karman_vortex_shedding/velocity.py', velocity)
velocity = np.load(
r'../figures/von_karman_vortex_shedding/velocity.py.npy')
np.save(r'../figures/von_karman_vortex_shedding/density.py', density)
density = np.load(r'../figures/von_karman_vortex_shedding/density.py.npy')
absolute_velocity = np.linalg.norm(velocity, axis=-1)
normalized_abs_velocity = absolute_velocity / np.amax(absolute_velocity)
plt.imshow(normalized_abs_velocity.T)
plt.colorbar()
plt.show()
plt.plot(np.arange(0, time_steps + 1), vel_at_p, linewidth=0.3)
plt.show()
vel_at_p = vel_at_p[70000:]
plt.plot(vel_at_p)
plt.show()
yf = np.fft.fft(vel_at_p)
freq = np.fft.fftfreq(len(vel_at_p), 1)
plt.plot(freq, np.abs(yf.imag))
plt.show()
vortex_frequency = np.abs(freq[np.argmax(yf.imag)])
print(vortex_frequency)
strouhal = strouhal_number(vortex_frequency, d, u0)
print(strouhal)
reynolds = reynolds_number(d, u0, kinematic_viscosity)
print(reynolds)
def milestone_5():
lx, ly = 200, 30
omega = 1.5
time_steps = 5000
delta_p = 0.001111
rho_0 = 1
delta_rho = delta_p * 3
rho_inlet = rho_0 + delta_rho
rho_outlet = rho_0
p_in = rho_inlet / 3
p_out = rho_outlet / 3
def boundary(f_pre_streaming, f_post_streaming, density, velocity):
boundary = np.zeros((lx, ly))
boundary[0, :] = np.ones(ly)
boundary[-1, :] = np.ones(ly)
f_post_streaming = periodic_with_pressure_variations(
boundary.astype(np.bool), p_in,
p_out)(f_pre_streaming, f_post_streaming, density, velocity)
boundary_rigid_wall = np.zeros((lx, ly))
boundary_rigid_wall[:, 0] = np.ones(lx)
f_post_streaming = rigid_wall(boundary_rigid_wall.astype(np.bool))(
f_pre_streaming, f_post_streaming)
boundary_rigid_wall = np.zeros((lx, ly))
boundary_rigid_wall[:, -1] = np.ones(lx)
f_post_streaming = rigid_wall(boundary_rigid_wall.astype(np.bool))(
f_pre_streaming, f_post_streaming)
return f_post_streaming
density, velocity = density_1_velocity_0_initial((lx, ly))
f = equilibrium_distr_func(density, velocity)
for i in trange(time_steps):
f, density, velocity = lattice_boltzmann_step(f, density, velocity,
omega, boundary)
vx = velocity[..., 0]
print(np.amax(velocity))
x_coord = lx // 2
centerline = ly // 2
for vec, y_coord in zip(vx[x_coord, :], np.arange(0, ly)):
origin = [0, y_coord]
plt.quiver(*origin,
*[vec, 0.0],
color='blue',
scale_units='xy',
scale=1,
headwidth=3,
width=0.0025)
plt.plot(vx[x_coord, :],
np.arange(0, ly),
label='Simulated Solution',
linewidth=1,
c='blue',
linestyle=':')
viscosity = (1 / 3) * (1 / omega - 0.5)
dynamic_viscosity = viscosity * np.mean(density[x_coord, :])
h = ly
y = np.arange(0, ly + 1)
dp_dx = np.divide(p_out - p_in, lx)
uy = -np.reciprocal(2 * dynamic_viscosity) * dp_dx * y * (h - y)
print(np.amax(uy))
