def test_linearized_mms_ldg_convergence():
# LDG Diffusion should converge at 1st order for 1 basis_cpt
# or at num_basis_cpts - 2 for more basis_cpts
t = 0.0
bc = boundary.Periodic()
p_class = convection_hyper_diffusion.NonlinearHyperDiffusion
p_func = p_class.linearized_manufactured_solution
exact_solution = flux_functions.AdvectingSine(offset=2.0)
for diffusion_function in diffusion_functions:
problem = p_func(exact_solution, diffusion_function)
exact_time_derivative = problem.exact_time_derivative(
exact_solution, t)
for num_basis_cpts in [1] + list(range(5, 6)):
for basis_class in basis.BASIS_LIST:
error_list = []
basis_ = basis_class(num_basis_cpts)
# 10 and 20 elems maybe not in asymptotic regime yet
for num_elems in [20, 40]:
mesh_ = mesh.Mesh1DUniform(0.0, 1.0, num_elems)
dg_solution = basis_.project(exact_solution, mesh_, t)
L = problem.ldg_operator(dg_solution, t, bc, bc)
dg_error = math_utils.compute_dg_error(
L, exact_time_derivative)
error = dg_error.norm()
error_list.append(error)
# plot.plot_dg_1d(L, function=exact_time_derivative)
order = utils.convergence_order(error_list)
# if already at machine precision don't check convergence
if error_list[-1] > tolerance:
if num_basis_cpts == 1:
assert order >= 1
else:
assert order >= num_basis_cpts - 4
def test_ldg_polynomials_convergence():
# LDG Diffusion should converge at 1st order for 1 basis_cpt
# or at num_basis_cpts - 4 for more basis_cpts
bc = boundary.Extrapolation()
t = 0.0
for i in range(4, 7):
hyper_diffusion.initial_condition = x_functions.Polynomial(degree=i)
exact_solution = hyper_diffusion.exact_time_derivative(
hyper_diffusion.initial_condition, t)
for num_basis_cpts in [1] + list(range(5, i + 1)):
for basis_class in basis.BASIS_LIST:
error_list = []
basis_ = basis_class(num_basis_cpts)
for num_elems in [10, 20]:
mesh_ = mesh.Mesh1DUniform(0.0, 1.0, num_elems)
dg_solution = basis_.project(
hyper_diffusion.initial_condition, mesh_)
L = hyper_diffusion.ldg_operator(dg_solution, t, bc, bc,
bc, bc)
dg_error = math_utils.compute_dg_error(L, exact_solution)
error = dg_error.norm(slice(2, -2))
error_list.append(error)
# plot.plot_dg_1d(L, function=exact_solution, elem_slice=slice(1, -1))
order = utils.convergence_order(error_list)
# if already at machine precision don't check convergence
if error_list[-1] > tolerance:
if num_basis_cpts == 1:
assert order >= 1
else:
assert order >= num_basis_cpts - 4
def test_evaluate_weak_form():
periodic_bc = boundary.Periodic()
t = 0.0
for problem in test_problems:
exact_time_derivative = problem.exact_time_derivative
initial_time_derivative = x_functions.FrozenT(exact_time_derivative,
0.0)
riemann_solver = riemann_solvers.LocalLaxFriedrichs(problem)
for basis_class in basis.BASIS_LIST:
for num_basis_cpts in range(1, 4):
error_list = []
basis_ = basis_class(num_basis_cpts)
for num_elems in [20, 40]:
mesh_ = mesh.Mesh1DUniform(0.0, 1.0, num_elems)
dg_solution = basis_.project(initial_condition, mesh_)
result = dg_utils.evaluate_weak_form(
dg_solution, t, problem.app_.flux_function,
riemann_solver, periodic_bc,
problem.app_.nonconservative_function,
problem.app_.regularization_path,
problem.app_.source_function)
error = math_utils.compute_error(result,
initial_time_derivative)
error_list.append(error)
order = utils.convergence_order(error_list)
if num_basis_cpts == 1:
assert order >= 1
else:
assert order >= num_basis_cpts - 1
def test_ldg_cos():
# LDG Diffusion should converge at 1st order for 1 basis_cpt
# or at num_basis_cpts - 4 for more basis_cpts
t = 0.0
bc = boundary.Periodic()
