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

The Burgers equation by the discontinous Galerkin method.

The Burgers equation by the discontinous Galerkin method

#include "rheolef.h"
using namespace rheolef;
using namespace std;
#include "harten.h"
#include "burgers.icc"
int main(int argc, char**argv) {
environment rheolef (argc, argv);
geo omega (argv[1]);
space Xh (omega, argv[2]);
Float cfl = 1;
size_t nmax = (argc > 3) ? atoi(argv[3]) : numeric_limits<size_t>::max();
Float tf = (argc > 4) ? atof(argv[4]) : 2.5;
size_t p = (argc > 5) ? atoi(argv[5]) : ssp::pmax;
lopt.M = (argc > 6) ? atoi(argv[6]) : u_init().M();
if (nmax == numeric_limits<size_t>::max()) {
nmax = (size_t)floor(1+tf/(cfl*omega.hmin()));
}
Float delta_t = tf/nmax;
iopt.invert = true;
trial u (Xh); test v (Xh);
form inv_m = integrate (u*v, iopt);
vector<field> uh(p+1, field(Xh,0));
uh[0] = lazy_interpolate (Xh, u_init());
branch even("t","u");
dout << catchmark("delta_t") << delta_t << endl
<< even(0,uh[0]);
for (size_t n = 1; n <= nmax; ++n) {
for (size_t i = 1; i <= p; ++i) {
uh[i] = 0;
for (size_t j = 0; j < i; ++j) {
field lh =
- integrate (dot(compose(f,uh[j]),grad_h(v)))
+ integrate ("internal_sides",
compose (phi, normal(), inner(uh[j]), outer(uh[j]))*jump(v))
+ integrate ("boundary",
compose (phi, normal(), uh[j], g(n*delta_t))*v);
uh[i] += ssp::alpha[p][i][j]*uh[j] - delta_t*ssp::beta[p][i][j]*(inv_m*lh);
}
uh[i] = limiter(uh[i], g(n*delta_t)(point(-1)), lopt);
}
uh[0] = uh[p];
dout << even(n*delta_t,uh[0]);
}
}
The Burgers equation – the f function.
int main(int argc, char **argv)
Definition: burgers_dg.cc:32
u_exact g
u_exact u_init
field lh(Float epsilon, Float t, 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 point 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)
The Burgers problem: the Harten exact solution.
class rheolef::details::field_expr_v2_nonlinear_node_unary compose
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
Float beta[][pmax+1][pmax+1]
Float alpha[][pmax+1][pmax+1]
constexpr size_t pmax
STL namespace.
rheolef - reference manual
The strong stability preserving Runge-Kutta scheme – coefficients.
Definition: cavity_dg.h:29
Definition: sphere.icc:25
Definition: phi.h:25
see the limiter page for the full documentation
Definition: limiter.h:72
Float M() const
Definition: leveque.h:25