plt.plot(uy, y - 0.5, label='Analytical Solution', c='red', linestyle='--')
plt.ylabel('y coordinate')
plt.xlabel('velocity in y-direction')
plt.legend()
plt.show()
plt.plot(np.arange(0, lx - 2),
density[1:-1, centerline] / 3,
label='Pressure along centerline')
plt.plot(np.arange(0, lx - 2),
np.ones_like(np.arange(0, lx - 2)) * p_out,
label='Outgoing Pressure')
plt.plot(np.arange(0, lx - 2),
np.ones_like(np.arange(0, lx - 2)) * p_in,
label='Ingoing Pressure')
plt.xlabel('x coordinate')
plt.ylabel('density along centerline')
plt.legend()
plt.show()
print(np.amax(density[1:-1, centerline]) / 3, p_in)
print(np.amin(density[1:-1, centerline]) / 3, p_out)
def milestone_4():
lx, ly = 50, 50
omega = 0.5
time_steps = 5000
U = 50
def boundary(f_pre_streaming, f_post_streaming, density, velocity):
boundary_rigid_wall = np.zeros((lx, ly))
boundary_rigid_wall[:, -1] = np.ones(ly)
f_post_streaming = rigid_wall(boundary_rigid_wall.astype(np.bool))(
f_pre_streaming, f_post_streaming)
boundary_moving_wall = np.zeros((lx, ly))
boundary_moving_wall[:, 0] = np.ones(ly)
u_w = np.array([U, 0])
f_post_streaming = moving_wall(boundary_moving_wall.astype(np.bool),
u_w, density)(f_pre_streaming,
f_post_streaming)
return f_post_streaming
density, velocity = density_1_velocity_0_initial((lx, ly))
f = equilibrium_distr_func(density, velocity)
for i in trange(time_steps):
f, density, velocity = lattice_boltzmann_step(f, density, velocity,
omega, boundary)
vx = velocity[..., 0]
for vec, y_coord in zip(vx[25, :], np.arange(0, ly)):
origin = [0, y_coord]
plt.quiver(*origin,
*[vec, 0.0],
color='blue',
scale_units='xy',
scale=1,
headwidth=3,
width=0.0025)
plt.plot(vx[25, :],
np.arange(0, ly),
label='Simulated Solution',
linewidth=1,
c='blue',
linestyle=':')
plt.plot(U * (ly - np.arange(0, ly + 1)) / ly,
np.arange(0, ly + 1) - 0.5,
label='Analyt. Sol.',
c='red',
linestyle='--')
max_vel = np.ceil(np.amax(vx[25, :])).astype(np.int) + 1
plt.plot(np.arange(0, max_vel),
np.ones(max_vel) * (ly - 1) + 0.5,
label='Rigid Wall',
linewidth=1.5,
c='orange',
linestyle='-.')
plt.plot(np.arange(0, max_vel),
np.zeros(max_vel) - 0.5,
label='Moving Wall',
linewidth=1.5,
c='green',
linestyle='-')
plt.ylabel('y coordinate')
plt.xlabel('velocity in y-direction')
plt.legend()
plt.show()
def plot_couette_flow_evolution(lattice_grid_shape: Tuple[int, int] = (20, 20),
omega: float = 1.0,
U: float = 0.01,
time_steps: int = 4000,
number_of_visualizations: int = 30):
"""
Executes the couette flow evolution experiment and saves the results.
Args:
lattice_grid_shape:
omega: relaxation parameter
U: velocity of moving wall
time_steps: number of time steps for simulation
number_of_visualizations: total number of visualizations. Has to be divisible by 5.