for nonlinear_hyper_diffusion in [hyper_diffusion_identity]:
nonlinear_hyper_diffusion.initial_condition = x_functions.Cosine(
offset=2.0)
exact_solution = nonlinear_hyper_diffusion.exact_time_derivative(
nonlinear_hyper_diffusion.initial_condition, t)
for num_basis_cpts in [1] + list(range(5, 6)):
for basis_class in basis.BASIS_LIST:
error_list = []
basis_ = basis_class(num_basis_cpts)
for num_elems in [10, 20]:
mesh_ = mesh.Mesh1DUniform(0.0, 1.0, num_elems)
dg_solution = basis_.project(
nonlinear_hyper_diffusion.initial_condition, mesh_)
L = nonlinear_hyper_diffusion.ldg_operator(
dg_solution, t, bc, bc, bc, bc)
dg_error = math_utils.compute_dg_error(L, exact_solution)
error = dg_error.norm()
error_list.append(error)
# plot.plot_dg_1d(L, function=exact_solution)
order = utils.convergence_order(error_list)
# if already at machine precision don't check convergence
if error_list[-1] > tolerance:
if num_basis_cpts == 1:
assert order >= 1
else:
assert order >= num_basis_cpts - 4
def test_imex_linear_diffusion():
# advection with linear diffusion
# (q_t + q_x = q_xx + s(x, t))
exact_solution = xt_functions.AdvectingSine(offset=2.0)
problem = convection_diffusion.ConvectionDiffusion.manufactured_solution(
exact_solution)
t_initial = 0.0
bc = boundary.Periodic()
error_dict = dict()
cfl_list = [0.9, 0.3, 0.1]
for num_basis_cpts in range(1, 4):
imex = imex_runge_kutta.get_time_stepper(num_basis_cpts)
cfl = cfl_list[num_basis_cpts - 1]
# take 10 timesteps at coarsest time interval
n = 20
t_final = cfl * (1.0 / n) / exact_solution.wavespeed
exact_solution_final = lambda x: exact_solution(x, t_final)
for basis_class in basis.BASIS_LIST:
basis_ = basis_class(num_basis_cpts)
error_list = []
for num_elems in [n, 2 * n]:
mesh_ = mesh.Mesh1DUniform(0.0, 1.0, num_elems)
delta_t = cfl * mesh_.delta_x / exact_solution.wavespeed
dg_solution = basis_.project(problem.initial_condition, mesh_)
# weak dg form with flux_function and source term
explicit_operator = problem.get_explicit_operator(bc)
# ldg discretization of diffusion_function
implicit_operator = problem.get_implicit_operator(
bc, bc, include_source=False)
# this is a constant matrix case
(matrix, vector) = problem.ldg_matrix(dg_solution,
t_initial,
bc,
bc,
include_source=False)
solve_operator = time_stepping.get_solve_function_constant_matrix(
matrix, vector)
final_solution = time_stepping.time_step_loop_imex(
dg_solution,
t_initial,
t_final,
delta_t,
imex,
explicit_operator,
implicit_operator,
solve_operator,
)
dg_error = math_utils.compute_dg_error(final_solution,
exact_solution_final)
error = dg_error.norm()
error_list.append(error)
# plot.plot_dg_1d(final_solution, function=exact_solution_final)
# plot.plot_dg_1d(dg_error)
error_dict[num_basis_cpts] = error_list
order = utils.convergence_order(error_list)
assert order >= num_basis_cpts
def test_compute_error():
f = lambda x: np.cos(x)
for basis_class in basis.BASIS_LIST:
for num_basis_cpts in range(1, 3):
errorList = []
basis_ = basis_class(num_basis_cpts)
for num_elems in [10, 20]:
mesh_ = mesh.Mesh1DUniform(0.0, 1.0, num_elems)
dg_solution = basis_.project(f, mesh_)
error = math_utils.compute_error(dg_solution, f)
errorList.append(error)
order = utils.convergence_order(errorList)
assert order >= num_basis_cpts
def test_linearized_mms_ldg_irk():
# g = functions.Sine(offset=2.0)
# r = -1.0
# exact_solution = flux_functions.ExponentialFunction(g, r)
exact_solution = flux_functions.AdvectingSine(offset=2.0)
t_initial = 0.0
t_final = 0.1
exact_solution_final = lambda x: exact_solution(x, t_final)
bc = boundary.Periodic()
