def take_time_step(self, solver):
physics = solver.physics
mesh = solver.mesh
U = solver.state_coeffs
res = self.res
# First stage
res = solver.get_residual(U, res)
dU1 = solver_tools.mult_inv_mass_matrix(mesh, solver, self.dt, res)
Utemp = U + 0.5 * dU1
solver.apply_limiter(Utemp)
# Second stage
solver.time += self.dt / 2.
res = solver.get_residual(Utemp, res)
dU2 = solver_tools.mult_inv_mass_matrix(mesh, solver, self.dt, res)
Utemp = U + 0.5 * dU2
solver.apply_limiter(Utemp)
# Third stage
res = solver.get_residual(Utemp, res)
dU3 = solver_tools.mult_inv_mass_matrix(mesh, solver, self.dt, res)
Utemp = U + dU3
solver.apply_limiter(Utemp)
# Fourth stage
solver.time += self.dt / 2.
res = solver.get_residual(Utemp, res)
dU4 = solver_tools.mult_inv_mass_matrix(mesh, solver, self.dt, res)
dU = 1. / 6. * (dU1 + 2. * dU2 + 2. * dU3 + dU4)
U += dU
solver.apply_limiter(U)
return res # [num_elems, nb, ns]
def take_time_step(self, solver):
physics = solver.physics
mesh = solver.mesh
U = solver.state_coeffs
res = self.res
res = solver.get_residual(U, res)
dU = solver_tools.mult_inv_mass_matrix(mesh, solver, self.dt, res)
U += dU
solver.apply_limiter(U)
return res # [num_elems, nb, ns]
def take_time_step(self, solver):
mesh = solver.mesh
U = solver.state_coeffs
res = self.res
res = solver.get_residual(U, res)
dU = mult_inv_mass_matrix(mesh, solver, self.dt, res)
A, iA = self.get_jacobian_matrix(mesh, solver)
res = np.einsum('ijkll, ijl -> ikl', A, U) + dU
U = np.einsum('ijkll, ijl -> ikl', iA, res)
solver.apply_limiter(U)
solver.state_coeffs = U
return res # [ne, nb, ns]
def take_time_step(self, solver):
physics = solver.physics
mesh = solver.mesh
W = solver.state_coeffs
Up = solver.state_coeffs_pred
res = self.res
# Prediction step
Up = solver.calculate_predictor_step(solver, self.dt, W, Up)
# Correction step
res = solver.get_residual(Up, res)
dU = solver_tools.mult_inv_mass_matrix(mesh, solver, self.dt / 2., res)
W += dU
solver.apply_limiter(W)
solver.state_coeffs_pred = Up
return res # [num_elems, nb, ns]
def take_time_step(self, solver):
physics = solver.physics
mesh = solver.mesh
U = solver.state_coeffs
res = self.res
dU = self.dU
Time = solver.time
for istage in range(self.nstages):
dt = self.dt
res = solver.get_residual(U, res)
dUtemp = solver_tools.mult_inv_mass_matrix(mesh, solver, dt, res)
solver.time = Time + dt
dU *= self.ssprk3a[istage]
dU += dUtemp
U += self.ssprk3b[istage] * dU
solver.apply_limiter(U)
return res # [num_elems, nb, ns]