"""
assert number_of_visualizations % 5 == 0
assert U <= 1 / np.sqrt(3)
lx, ly = lattice_grid_shape
fig, ax = plt.subplots(int(number_of_visualizations / 5),
5,
sharex=True,
sharey=True)
row_index, col_index = 0, 0
density, velocity = density_1_velocity_0_initial((lx, ly))
f = equilibrium_distr_func(density, velocity)
velocities = [velocity]
boundary_func = couette_flow_boundary_conditions(lx, ly, U,
np.mean(density))
for _ in trange(time_steps):
f, density, velocity = lattice_boltzmann_step(f, density, velocity,
omega, boundary_func)
velocities.append(velocity)
velocities_for_viz = [
velocity for i, velocity in enumerate(velocities)
if i % int(time_steps / (number_of_visualizations - 1)) == 0
] # -1 for the initial viz
indizes_for_viz = [
i for i, velocity in enumerate(velocities)
if i % int(time_steps / (number_of_visualizations - 1)) == 0
] # -1 for the initial viz
max_vel = np.amax(
np.array(velocities_for_viz)[:, int(lx / 2), :, 0]) + np.amax(
np.array(velocities_for_viz)[:, int(lx / 2), :, 0]) * 0.1
for i, velocity in zip(indizes_for_viz, velocities_for_viz):
vx = velocity[..., 0]
for vec, y_coord in zip(vx[int(lx / 2), :], np.arange(0, ly)):
origin = [0, y_coord]
ax[row_index, col_index].quiver(*origin,
*[vec, 0.0],
color='blue',
scale_units='xy',
scale=1,
headwidth=3,
width=0.0025)
ax[row_index, col_index].plot(vx[int(lx / 2), :],
np.arange(0, ly),
label='Simul. Sol.',
linewidth=1,
c='blue',
linestyle=':')
ax[row_index, col_index].plot(U * (ly - np.arange(0, ly + 1)) / ly,
np.arange(0, ly + 1) - 0.5,
label='Analyt. Sol.',
c='red',
linestyle='--')
ax[row_index, col_index].plot(
np.linspace(0, max_vel, 100),
np.ones_like(np.linspace(0, max_vel, 100)) * (ly - 1) + 0.5,
label='Rigid Wall',
linewidth=1.5,
c='orange',
linestyle='-.')
ax[row_index,
col_index].plot(np.linspace(0, max_vel, 100),
np.zeros_like(np.linspace(0, max_vel, 100)) - 0.5,
label='Moving Wall',
linewidth=1.5,
c='green',
linestyle='-')
if i == 0:
ax[row_index, col_index].set_title('initial')
else:
ax[row_index, col_index].set_title('step ' + str(i))
col_index += 1
if col_index == 5:
col_index = 0
row_index += 1
handles, labels = ax[1, 1].get_legend_handles_labels()
fig.legend(handles, labels, loc='center right', borderaxespad=0.1)
fig.subplots_adjust(left=0.125,
right=0.9,
bottom=0.1,
top=0.9,
wspace=0.75,
hspace=1.5)
plt.subplots_adjust(right=0.77)
plt.savefig(r'./figures/couette_flow/vel_vectors_evolution.svg',
bbox_inches='tight')
plt.savefig(r'./figures/couette_flow/vel_vectors_evolution.pgf',
bbox_inches='tight')
def x_strouhal(folder_name: str,
lattice_grid_shape: Tuple[int, int] = (420, 180),
plate_size: int = 40,
inlet_density: float = 1.0,
inlet_velocity: float = 0.1,
kinematic_viscosity: float = 0.04,
time_steps: int = 200000):
"""
General functions to execute experiments to study the relationship of the strouhal numbers to a given x
(e.g. reynolds number, nx, blockage ratio)
Args:
folder_name: folder to save the files to
lattice_grid_shape: lattice size
plate_size: size of the plate
inlet_density: density into the domain
inlet_velocity: velocity into the domain
kinematic_viscosity: kinematic viscosity
time_steps: number of time steps for the simulation
"""
# setup
lx, ly = lattice_grid_shape
omega = np.reciprocal(3 * kinematic_viscosity + 0.5)
p_coords = [3 * lx // 4, ly // 2]
size = MPI.COMM_WORLD.Get_size()
rank = MPI.COMM_WORLD.Get_rank()
comm = MPI.COMM_WORLD
x_size, y_size = get_xy_size(size)
cartesian2d = comm.Create_cart(dims=[x_size, y_size],
periods=[True, True],
reorder=False)
coords2d = cartesian2d.Get_coords(rank)
n_local_x, n_local_y = get_local_coords(coords2d, lx, ly, x_size, y_size)
density, velocity = density_1_velocity_x_u0_velocity_y_0_initial(
(n_local_x + 2, n_local_y + 2), inlet_velocity)
f = equilibrium_distr_func(density, velocity)
process_coord, px, py = global_coord_to_local_coord(
coords2d, p_coords[0], p_coords[1], lx, ly, x_size, y_size)
if process_coord is not None:
vel_at_p = [np.linalg.norm(velocity[px, py, ...])]