p_class = convection_hyper_diffusion.NonlinearHyperDiffusion
p_func = p_class.linearized_manufactured_solution
for diffusion_function in diffusion_functions:
problem = p_func(exact_solution, diffusion_function)
for num_basis_cpts in range(1, 3):
irk = implicit_runge_kutta.get_time_stepper(num_basis_cpts)
for basis_class in basis.BASIS_LIST:
basis_ = basis_class(num_basis_cpts)
error_list = []
for i in [1, 2]:
if i == 1:
delta_t = 0.01
num_elems = 20
else:
delta_t = 0.005
num_elems = 40
mesh_ = mesh.Mesh1DUniform(0.0, 1.0, num_elems)
dg_solution = basis_.project(problem.initial_condition,
mesh_)
# time_dependent_matrix time does matter
matrix_function = lambda t: problem.ldg_matrix(
dg_solution, t, bc, bc, bc, bc)
rhs_function = problem.get_implicit_operator(
bc, bc, bc, bc)
solve_function = time_stepping.get_solve_function_matrix(
matrix_function)
new_solution = time_stepping.time_step_loop_implicit(
dg_solution,
t_initial,
t_final,
delta_t,
irk,
rhs_function,
solve_function,
)
error = math_utils.compute_error(new_solution,
exact_solution_final)
error_list.append(error)
# plot.plot_dg_1d(new_solution, function=exact_solution_final)
order = utils.convergence_order(error_list)
assert order >= num_basis_cpts
def test_nonlinear_mms_ldg_irk():
exact_solution = flux_functions.AdvectingSine(amplitude=0.1, offset=0.15)
t_initial = 0.0
t_final = 0.1
exact_solution_final = lambda x: exact_solution(x, t_final)
bc = boundary.Periodic()
p_func = thin_film.ThinFilmDiffusion.manufactured_solution
problem = p_func(exact_solution)
for num_basis_cpts in range(1, 3):
irk = implicit_runge_kutta.get_time_stepper(num_basis_cpts)
cfl = 0.5
for basis_class in basis.BASIS_LIST:
basis_ = basis_class(num_basis_cpts)
error_list = []
n = 40
for num_elems in [n, 2 * n]:
mesh_ = mesh.Mesh1DUniform(0.0, 1.0, num_elems)
delta_t = cfl * mesh_.delta_x / exact_solution.wavespeed
dg_solution = basis_.project(problem.initial_condition, mesh_)
# time_dependent_matrix time does matter
matrix_function = lambda t, q: problem.ldg_matrix(q, t, bc, bc, bc, bc)
rhs_function = problem.get_implicit_operator(bc, bc, bc, bc)
solve_function = time_stepping.get_solve_function_picard(
matrix_function, num_basis_cpts, num_elems * num_basis_cpts
)
new_solution = time_stepping.time_step_loop_implicit(
dg_solution,
t_initial,
t_final,
delta_t,
irk,
rhs_function,
solve_function,
)
error = math_utils.compute_error(new_solution, exact_solution_final)
error_list.append(error)
# plot.plot_dg_1d(new_solution, function=exact_solution_final)
with open("thin_film_nonlinear_irk_test.yml", "a") as file:
dict_ = dict()
subdict = dict()
subdict["cfl"] = cfl
subdict["n"] = n
subdict["error0"] = float(error_list[0])
subdict["error1"] = float(error_list[1])
subdict["order"] = float(np.log2(error_list[0] / error_list[1]))
dict_[num_basis_cpts] = subdict
yaml.dump(dict_, file, default_flow_style=False)
order = utils.convergence_order(error_list)
assert order >= num_basis_cpts
def test_ldg_matrix_irk():
p_func = convection_hyper_diffusion.HyperDiffusion.periodic_exact_solution
problem = p_func(x_functions.Sine(offset=2.0), diffusion_constant=1.0)
t_initial = 0.0
t_final = 0.1
bc = boundary.Periodic()
exact_solution = lambda x: problem.exact_solution(x, t_final)
for num_basis_cpts in range(1, 3):
irk = implicit_runge_kutta.get_time_stepper(num_basis_cpts)
for basis_class in basis.BASIS_LIST:
basis_ = basis_class(num_basis_cpts)
error_list = []
# constant matrix
n = 20
for num_elems in [n, 2 * n]:
mesh_ = mesh.Mesh1DUniform(0.0, 1.0, num_elems)
delta_t = mesh_.delta_x / 5
