def nucleation_and_motion_in_G_gradient_2D(N=128, R=16):
params = {
"A": 3.42,
"B": 13.5,
"k2": 1.0,
"k-2": 0.1,
"k5": 0.9,
"D_G": 1.0,
"D_X": 1.0,
"D_Y": 1.95,
"density_G": 2.0,
"density_X": 1.0,
"density_Y": 1.5,
"base-density": 35.0,
"viscosity": 0.4,
"speed-of-sound": 1.0,
}
x = np.linspace(-R, R, N)
dx = x[1] - x[0]
x, y = np.meshgrid(x, x, indexing='ij')
def source_G(t):
center = np.exp(-0.5 * (t - 5)**2) * 10
gradient = (1 + np.tanh(t - 40)) * 0.0005
return -np.exp(-0.5 * (x * x + y * y)) * center + (x + 8) * gradient
source_functions = {
'G': source_G,
}
flow = [0 * x, 0 * x]
fluid_model_g = FluidModelG(
x * 0,
x * 0,
x * 0,
flow,
dx,
dt=0.25 * dx,
params=params,
source_functions=source_functions,
)
times = []
locs = []
def get_data():
G, X, Y, (u, v) = fluid_model_g.numpy()
loc = l2_location(X, x, y)
times.append(fluid_model_g.t)
locs.append(loc[0])
print("t={}\tL2 location: {}".format(fluid_model_g.t, tuple(loc)))
x_scale = 0.1
y_scale = 0.1
return (
G[:, N // 2],
X[:, N // 2] * x_scale,
Y[:, N // 2] * y_scale,
u[:, N // 2],
v[:, N // 2],
)
G, X, Y, u, v = get_data()
plots = []
plots.extend(pylab.plot(x[:, 0], G))
plots.extend(pylab.plot(x[:, 0], X))
plots.extend(pylab.plot(x[:, 0], Y))
plots.extend(pylab.plot(x[:, 0], u))
plots.extend(pylab.plot(x[:, 0], v))
pylab.ylim(-0.1, 0.1)
def update(frame):
for _ in range(20):
fluid_model_g.step()
G, X, Y, u, v = get_data()
plots[0].set_ydata(G)
plots[1].set_ydata(X)
plots[2].set_ydata(Y)
plots[3].set_ydata(u)
plots[4].set_ydata(v)
return plots
FuncAnimation(pylab.gcf(),
update,
frames=range(100),
init_func=lambda: plots,
blit=True,
repeat=True,
interval=20)
pylab.show()
G, X, Y, (u, v) = fluid_model_g.numpy()
pylab.imshow(X)
pylab.show()
pylab.plot(times, locs)
pylab.show()
def nucleation_3D(animated=False, N=128, R=20):
params = {
"A": 3.4,
"B": 13.5,
"k2": 1.0,
"k-2": 0.1,
"k5": 0.9,
"D_G": 1.0,
"D_X": 1.0,
"D_Y": 1.95,
"density_G": 1.0,
"density_X": 0.0002,
"density_Y": 0.043,
"base-density": 20.0,
"viscosity": 0.4,
"speed-of-sound": 1.0,
}
x = np.linspace(-R, R, N)
dx = x[1] - x[0]
x, y, z = np.meshgrid(x, x, x, indexing='ij')
def source_G(t):
center = np.exp(-0.5 * (t - 5)**2) * 10
return -np.exp(-0.5 * (x * x + y * y + z * z)) * center
source_functions = {
'G': source_G,
}
# We need some noise to break spherical symmetry
noise_scale = 1e-4
G = bl_noise(x.shape) * noise_scale
X = bl_noise(x.shape) * noise_scale
Y = bl_noise(x.shape) * noise_scale
flow = [
bl_noise(x.shape) * noise_scale,
bl_noise(x.shape) * noise_scale,
bl_noise(x.shape) * noise_scale
]
dt = 0.2 * dx
fluid_model_g = FluidModelG(
G,
X,
Y,
flow,
dx,
dt=dt,
params=params,
source_functions=source_functions,
)
if animated:
def get_data():
G, X, Y, (u, v, w) = fluid_model_g.numpy()
x_scale = 0.1
y_scale = 0.1
return (
G[N // 2, N // 2],
X[N // 2, N // 2] * x_scale,
Y[N // 2, N // 2] * y_scale,
u[N // 2, N // 2],
v[N // 2, N // 2],
w[N // 2, N // 2],
)
G, X, Y, u, v, w = get_data()
plots = []
plots.extend(pylab.plot(z[0, 0], G))
plots.extend(pylab.plot(z[0, 0], X))
plots.extend(pylab.plot(z[0, 0], Y))
plots.extend(pylab.plot(z[0, 0], u))
plots.extend(pylab.plot(z[0, 0], v))
pylab.ylim(-0.1, 0.1)
def update(frame):
fluid_model_g.step()
G, X, Y, u, v, w = get_data()
print(fluid_model_g.t, abs(G).max(), abs(u).max())
plots[0].set_ydata(G)
plots[1].set_ydata(X)
plots[2].set_ydata(Y)
plots[3].set_ydata(u)
plots[4].set_ydata(v)
plots[4].set_ydata(w)
return plots
FuncAnimation(pylab.gcf(),
update,
frames=range(100),
init_func=lambda: plots,
blit=True,
repeat=True,
interval=20)
pylab.show()
else:
from datetime import datetime
from pathlib import Path
start = datetime.now()
num_steps = int(1.0 / dt)
print("Starting simulation {} steps at a time".format(num_steps))
path = Path("/tmp/model_g")
path.mkdir(exist_ok=True)
while True:
for _ in range(num_steps):
fluid_model_g.step()
print("Saving a snapshot into {}".format(path))
G, X, Y, (u, v, w) = fluid_model_g.numpy()
np.save(path / 'G.npy', G)
np.save(path / 'X.npy', X)
np.save(path / 'Y.npy', Y)
np.save(path / 'u.npy', u)
np.save(path / 'v.npy', v)
np.save(path / 'w.npy', w)
print("Saved everything")
wall_clock_time = (datetime.now() - start).total_seconds()
print("t={}, wall clock time={} s, efficiency={}".format(
fluid_model_g.t, wall_clock_time,
fluid_model_g.t / wall_clock_time))
print("max|G|={}, max|u|={}".format(abs(G).max(), abs(u).max()))