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transport_tensor_dg.cc

The tensorial transport benchmark by the discontinuous Galerkin method.

The tensorial transport benchmark by the discontinuous Galerkin method

#include "rheolef.h"
using namespace rheolef;
using namespace std;
#include "transport_tensor_exact.icc"
int main(int argc, char**argv) {
environment rheolef (argc, argv);
geo omega (argv[1]);
space Xh (omega, argv[2], "tensor");
Float alpha = (argc > 3) ? atof(argv[3]) : 1;
Float nu = (argc > 4) ? atof(argv[4]) : 3;
Float t0 = (argc > 5) ? atof(argv[5]) : acos(-1.)/8;
Float a = 0;
trial sigma (Xh); test tau (Xh);
tensor ma = 0.5*((1-a)*grad_u - (1+a)*trans(grad_u));
auto beta_a = sigma*ma + trans(ma)*sigma;
form ah = integrate (ddot(grad_h(sigma)*u + beta_a + nu*sigma,tau))
+ integrate ("boundary",
max(0, -dot(u,normal()))*ddot(sigma,tau))
+ integrate ("internal_sides",
- dot(u,normal())*ddot(jump(sigma),average(tau))
+ 0.5*alpha*abs(dot(u,normal()))
*ddot(jump(sigma),jump(tau)));
field lh = integrate (ddot(chi(nu,t0),tau))
+ integrate ("boundary",
max(0, -dot(u,normal()))*ddot(sigma_g(nu,t0),tau));
field sigma_h(Xh);
problem p (ah);
p.solve (lh, sigma_h);
dout << catchmark("nu") << nu << endl
<< catchmark("t0") << t0 << endl
<< catchmark("sigma") << sigma_h;
}
lh
field lh(Float epsilon, Float t, const test &v)
Definition burgers_diffusion_operators.icc:25
Float
see the Float page for the full documentation
field
see the field page for the full documentation
form
see the form page for the full documentation
geo
see the geo page for the full documentation
problem
see the problem page for the full documentation
rheolef::catchmark
see the catchmark page for the full documentation
Definition catchmark.h:67
rheolef::environment
see the environment page for the full documentation
Definition environment.h:121
space
see the space page for the full documentation
tensor
see the tensor page for the full documentation
test
see the test page for the full documentation
trial
see the test page for the full documentation
sigma_g
sigma_exact sigma_g
Definition diffusion_tensor_exact.icc:50
main
int main()
Definition field2bb.cc:58
rheolef
This file is part of Rheolef.
Definition compiler_eigen.h:39
rheolef::ddot
T ddot(const tensor_basic< T > &a, const tensor_basic< T > &b)
ddot(x,y): see the expression page for the full documentation
Definition tensor.cc:278
rheolef::grad_h
std::enable_if< details::has_field_rdof_interface< Expr >::value, details::field_expr_v2_nonlinear_terminal_field< typenameExpr::scalar_type, typenameExpr::memory_type, details::differentiate_option::gradient > >::type grad_h(const Expr &expr)
grad_h(uh): see the expression page for the full documentation
Definition field_expr_terminal.h:968
rheolef::normal
details::field_expr_v2_nonlinear_terminal_function< details::normal_pseudo_function< Float > > normal()
normal: see the expression page for the full documentation
Definition field_expr_terminal.h:432
rheolef::integrate
std::enable_if< details::is_field_expr_v2_nonlinear_arg< Expr >::value &&!is_undeterminated< Result >::value, Result >::type integrate(const geo_basic< T, M > &omega, const Expr &expr, const integrate_option &iopt, Result dummy=Result())
see the integrate page for the full documentation
Definition integrate.h:211
rheolef::trans
csr< T, sequential > trans(const csr< T, sequential > &a)
trans(a): see the form page for the full documentation
Definition csr.h:455
rheolef::dot
rheolef::std::enable_if< details::is_vec_expr_v2_arg< Expr1 >::value &&details::is_vec_expr_v2_arg< Expr2 >::value, promote< Expr1::float_type, Expr2::float_type >::type > type dot const Expr1 expr1, const Expr2 expr2 dot(const Expr1 &expr1, const Expr2 &expr2)
Definition vec_expr_v2.h:415
std
STL namespace.
rheolef.h
rheolef - reference manual
chi
Definition diffusion_tensor_exact.icc:38
grad_u
Definition combustion_exact.icc:34
nu
Definition nu.h:26
p
Definition sphere.icc:25
sigma
Definition mosolov_exact_circle.h:40
u
Definition leveque.h:25
transport_tensor_exact.icc
The tensorial transport benchmark – right-hand-side and exact solution.