dg_solution = basis_.project(problem.initial_condition, mesh_)
# constant matrix time doesn't matter
tuple_ = problem.ldg_matrix(dg_solution, t_initial, bc, bc, bc,
bc)
matrix = tuple_[0]
vector = tuple_[1]
rhs_function = problem.get_implicit_operator(bc, bc, bc, bc)
solve_function = time_stepping.get_solve_function_constant_matrix(
matrix, vector)
new_solution = time_stepping.time_step_loop_implicit(
dg_solution,
t_initial,
t_final,
delta_t,
irk,
rhs_function,
solve_function,
)
dg_error = math_utils.compute_dg_error(new_solution,
exact_solution)
error = dg_error.norm()
error_list.append(error)
# plot.plot_dg_1d(new_solution, function=exact_solution)
# plot.plot(dg_error)
order = utils.convergence_order(error_list)
# if not already at machine error
if error_list[0] > 1e-10 and error_list[1] > 1e-10:
assert order >= num_basis_cpts
def test_compute_quadrature_matrix():
squared = flux_functions.Polynomial(degree=2)
cubed = flux_functions.Polynomial(degree=3)
initial_condition = functions.Sine()
t = 0.0
x_left = 0.0
x_right = 1.0
for f in [squared, cubed]:
for basis_class in basis.BASIS_LIST:
for num_basis_cpts in range(1, 6):
error_list = []
basis_ = basis_class(num_basis_cpts)
for num_elems in [10, 20]:
mesh_ = mesh.Mesh1DUniform(x_left, x_right, num_elems)
dg_solution = basis_.project(initial_condition, mesh_)
quadrature_matrix = ldg_utils.compute_quadrature_matrix(
dg_solution, t, f)
result = solution.DGSolution(None, basis_, mesh_)
direct_quadrature = solution.DGSolution(
None, basis_, mesh_)
for i in range(mesh_.num_elems):
# compute value as B_i Q_i
result[i] = np.matmul(quadrature_matrix[i],
dg_solution[i])
# also compute quadrature directly
for l in range(basis_.num_basis_cpts):
quadrature_function = (lambda xi: f(
initial_condition(
mesh_.transform_to_mesh(xi, i)),
xi,
) * initial_condition(
mesh_.transform_to_mesh(xi, i)) * basis_.
derivative(xi, l))
direct_quadrature[i, l] = math_utils.quadrature(
quadrature_function, -1.0, 1.0)
# need to multiply by mass inverse
direct_quadrature[i] = np.matmul(
basis_.mass_matrix_inverse, direct_quadrature[i])
error = (result - direct_quadrature).norm()
error_list.append(error)
if error_list[-1] != 0.0:
order = utils.convergence_order(error_list)
assert order >= (num_basis_cpts - 1)
def test_ldg_matrix_irk():
diffusion = convection_diffusion.Diffusion.periodic_exact_solution()
t_initial = 0.0
t_final = 0.1
bc = boundary.Periodic()
basis_ = basis.LegendreBasis1D(1)
exact_solution = lambda x: diffusion.exact_solution(x, t_final)
for num_basis_cpts in range(1, 3):
irk = implicit_runge_kutta.get_time_stepper(num_basis_cpts)
for basis_class in basis.BASIS_LIST:
basis_ = basis_class(num_basis_cpts)
error_list = []
# constant matrix
for i in [1, 2]:
if i == 1:
delta_t = 0.01
num_elems = 20
else:
delta_t = 0.005
num_elems = 40
mesh_ = mesh.Mesh1DUniform(0.0, 1.0, num_elems)
dg_solution = basis_.project(diffusion.initial_condition,
mesh_)
# constant matrix time doesn't matter
tuple_ = diffusion.ldg_matrix(dg_solution, t_initial, bc, bc)
matrix = tuple_[0]
# vector = tuple_[1]
rhs_function = diffusion.get_implicit_operator(bc, bc)
solve_function = time_stepping.get_solve_function_constant_matrix(
matrix)
new_solution = time_stepping.time_step_loop_implicit(
dg_solution,
t_initial,
t_final,
delta_t,
irk,
rhs_function,
solve_function,
)
error = math_utils.compute_error(new_solution, exact_solution)
error_list.append(error)
order = utils.convergence_order(error_list)
assert order >= num_basis_cpts
def test_diffusion_ldg_polynomials_convergence():
