Rheolef  7.2
an efficient C++ finite element environment
 
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burgers_dg.cc
Go to the documentation of this file.
1
25#include "rheolef.h"
26using namespace rheolef;
27using namespace std;
28#include "harten.h"
29#include "burgers.icc"
31#include "runge_kutta_ssp.icc"
32int main(int argc, char**argv) {
33 environment rheolef (argc, argv);
34 geo omega (argv[1]);
35 space Xh (omega, argv[2]);
36 Float cfl = 1;
37 limiter_option lopt;
38 size_t nmax = (argc > 3) ? atoi(argv[3]) : numeric_limits<size_t>::max();
39 Float tf = (argc > 4) ? atof(argv[4]) : 2.5;
40 size_t p = (argc > 5) ? atoi(argv[5]) : ssp::pmax;
41 lopt.M = (argc > 6) ? atoi(argv[6]) : u_init().M();
42 if (nmax == numeric_limits<size_t>::max()) {
43 nmax = (size_t)floor(1+tf/(cfl*omega.hmin()));
44 }
45 Float delta_t = tf/nmax;
47 iopt.invert = true;
48 trial u (Xh); test v (Xh);
49 form inv_m = integrate (u*v, iopt);
50 vector<field> uh(p+1, field(Xh,0));
51 uh[0] = lazy_interpolate (Xh, u_init());
52 branch even("t","u");
53 dout << catchmark("delta_t") << delta_t << endl
54 << even(0,uh[0]);
55 for (size_t n = 1; n <= nmax; ++n) {
56 for (size_t i = 1; i <= p; ++i) {
57 uh[i] = 0;
58 for (size_t j = 0; j < i; ++j) {
59 field lh =
60 - integrate (dot(compose(f,uh[j]),grad_h(v)))
61 + integrate ("internal_sides",
62 compose (phi, normal(), inner(uh[j]), outer(uh[j]))*jump(v))
63 + integrate ("boundary",
64 compose (phi, normal(), uh[j], g(n*delta_t))*v);
65 uh[i] += ssp::alpha[p][i][j]*uh[j] - delta_t*ssp::beta[p][i][j]*(inv_m*lh);
66 }
67 uh[i] = limiter(uh[i], g(n*delta_t)(point(-1)), lopt);
68 }
69 uh[0] = uh[p];
70 dout << even(n*delta_t,uh[0]);
71 }
72}
The Burgers equation – the f function.
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
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
int main()
Definition field2bb.cc:58
The Burgers problem: the Harten exact solution.
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
rheolef::std enable_if ::type dot const Expr1 expr1, const Expr2 expr2 dot(const Expr1 &expr1, const Expr2 &expr2)
details::field_expr_v2_nonlinear_node_nary< typename details::function_traits< Function >::functor_type, typename details::field_expr_v2_nonlinear_terminal_wrapper_traits< Exprs >::type... > ::type compose(const Function &f, const Exprs &... exprs)
see the compose page for the full documentation
Definition compose.h:247
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 cavity_dg.h:25
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