bound_func = parallel_von_karman_boundary_conditions(
coords2d, n_local_x, n_local_y, lx, ly, x_size, y_size, inlet_density,
inlet_velocity, plate_size)
communication_func = communication(cartesian2d)
# main loop
if rank == 0:
pbar = tqdm(total=time_steps)
for i in range(time_steps):
if rank == 0:
pbar.update(1)
f, density, velocity = lattice_boltzmann_step(f, density, velocity,
omega, bound_func,
communication_func)
if process_coord is not None:
vel_at_p.append(np.linalg.norm(velocity[px, py, ...]))
if process_coord is not None:
if 'reynold' in folder_name:
reynolds_number = plate_size * inlet_velocity / kinematic_viscosity
np.save(
r'./figures/von_karman_vortex_shedding/' + folder_name +
'/vel_at_p_' + str(round(reynolds_number)) + '.npy', vel_at_p)
elif 'nx' in folder_name:
np.save(
r'./figures/von_karman_vortex_shedding/' + folder_name +
'/vel_at_p_' + str(int(lx)) + '.npy', vel_at_p)
elif 'blockage' in folder_name:
blockage_ratio = plate_size / ly
np.save(
r'./figures/von_karman_vortex_shedding/' + folder_name +
'/vel_at_p_' + str(blockage_ratio) + '.npy', vel_at_p)
else:
raise Exception('Unknown experiment')
def plot_parallel_von_karman_vortex_street(
lattice_grid_shape: Tuple[int, int] = (420, 180),
plate_size: int = 40,
inlet_density: float = 1.0,
inlet_velocity: float = 0.1,
kinematic_viscosity: float = 0.04,
time_steps: int = 100000):
"""
Executes the parallel version of the code of the von Karman vortex street and saves each 100 time steps the
current velocity magnitude field.
Args:
lattice_grid_shape: lattice size
plate_size: size of the plate
inlet_density: density into the domain
inlet_velocity: velocity into the domain
kinematic_viscosity: kinematic viscosity
time_steps: number of time steps for simulation
"""
# setup
lx, ly = lattice_grid_shape
omega = np.reciprocal(3 * kinematic_viscosity + 0.5)
p_coords = [3 * lx // 4, ly // 2]
size = MPI.COMM_WORLD.Get_size()
rank = MPI.COMM_WORLD.Get_rank()
comm = MPI.COMM_WORLD
x_size, y_size = get_xy_size(size)
cartesian2d = comm.Create_cart(dims=[x_size, y_size],
periods=[True, True],
reorder=False)
coords2d = cartesian2d.Get_coords(rank)
n_local_x, n_local_y = get_local_coords(coords2d, lx, ly, x_size, y_size)
density, velocity = density_1_velocity_x_u0_velocity_y_0_initial(
(n_local_x + 2, n_local_y + 2), inlet_velocity)
f = equilibrium_distr_func(density, velocity)
process_coord, px, py = global_coord_to_local_coord(
coords2d, p_coords[0], p_coords[1], lx, ly, x_size, y_size)
if process_coord is not None:
vel_at_p = [np.linalg.norm(velocity[px, py, ...])]
bound_func = parallel_von_karman_boundary_conditions(
coords2d, n_local_x, n_local_y, lx, ly, x_size, y_size, inlet_density,
inlet_velocity, plate_size)
communication_func = communication(cartesian2d)
# main loop
if rank == 0:
pbar = tqdm(total=time_steps)
for i in range(time_steps):
if rank == 0:
pbar.update(1)
f, density, velocity = lattice_boltzmann_step(f, density, velocity,
omega, bound_func,
communication_func)
if process_coord is not None:
vel_at_p.append(np.linalg.norm(velocity[px, py, ...]))