# LDG Diffusion should converge at 1st order for 1 basis_cpt
# or at num_basis_cpts - 2 for more basis_cpts
bc = boundary.Extrapolation()
t = 0.0
for nonlinear_diffusion in test_problems:
d = nonlinear_diffusion.diffusion_function.degree
# having problems at i >= d with convergence rate
# still small error just not converging properly
# exact solution is grows rapidly as x increases in this situation
# error must larger at x = 1 then at x = 0
# could also not be in asymptotic regime
for i in range(1, d):
nonlinear_diffusion.initial_condition = x_functions.Polynomial(
degree=i)
exact_solution = nonlinear_diffusion.exact_time_derivative(
nonlinear_diffusion.initial_condition, t)
for num_basis_cpts in [1] + list(range(3, i + 1)):
for basis_class in basis.BASIS_LIST:
error_list = []
basis_ = basis_class(num_basis_cpts)
for num_elems in [30, 60]:
mesh_ = mesh.Mesh1DUniform(0.0, 1.0, num_elems)
dg_solution = basis_.project(
nonlinear_diffusion.initial_condition, mesh_)
L = nonlinear_diffusion.ldg_operator(
dg_solution, t, bc, bc)
dg_error = math_utils.compute_dg_error(
L, exact_solution)
error = dg_error.norm(slice(1, -1))
error_list.append(error)
# plot.plot_dg_1d(
# L, function=exact_solution, elem_slice=slice(1, -1)
# )
order = utils.convergence_order(error_list)
# if already at machine precision don't check convergence
if error_list[-1] > tolerance:
if num_basis_cpts == 1:
assert order >= 1
else:
assert order >= num_basis_cpts - 2
def test_advection_one_time_step():
def initial_condition(x):
return np.sin(2.0 * np.pi * x)
advection_ = advection.Advection(initial_condition=initial_condition)
riemann_solver = riemann_solvers.LocalLaxFriedrichs(
advection_.flux_function, advection_.wavespeed_function
)
explicit_time_stepper = explicit_runge_kutta.ForwardEuler()
boundary_condition = boundary.Periodic()
cfl = 1.0
for basis_class in basis.BASIS_LIST:
basis_ = basis_class(1)
error_list = []
for num_elems in [20, 40]:
mesh_ = mesh.Mesh1DUniform(0.0, 1.0, num_elems)
dg_solution = basis_.project(advection_.initial_condition, mesh_)
delta_t = dg_utils.get_delta_t(cfl, advection_.wavespeed, mesh_.delta_x)
time_initial = 0.0
time_final = delta_t
rhs_function = lambda time, q: dg_utils.dg_weak_formulation(
q, advection_.flux_function, riemann_solver, boundary_condition
)
final_solution = time_stepping.time_step_loop_explicit(
dg_solution,
time_initial,
time_final,
delta_t,
explicit_time_stepper,
rhs_function,
)
error = math_utils.compute_error(
final_solution, lambda x: advection_.exact_solution(x, time_final)
)
error_list.append(error)
order = utils.convergence_order(error_list)
assert order >= 1
def test_advection_operator():
# test that dg_operator acting on projected initial condition converges to
# exact time derivative
# will lose one order of accuracy
for i in range(2):
if i == 0:
sin = x_functions.Sine()
cos = x_functions.Cosine()
initial_condition = x_functions.ComposedVector([sin, cos])
else:
initial_condition = x_functions.Sine()
wavespeed = 1.0
exact_solution = advection.ExactSolution(initial_condition, wavespeed)
exact_time_derivative = advection.ExactTimeDerivative(exact_solution, wavespeed)
initial_time_derivative = x_functions.FrozenT(exact_time_derivative, 0.0)
app_ = advection.Advection(wavespeed)
riemann_solver = riemann_solvers.LocalLaxFriedrichs(app_.flux_function)
boundary_condition = boundary.Periodic()
for basis_class in basis.BASIS_LIST:
for num_basis_cpts in range(1, 5):
basis_ = basis_class(num_basis_cpts)
error_list = []
for num_elems in [20, 40]:
mesh_ = mesh.Mesh1DUniform(0.0, 1.0, num_elems)
dg_sol = basis_.project(initial_condition, mesh_)
