def linearized_manufactured_solution(
exact_solution, flux_function=None, diffusion_function=None, max_wavespeed=1.0
):
if flux_function is None:
flux_function = flux_functions.Identity()
if diffusion_function is None:
diffusion_function = flux_functions.Polynomial(degree=0)
# source_function could be computed with original diffusion function
# or with linearized diffusion function
# ? Would that make a difference?
source_function = ExactOperator(
exact_solution, flux_function, diffusion_function, flux_functions.Zero()
)
initial_condition = x_functions.FrozenT(exact_solution, 0.0)
linearized_diffusion_function = xt_functions.LinearizedAboutQ(
diffusion_function, exact_solution
)
problem = ConvectionDiffusion(
flux_function,
linearized_diffusion_function,
source_function,
initial_condition,
max_wavespeed,
)
problem.exact_solution = exact_solution
return problem
def linearized_manufactured_solution(
exact_solution, flux_function=None, diffusion_function=None, max_wavespeed=1.0
):
if flux_function is None:
flux_function = flux_functions.Identity()
if diffusion_function is None:
diffusion_function = flux_functions.Polynomial(degree=0)
source_function = ExactOperator(
exact_solution, flux_function, diffusion_function, flux_functions.Zero()
)
initial_condition = x_functions.FrozenT(exact_solution, 0.0)
linearized_diffusion_function = flux_functions.LinearizedAboutQ(
diffusion_function, exact_solution
)
problem = ConvectionHyperDiffusion(
flux_function,
linearized_diffusion_function,
source_function,
initial_condition,
max_wavespeed,
)
problem.exact_solution = exact_solution
return problem
def test_identity():
flux_function = flux_functions.Identity()
utils.check_to_from_dict(flux_function, flux_functions)
# should always give q back out
for q in range(-10, 10):
assert flux_function(q) == q
for x in range(-10, 10):
assert flux_function(q, x) == q
for t in range(-10, 10):
assert flux_function(q, x, t) == q
from pydogpack.basis import basis
from pydogpack.mesh import mesh
from pydogpack.mesh import boundary
from pydogpack.localdiscontinuousgalerkin import utils as ldg_utils
from pydogpack.solution import solution
from pydogpack.tests.utils import utils
from pydogpack.timestepping import time_stepping
from pydogpack.timestepping import implicit_runge_kutta
from pydogpack.utils import flux_functions
from pydogpack.utils import math_utils
from pydogpack.utils import x_functions
from pydogpack.visualize import plot
import numpy as np
identity = flux_functions.Identity()
squared = flux_functions.Polynomial(degree=2)
diffusion_functions = [identity, squared]
# (q q_x)_x
hyper_diffusion_identity = convection_hyper_diffusion.NonlinearHyperDiffusion(
identity)
# (q^2 q_x)_x
hyper_diffusion_squared = convection_hyper_diffusion.NonlinearHyperDiffusion(
squared)
test_problems = [hyper_diffusion_identity, hyper_diffusion_squared]
tolerance = 1e-5
def test_ldg_constant():
# LDG of one should be zero
t = 0.0