if i % 100 == 0:
abs_vel = np.linalg.norm(velocity[1:-1, 1:-1, :], axis=-1)
save_mpiio(
cartesian2d,
r'./figures/von_karman_vortex_shedding/all_png_parallel/vel_norm.npy',
abs_vel)
if rank == 0:
abs_vel = np.load(
r'./figures/von_karman_vortex_shedding/all_png_parallel/vel_norm.npy'
)
normalized_vel = abs_vel / np.amax(abs_vel)
img = Image.fromarray(
np.uint8(cm.viridis(normalized_vel.T) * 255))
img.save(
r'./figures/von_karman_vortex_shedding/all_png_parallel/' +
str(i) + '.png')
os.remove(
r'./figures/von_karman_vortex_shedding/all_png_parallel/vel_norm.npy'
)
def plot_poiseuille_flow_evolution(lattice_grid_shape: Tuple[int,
int] = (200, 30),
omega: float = 1.5,
delta_p: float = 0.001,
time_steps: int = 10000,
number_of_visualizations: int = 30):
"""
Executes the poiseuille flow evolution experiment and saves results.
Args:
lattice_grid_shape: lattice size
omega: relaxation parameter
delta_p: pressure difference at inlet and outlet
time_steps: number of time steps for the simulation
number_of_visualizations: total number of visualization. Has to be divisible by 5.
"""
assert number_of_visualizations % 5 == 0
lx, ly = lattice_grid_shape
fig, ax = plt.subplots(int(number_of_visualizations / 5),
5,
sharex=True,
sharey=True)
row_index, col_index = 0, 0
rho_0 = 1
delta_rho = delta_p * 3
rho_inlet = rho_0 + delta_rho
rho_outlet = rho_0
p_in = rho_inlet / 3
p_out = rho_outlet / 3
boundary_func = poiseuille_flow_boundary_conditions(lx, ly, p_in, p_out)
density, velocity = density_1_velocity_0_initial((lx, ly))
f = equilibrium_distr_func(density, velocity)
velocities = [velocity]
for _ in trange(time_steps):
f, density, velocity = lattice_boltzmann_step(f, density, velocity,
omega, boundary_func)
velocities.append(velocity)
x_coord = lx // 2
viscosity = (1 / 3) * (1 / omega - 0.5)
dynamic_viscosity = viscosity * np.mean(density[x_coord, :])
h = ly
y = np.arange(0, ly + 1)
dp_dx = np.divide(p_out - p_in, lx)
uy = -np.reciprocal(2 * dynamic_viscosity) * dp_dx * y * (h - y)
for i, velocity in enumerate(velocities):
if i % int(time_steps / (number_of_visualizations - 1)) == 0:
vx = velocity[..., 0]
ax[row_index, col_index].plot(uy,
y - 0.5,
label='Analyt. sol.',
c='red',
linewidth=0.5)
for vec, y_coord in zip(vx[x_coord, :], np.arange(0, ly)):
origin = [0, y_coord]
ax[row_index, col_index].quiver(*origin,
*[vec, 0.0],
color='blue',
scale_units='xy',
scale=1,
headwidth=3,
width=0.0025)
ax[row_index, col_index].plot(vx[x_coord, :],
np.arange(0, ly),
label='Sim. sol.',
linewidth=1,
c='blue',
linestyle=':')
if i == 0:
ax[row_index, col_index].set_title('initial')
else:
ax[row_index, col_index].set_title('step ' + str(i))
col_index += 1
if col_index == 5:
col_index = 0
row_index += 1
handles, labels = ax[1, 1].get_legend_handles_labels()
fig.legend(handles, labels, loc='center right', borderaxespad=0.1)
fig.subplots_adjust(left=0.125,
right=0.9,
bottom=0.1,
top=0.9,
wspace=0.75,
hspace=1.5)
plt.subplots_adjust(right=0.77)
plt.savefig(r'./figures/poiseuille_flow/vel_vectors_evolution.svg',
bbox_inches='tight')
plt.savefig(r'./figures/poiseuille_flow/vel_vectors_evolution.pgf',
bbox_inches='tight')