dg_operator = app_.get_explicit_operator(
riemann_solver, boundary_condition
)
F = dg_operator(0.0, dg_sol)
error = math_utils.compute_error(F, initial_time_derivative)
error_list.append(error)
order = utils.convergence_order(error_list)
assert order >= max([1.0, num_basis_cpts - 1])
def test_ldg_polynomials_convergence():
# LDG Diffusion should converge at 1st order for 1 basis_cpt
# or at num_basis_cpts - 4 for more basis_cpts
bc = boundary.Extrapolation()
t = 0.0
# having problems at i >= 3 with convergence rate
# still small error just not converging properly
for i in range(3, 5):
thin_film_diffusion.initial_condition = x_functions.Polynomial(degree=i)
thin_film_diffusion.initial_condition.set_coeff((1.0 / i), i)
exact_solution = thin_film_diffusion.exact_time_derivative(
thin_film_diffusion.initial_condition, t
)
for num_basis_cpts in [1] + list(range(5, 6)):
for basis_class in basis.BASIS_LIST:
error_list = []
basis_ = basis_class(num_basis_cpts)
for num_elems in [40, 80]:
mesh_ = mesh.Mesh1DUniform(0.0, 1.0, num_elems)
dg_solution = basis_.project(
thin_film_diffusion.initial_condition, mesh_
)
L = thin_film_diffusion.ldg_operator(dg_solution, t, bc, bc, bc, bc)
dg_error = math_utils.compute_dg_error(L, exact_solution)
error = dg_error.norm(slice(2, -2))
error_list.append(error)
# plot.plot_dg_1d(
# L, function=exact_solution, elem_slice=slice(1, -1)
# )
order = utils.convergence_order(error_list)
# if already at machine precision don't check convergence
if error_list[-1] > tolerance and error_list[0] > tolerance:
if num_basis_cpts == 1:
assert order >= 1
else:
assert order >= num_basis_cpts - 4
def test_dg_operator():
# test that dg_operator converges to exact_time_derivative in smooth case
initial_condition = x_functions.Sine(offset=2.0)
max_wavespeed = 3.0
problem = smooth_example.SmoothExample(initial_condition, max_wavespeed)
riemann_solver = riemann_solvers.LocalLaxFriedrichs(problem)
boundary_condition = boundary.Periodic()
x_left = 0.0
x_right = 1.0
exact_time_derivative = burgers.ExactTimeDerivative(
problem.initial_condition)
exact_time_derivative_initial = x_functions.FrozenT(
exact_time_derivative, 0.0)
for basis_class in basis.BASIS_LIST:
for num_basis_cpts in range(1, 5):
basis_ = basis_class(num_basis_cpts)
error_list = []
for num_elems in [40, 80]:
mesh_ = mesh.Mesh1DUniform(x_left, x_right, num_elems)
dg_solution = basis_.project(problem.initial_condition, mesh_)
explicit_operator = problem.app_.get_explicit_operator(
riemann_solver, boundary_condition)
dg_time_derivative = explicit_operator(0.0, dg_solution)
error = math_utils.compute_error(
dg_time_derivative, exact_time_derivative_initial)
error_list.append(error)
order = test_utils.convergence_order(error_list)
if num_basis_cpts > 1:
assert order >= num_basis_cpts - 1
else:
assert order >= 1
def test_imex_nonlinear_mms():
wavenumber = 1.0 / 20.0
x_left = 0.0
x_right = 40.0
exact_solution = flux_functions.AdvectingSine(
amplitude=0.1, wavenumber=wavenumber, offset=0.15
)
p_func = thin_film.ThinFilm.manufactured_solution
t_initial = 0.0
bc = boundary.Periodic()
problem = p_func(exact_solution)
cfl_list = [0.5, 0.1, 0.1]
n = 40
for num_basis_cpts in range(3, 4):
imex = imex_runge_kutta.get_time_stepper(num_basis_cpts)
cfl = cfl_list[num_basis_cpts - 1]
t_final = 10 * cfl * ((x_right - x_left) / n) / exact_solution.wavespeed
exact_solution_final = lambda x: exact_solution(x, t_final)
for basis_class in [basis.LegendreBasis1D]:
basis_ = basis_class(num_basis_cpts)
error_list = []
for num_elems in [n, 2 * n]:
