Rheolef  7.2
an efficient C++ finite element environment
 
Loading...
Searching...
No Matches
burgers_diffusion_dg.cc
Go to the documentation of this file.
1
25#include "rheolef.h"
26using namespace rheolef;
27using namespace std;
28#include "burgers.icc"
32#undef NEUMANN
34int main(int argc, char**argv) {
35 environment rheolef (argc, argv);
36 geo omega (argv[1]);
37 space Xh (omega, argv[2]);
38 size_t k = Xh.degree();
39 Float epsilon = (argc > 3) ? atof(argv[3]) : 0.1;
40 size_t nmax = (argc > 4) ? atoi(argv[4]) : 500;
41 Float tf = (argc > 5) ? atof(argv[5]) : 1;
42 size_t p = (argc > 6) ? atoi(argv[6]) : min(k+1,rk::pmax);
43 Float delta_t = tf/nmax;
44 size_t d = omega.dimension();
45 Float beta = (k+1)*(k+d)/Float(d);
46 trial u (Xh); test v (Xh);
47 form m = integrate (u*v);
49 iopt.invert = true;
50 form inv_m = integrate (u*v, iopt);
51 form a = epsilon*(
53#ifdef NEUMANN
54 + integrate ("internal_sides",
55#else // NEUMANN
56 + integrate ("sides",
57#endif // NEUMANN
58 beta*penalty()*jump(u)*jump(v)
59 - jump(u)*average(dot(grad_h(v),normal()))
60 - jump(v)*average(dot(grad_h(u),normal()))));
61 vector<problem> pb (p+1);
62 for (size_t i = 1; i <= p; ++i) {
63 form ci = m + delta_t*rk::alpha[p][i][i]*a;
64 pb[i] = problem(ci);
65 }
66 vector<field> uh(p+1, field(Xh,0));
67 uh[0] = lazy_interpolate (Xh, u_init(epsilon));
68 branch even("t","u");
69 dout << catchmark("epsilon") << epsilon << endl
70 << even(0,uh[0]);
71 for (size_t n = 0; n < nmax; ++n) {
72 Float tn = n*delta_t;
73 Float t = tn + delta_t;
74 field uh_next = uh[0] - delta_t*rk::tilde_beta[p][0]*(inv_m*gh(epsilon, tn, uh[0], v));
75 for (size_t i = 1; i <= p; ++i) {
76 Float ti = tn + rk::gamma[p][i]*delta_t;
77 field rhs = m*uh[0] - delta_t*rk::tilde_alpha[p][i][0]*gh(epsilon, tn, uh[0], v);
78 for (size_t j = 1; j <= i-1; ++j) {
79 Float tj = tn + rk::gamma[p][j]*delta_t;
80 rhs -= delta_t*( rk::alpha[p][i][j]*(a*uh[j] - lh(epsilon,tj,v))
81 + rk::tilde_alpha[p][i][j]*gh(epsilon, tj, uh[j], v));
82 }
83 rhs += delta_t*rk::alpha[p][i][i]*lh (epsilon, ti, v);
84 pb[i].solve (rhs, uh[i]);
85 uh_next -= delta_t*(inv_m*( rk::beta[p][i]*(a*uh[i] - lh(epsilon,ti,v))
86 + rk::tilde_beta[p][i]*gh(epsilon, ti, uh[i], v)));
87 }
88 uh_next = limiter(uh_next);
89 dout << even(tn+delta_t,uh_next);
90 uh[0] = uh_next;
91 }
92}
The Burgers equation – the f function.
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
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
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_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