The Burgers equation by the discontinous Galerkin method.
int main(
int argc,
char**argv) {
space Xh (omega, argv[2]);
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()));
}
form inv_m = integrate (
u*v, iopt);
vector<field> uh(
p+1,
field(Xh,0));
uh[0] = lazy_interpolate (Xh,
u_init());
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) {
- 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] = limiter(uh[i],
g(n*delta_t)(
point(-1)), lopt);
}
dout << even(n*delta_t,uh[0]);
}
}
The Burgers equation – the f function.
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 geo page for the full documentation
see the point page for the full documentation
see the catchmark page for the full documentation
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
The Burgers problem: the Harten exact solution.
This file is part of Rheolef.
Float beta[][pmax+1][pmax+1]
Float alpha[][pmax+1][pmax+1]
rheolef - reference manual
The strong stability preserving Runge-Kutta scheme – coefficients.
see the limiter page for the full documentation