def test_transport_rectangle_zero_source(self):
m, n = 5, 100
v = np.zeros((m, n))
# Define mesh.
mesh = UnitIntervalMesh(n - 1)
# Define function spaces
V = FunctionSpace(mesh, 'CG', 1)
f0 = Rectangle(degree=1)
f0 = interpolate(f0, V)
f0 = f0.vector().get_local()
# Create source.
src = np.tile(f0, (m, 1))
# Compute transport
f = transport1d(v, src, f0)
fig, ax = plt.subplots(figsize=(10, 5))
cax = ax.imshow(f, cmap=cm.coolwarm)
fig.colorbar(cax, orientation='vertical')
plt.show()
plt.close(fig)
np.testing.assert_equal(f.shape, (m + 1, n))
def test_transport_rectangle_zero(self):
m, n = 5, 50
v = np.zeros((m, n))
# Define mesh.
mesh = UnitIntervalMesh(n - 1)
# Define function spaces
V = FunctionSpace(mesh, 'CG', 1)
f0 = Rectangle(degree=1)
f0 = interpolate(f0, V)
f0 = f0.vector().get_local()
# Compute transport
f = transport1d(v, np.zeros_like(v), f0)
fig = plt.figure()
plt.imshow(f, cmap=cm.coolwarm)
plt.show()
plt.close(fig)
np.testing.assert_equal(f.shape, (m + 1, n))
np.testing.assert_allclose(f,
np.tile(f0, (m + 1, 1)),
atol=1e-6,
rtol=1e-6)
def test_transport_hat_source(self):
m, n = 10, 100
v = 0.1 * np.ones((m, n))
# Define mesh and function space.
mesh = UnitIntervalMesh(n - 1)
V = FunctionSpace(mesh, 'CG', 1)
# Define initial condition.
f0 = Hat(degree=1)
f0 = interpolate(f0, V)
# Compute transport
f = transport1d(v, np.zeros_like(v), f0.vector().get_local())
np.testing.assert_equal(f.shape, (m + 1, n))
# Compute transport with f as source.
f = transport1d(v, f[:-1], f0.vector().get_local())
fig, ax = plt.subplots(figsize=(10, 5))
cax = ax.imshow(f, cmap=cm.coolwarm)
fig.colorbar(cax, orientation='vertical')
plt.show()
plt.close(fig)
def test_transport_hat_zero(self):
m, n = 10, 100
v = np.zeros((m, n))
# Define mesh and function space.
mesh = UnitIntervalMesh(n - 1)
V = FunctionSpace(mesh, 'CG', 1)
# Define initial condition.
f0 = Hat(degree=1)
f0 = interpolate(f0, V)
# Compute transport
f = transport1d(v, np.zeros_like(v), f0.vector().get_local())
finit = f0.vector().get_local().reshape(1, n)
np.testing.assert_equal(f.shape, (m + 1, n))
np.testing.assert_allclose(f, np.tile(finit, (m + 1, 1)), atol=1e-3)
def test_transport_hat(self):
m, n = 10, 100
v = 0.1 * np.ones((m, n))
# Define mesh and function space.
mesh = UnitIntervalMesh(n - 1)
V = FunctionSpace(mesh, 'CG', 1)
# Define initial condition.
f0 = Hat(degree=1)
f0 = interpolate(f0, V)
# Compute transport
f = transport1d(v, np.zeros_like(v), f0.vector().get_local())
np.testing.assert_equal(f.shape, (m + 1, n))
fig = plt.figure()
plt.imshow(f, cmap=cm.coolwarm)
plt.show()
plt.close(fig)
class InitialData(UserExpression):
def eval(self, value, x):
value[0] = stats.uniform.pdf(x[0], 0, 1) \
+ (1 + math.sin(40 * x[0] + math.cos(40 * x[0]))) / 10
def value_shape(self):
return ()
f0 = DoubleHat(degree=1)
# f0 = InitialData(degree=1)
f0 = interpolate(f0, V)
# Compute transport
f = transport1d(v, np.zeros_like(v), f0.vector().get_local())
# Normalise to [0, 1].
f = np.array(f, dtype=float)
f = (f - f.min()) / (f.max() - f.min())
# Add some noise.
# f = f + 0.05 * np.random.randn(m + 1, n)
# Check continuity equation for rho.
def flux(v, f):
return f * v
fv = np.array([flux(a, b) for a, b in zip(v, f)])