Rheolef  7.2
an efficient C++ finite element environment
burgers_diffusion_dg.cc

The diffusive Burgers equation by the discontinuous Galerkin method.

The diffusive Burgers equation by the discontinuous Galerkin method

#include "rheolef.h"
using namespace rheolef;
using namespace std;
#include "burgers.icc"
#undef NEUMANN
int main(int argc, char**argv) {
environment rheolef (argc, argv);
geo omega (argv[1]);
space Xh (omega, argv[2]);
size_t k = Xh.degree();
Float epsilon = (argc > 3) ? atof(argv[3]) : 0.1;
size_t nmax = (argc > 4) ? atoi(argv[4]) : 500;
Float tf = (argc > 5) ? atof(argv[5]) : 1;
size_t p = (argc > 6) ? atoi(argv[6]) : min(k+1,rk::pmax);
Float delta_t = tf/nmax;
size_t d = omega.dimension();
Float beta = (k+1)*(k+d)/Float(d);
trial u (Xh); test v (Xh);
form m = integrate (u*v);
iopt.invert = true;
form inv_m = integrate (u*v, iopt);
#ifdef NEUMANN
+ integrate ("internal_sides",
#else // NEUMANN
+ integrate ("sides",
#endif // NEUMANN
beta*penalty()*jump(u)*jump(v)
- jump(u)*average(dot(grad_h(v),normal()))
- jump(v)*average(dot(grad_h(u),normal()))));
vector<problem> pb (p+1);
for (size_t i = 1; i <= p; ++i) {
form ci = m + delta_t*rk::alpha[p][i][i]*a;
pb[i] = problem(ci);
}
vector<field> uh(p+1, field(Xh,0));
branch even("t","u");
dout << catchmark("epsilon") << epsilon << endl
<< even(0,uh[0]);
for (size_t n = 0; n < nmax; ++n) {
Float tn = n*delta_t;
Float t = tn + delta_t;
field uh_next = uh[0] - delta_t*rk::tilde_beta[p][0]*(inv_m*gh(epsilon, tn, uh[0], v));
for (size_t i = 1; i <= p; ++i) {
Float ti = tn + rk::gamma[p][i]*delta_t;
field rhs = m*uh[0] - delta_t*rk::tilde_alpha[p][i][0]*gh(epsilon, tn, uh[0], v);
for (size_t j = 1; j <= i-1; ++j) {
Float tj = tn + rk::gamma[p][j]*delta_t;
rhs -= delta_t*( rk::alpha[p][i][j]*(a*uh[j] - lh(epsilon,tj,v))
+ rk::tilde_alpha[p][i][j]*gh(epsilon, tj, uh[j], v));
}
rhs += delta_t*rk::alpha[p][i][i]*lh (epsilon, ti, v);
pb[i].solve (rhs, uh[i]);
uh_next -= delta_t*(inv_m*( rk::beta[p][i]*(a*uh[i] - lh(epsilon,ti,v))
+ rk::tilde_beta[p][i]*gh(epsilon, ti, uh[i], v)));
}
uh_next = limiter(uh_next);
dout << even(tn+delta_t,uh_next);
uh[0] = uh_next;
}
}
The Burgers equation – the f function.
int main(int argc, char **argv)
The diffusive Burgers equation – its exact solution.
u_exact u_init
The diffusive Burgers equation – operators.
field lh(Float epsilon, Float t, const test &v)
field gh(Float epsilon, Float t, const field &uh, const test &v)
The Burgers equation – the Godonov flux.
see the Float page for the full documentation
see the branch page for the full documentation
see the field page for the full documentation
see the form page for the full documentation
see the geo page for the full documentation
see the problem page for the full documentation
see the catchmark page for the full documentation
Definition: catchmark.h:67
see the environment page for the full documentation
Definition: environment.h:121
see the integrate_option page for the full documentation
see the space page for the full documentation
see the test page for the full documentation
see the test page for the full documentation
point u(const point &x)
rheolef::details::is_vec dot
This file is part of Rheolef.
field_basic< T, M > lazy_interpolate(const space_basic< T, M > &X2h, const field_basic< T, M > &u1h)
see the interpolate page for the full documentation
Definition: field.h:871
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
details::field_expr_v2_nonlinear_terminal_function< details::normal_pseudo_function< Float > > normal()
normal: see the expression page for the full documentation
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
field_basic< T, M > limiter(const field_basic< T, M > &uh, const T &bar_g_S, const limiter_option &opt)
see the limiter page for the full documentation
Definition: limiter.cc:65
details::field_expr_v2_nonlinear_terminal_function< details::penalty_pseudo_function< Float > > penalty()
penalty(): see the expression page for the full documentation
Float tilde_alpha[][pmax+1][pmax+1]
Float tilde_beta[][pmax+1]
Float gamma[][pmax+1]
Float beta[][pmax+1]
Float alpha[][pmax+1][pmax+1]
constexpr size_t pmax
STL namespace.
rheolef - reference manual
The semi-implicit Runge-Kutta scheme – coefficients.
Definition: sphere.icc:25
Definition: leveque.h:25
Float epsilon