def u_0_function(x, jump=True):
if jump:
return 1. * (x <= 0.25)
return 0.5 * (1.0 +
np.cos(2.0 * np.pi * x)) * (0.0 <= x <= 0.5) + 0. * (x > 0.5)
grid = create_uniform_grid(GLOBAL_SPACE_GRID_SIZE)
space_time_grid = perform_tent_pitching(grid,
T_MAX,
characteristic_speed,
n_max=1000)
lambda_ = LOCAL_TIME_GRID_SIZE / LOCAL_SPACE_GRID_SIZE
numerical_flux = LaxFriedrichsFlux(linear_transport_flux,
linear_transport_flux_derivative, lambda_)
discretization = DiscontinuousGalerkin(numerical_flux, inverse_transformation,
LOCAL_SPACE_GRID_SIZE)
grid_operator = GridOperator(space_time_grid,
discretization,
DGFunction,
u_0_function,
TimeStepperType=RungeKutta4,
local_space_grid_size=LOCAL_SPACE_GRID_SIZE,
local_time_grid_size=LOCAL_TIME_GRID_SIZE)
fom = SpacetimeModel(grid_operator, inverse_transformation, n_x=N_X, n_t=N_T)
parameters = []
def inverse_transformation(u, phi_2, phi_2_dt, phi_2_dx, mu=1.):
return 2 * u / (1 + np.sqrt(1 - 2 * u * phi_2_dx * mu))
def u_0_function(x, jump=False):
if jump:
return 1. * (x <= 0.25)
return 0.5 * (1.0 + np.cos(2.0 * np.pi * x)) * (0.0 <= x <= 0.5) + 0. * (x > 0.5)
grid = create_uniform_grid(GLOBAL_SPACE_GRID_SIZE)
space_time_grid = perform_tent_pitching(grid, T_MAX, characteristic_speed, n_max=1000)
lambda_ = LOCAL_TIME_GRID_SIZE / LOCAL_SPACE_GRID_SIZE
numerical_flux = LaxFriedrichsFlux(burgers_flux, burgers_flux_derivative, lambda_)
discretization = DiscontinuousGalerkin(numerical_flux, inverse_transformation,
LOCAL_SPACE_GRID_SIZE)
grid_operator = GridOperator(space_time_grid, discretization, DGFunction, u_0_function,
TimeStepperType=RungeKutta4,
local_space_grid_size=LOCAL_SPACE_GRID_SIZE,
local_time_grid_size=LOCAL_TIME_GRID_SIZE)
fom = SpacetimeModel(grid_operator, inverse_transformation, n_x=N_X, n_t=N_T)
parameters = []
reference_parameter = 1.
gs_smoothing_params = {'alpha': 100., 'exponent': 3}