def bump_const_inflow_pressure_speed_outflow(Nx=49,
Ny=17,
num_timesteps=10,
dt=0.1):
X, Y = get_bump_grid(N)
grid = MultiblockGrid([(X, Y)])
sbp = MultiblockSBP(grid, accuracy=2)
initu = np.array([np.ones(X.shape)])
initv = np.array([np.zeros(X.shape)])
initp = np.array([np.ones(X.shape)])
plt.quiver(X, Y, initu[0], initv[0])
plt.show()
def spatial_op(state):
S,J = euler_operator(sbp, state) + \
inflow_operator(sbp, state, 0, 'w', -1, 0) + \
outflow_operator(sbp, state, 0, 'e') + \
wall_operator(sbp, state, 0, 's') + \
wall_operator(sbp, state, 0, 'n')
return S, J
U, V, P = solve(grid, spatial_op, initu, initv, initp, dt, num_timesteps)
return grid, U, V, P, dt
def circle_sector_cavity_flow(N=40,
num_timesteps=30,
dt=0.1,
angle=0.5 * np.pi):
(X, Y) = get_circle_sector_grid(N, 0.0, angle, 0.2, 1.0)
grid = MultiblockGrid([(X, Y)])
sbp = MultiblockSBP(grid, accuracy=2)
initu, initv, initp = get_gauss_initial_data(X, Y, 0.4, 0.4)
plt.quiver(X, Y, initu[0], initv[0])
plt.show()
def spatial_op(state):
S,J = euler_operator(sbp, state) + \
wall_operator(sbp, state, 0, 'w') + \
wall_operator(sbp, state, 0, 'e') + \
wall_operator(sbp, state, 0, 's') + \
wall_operator(sbp, state, 0, 'n')
return S, J
U, V, P = solve(grid, spatial_op, initu, initv, initp, dt, num_timesteps)
return grid, U, V, P, dt
def square_pressure_speed_outflow_everywhere(N=30, num_timesteps=10, dt=0.1):
(X, Y) = np.meshgrid(np.linspace(0, 1, N), np.linspace(0, 1, N))
X = np.transpose(X)
Y = np.transpose(Y)
grid = MultiblockGrid([(X, Y)])
sbp = MultiblockSBP(grid, accuracy=2)
initu, initv, initp = get_gauss_initial_data(X, Y, 0.5, 0.5)
plt.quiver(X, Y, initu[0], initv[0])
plt.show()
def spatial_op(state):
S,J = euler_operator(sbp, state) + \
outflow_operator(sbp, state, 0, 'w') + \
outflow_operator(sbp, state, 0, 'e') + \
outflow_operator(sbp, state, 0, 's') + \
outflow_operator(sbp, state, 0, 'n')
return S, J
U, V, P = solve(grid, spatial_op, initu, initv, initp, dt, num_timesteps)
return grid, U, V, P, dt
def bump_walls_and_pressure_speed_outflow(Nx=49,
Ny=17,
num_timesteps=10,
dt=0.1):
X, Y = get_bump_grid(N)
grid = MultiblockGrid([(X, Y)])
sbp = MultiblockSBP(grid, accuracy=2)
initu, initv, initp = get_gauss_initial_data(X, Y, -0.5, 0.4)
plt.quiver(X, Y, initu[0], initv[0])
plt.show()
def spatial_op(state):
S,J = euler_operator(sbp, state) + \
wall_operator(sbp, state, 0, 'w') + \
outflow_operator(sbp, state, 0, 'e') + \
wall_operator(sbp, state, 0, 's') + \
wall_operator(sbp, state, 0, 'n')
return S, J
U, V, P = solve(grid, spatial_op, initu, initv, initp, dt, num_timesteps)
return grid, U, V, P, dt
class TestJacobians(unittest.TestCase):
(X, Y) = get_circle_sector_grid(3, 0.0, 3.14 / 2, 0.2, 1.0)
grid = MultiblockGrid([(X, Y)])
sbp = MultiblockSBP(grid)
U = X
V = Y
P = X**2 + Y**2
state = np.array([U, V, P]).flatten()
def test_euler_jacobian(self):
S, J = euler_operator(self.sbp, self.state)
for i, grad in enumerate(J):
f = lambda x: euler_operator(self.sbp, x)[0][i]
grad_approx = approx_fprime(self.state, f, 1e-8)
grad_exact = J[i, :]
err = np.linalg.norm(grad_approx - grad_exact, ord=np.inf)
print("Euler OP, Gradient error = {:.2e}".format(err))
self.assertTrue(err < 1e-5)
def test_wall_jacobian(self):
S, J = wall_operator(self.sbp, self.state, 0, 'w')
J = J.todense()
for i, grad in enumerate(J):
f = lambda x: wall_operator(self.sbp, x, 0, 'w')[0][i]
grad_approx = approx_fprime(self.state, f, 1e-8)
grad_exact = J[i, :]
err = np.linalg.norm(grad_approx - grad_exact, ord=np.inf)
print("Wall SAT, Gradient error = {:.2e}".format(err))
self.assertTrue(err < 1e-5)
def test_pressure_jacobian(self):
S, J = pressure_operator(self.sbp, self.state, 0, 'w')
J = J.todense()
for i, grad in enumerate(J):
f = lambda x: pressure_operator(self.sbp, x, 0, 'w')[0][i]
grad_approx = approx_fprime(self.state, f, 1e-8)
grad_exact = J[i, :]
err = np.linalg.norm(grad_approx - grad_exact, ord=np.inf)
print("Pressure SAT, Gradient error = {:.2e}".format(err))
self.assertTrue(err < 1e-5)
def test_inflow_jacobian(self):
S, J = inflow_operator(self.sbp, self.state, 0, 'w', -1, 1)
J = J.todense()
for i, grad in enumerate(J):
f = lambda x: inflow_operator(self.sbp, x, 0, 'w', -1, 1)[0][i]
grad_approx = approx_fprime(self.state, f, 1e-8)
grad_exact = J[i, :]
err = np.linalg.norm(grad_approx - grad_exact, ord=np.inf)
print("Inflow SAT, Gradient error = {:.2e}".format(err))
self.assertTrue(err < 1e-5)
def test_outflow_jacobian(self):
S, J = outflow_operator(self.sbp, self.state, 0, 'w')
J = J.todense()
for i, grad in enumerate(J):
f = lambda x: outflow_operator(self.sbp, x, 0, 'w')[0][i]
grad_approx = approx_fprime(self.state, f, 1e-8)
grad_exact = J[i, :]
err = np.linalg.norm(grad_approx - grad_exact, ord=np.inf)
print("Outflow SAT, Gradient error = {:.2e}".format(err))
self.assertTrue(err < 1e-5)