mesh_ = mesh.Mesh1DUniform(x_left, x_right, num_elems)
delta_t = cfl * mesh_.delta_x / exact_solution.wavespeed
dg_solution = basis_.project(problem.initial_condition, mesh_)
# weak dg form with flux_function and source term
explicit_operator = problem.get_explicit_operator(bc)
# ldg discretization of diffusion_function
implicit_operator = problem.get_implicit_operator(
bc, bc, bc, bc, include_source=False
)
matrix_function = lambda t, q: problem.ldg_matrix(
q, t, bc, bc, bc, bc, include_source=False
)
solve_operator = time_stepping.get_solve_function_picard(
matrix_function, num_basis_cpts, num_elems * num_basis_cpts
)
final_solution = time_stepping.time_step_loop_imex(
dg_solution,
t_initial,
t_final,
delta_t,
imex,
explicit_operator,
implicit_operator,
solve_operator,
)
error = math_utils.compute_error(final_solution, exact_solution_final)
error_list.append(error)
# plot.plot_dg_1d(final_solution, function=exact_solution_final)
with open("thin_film_nonlinear_mms_test.yml", "a") as file:
dict_ = dict()
subdict = dict()
subdict["cfl"] = cfl
subdict["n"] = n
subdict["error0"] = float(error_list[0])
subdict["error1"] = float(error_list[1])
subdict["order"] = float(np.log2(error_list[0] / error_list[1]))
dict_[num_basis_cpts] = subdict
yaml.dump(dict_, file, default_flow_style=False)
order = utils.convergence_order(error_list)
assert order >= num_basis_cpts
def test_imex_linearized_mms():
# advection with linearized diffusion
# (q_t + q_x = (f(x, t) q_xx + s(x, t))
exact_solution = flux_functions.AdvectingSine(amplitude=0.1, offset=0.15)
p_class = convection_hyper_diffusion.ConvectionHyperDiffusion
p_func = p_class.linearized_manufactured_solution
t_initial = 0.0
bc = boundary.Periodic()
for diffusion_function in [squared]:
problem = p_func(exact_solution, None, diffusion_function)
cfl_list = [0.9, 0.15, 0.1]
for num_basis_cpts in range(2, 4):
imex = imex_runge_kutta.get_time_stepper(num_basis_cpts)
cfl = cfl_list[num_basis_cpts - 1]
n = 20
t_final = cfl * (1.0 / n) / exact_solution.wavespeed
exact_solution_final = lambda x: exact_solution(x, t_final)
for basis_class in [basis.LegendreBasis1D]:
basis_ = basis_class(num_basis_cpts)
error_list = []
for num_elems in [n, 2 * n]:
mesh_ = mesh.Mesh1DUniform(0.0, 1.0, num_elems)
delta_t = cfl * mesh_.delta_x / exact_solution.wavespeed
dg_solution = basis_.project(problem.initial_condition,
mesh_)
# weak dg form with flux_function and source term
explicit_operator = problem.get_explicit_operator(bc)
# ldg discretization of diffusion_function
implicit_operator = problem.get_implicit_operator(
bc, bc, bc, bc, include_source=False)
# this is a constant matrix case
matrix_function = lambda t: problem.ldg_matrix(
dg_solution, t, bc, bc, bc, bc, include_source=False)
solve_operator = time_stepping.get_solve_function_matrix(
matrix_function)
final_solution = time_stepping.time_step_loop_imex(
dg_solution,
t_initial,
t_final,
delta_t,
imex,
explicit_operator,
implicit_operator,
solve_operator,
)
error = math_utils.compute_error(final_solution,
exact_solution_final)
error_list.append(error)
# plot.plot_dg_1d(final_solution, function=exact_solution_final)
order = utils.convergence_order(error_list)
with open("hyper_diffusion_linearized_mms_test.yml",
"a") as file:
dict_ = dict()
subdict = dict()
subdict["cfl"] = cfl
subdict["n"] = n
subdict["error0"] = float(error_list[0])
subdict["error1"] = float(error_list[1])
subdict["order"] = float(
np.log2(error_list[0] / error_list[1]))
dict_[num_basis_cpts] = subdict
yaml.dump(dict_, file, default_flow_style=False)
assert order >= num_basis_cpts
