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zalesak_dg.cc
Go to the documentation of this file.
#include "rheolef.h"
using namespace rheolef;
using namespace std;
#include "zalesak.h"
#include "bdf.icc"
int main(int argc, char**argv) {
environment rheolef (argc, argv);
geo omega (argv[1]);
space Xh (omega, argv[2]);
size_t n_max = (argc > 3) ? atoi(argv[3]) : 1000;
size_t strip = (argc > 4) ? string(argv[4]) == "true" : false;
size_t p = (argc > 5) ? atoi(argv[5]) : min(Xh.degree()+1,bdf::pmax);
Float tf = u::period(), delta_t = tf/n_max;
trial phi (Xh); test xi (Xh);
form m = integrate (phi*xi),
a0 = integrate (dot(u(),grad_h(phi))*xi)
+ integrate ("boundary", max(0, -dot(u(),normal()))*phi*xi)
+ integrate ("internal_sides",
- dot(u(),normal())*jump(phi)*average(xi)
+ 0.5*abs(dot(u(),normal()))*jump(phi)*jump(xi));
problem pb;
branch event ("t","phi");
vector<field> phi_h (p+1);
phi_h[0] = phi_h[1] = lazy_interpolate (Xh, phi0());
dout << event (0, phi_h[0]);
for (size_t n = 1; n <= n_max; n++) {
Float t = n*delta_t;
if (n % 10 == 0) derr << "[" << n << "]";
size_t pn = min(n,p);
field rhs(Xh, 0);
for (size_t i = 1; i <= pn; i++)
rhs += (bdf::alpha[pn][i]/delta_t)*phi_h[i];
field lh = integrate(rhs*xi)
+ integrate("boundary", max(0,-dot(u(),normal()))*phi_exact(t)*xi);
if (pn <= p) {
form an = a0 + (bdf::alpha[pn][0]/delta_t)*m;
pb = problem (an);
}
pb.solve (lh, phi_h[0]);
check_macro (phi_h[0].max_abs() < 100, "BDF failed -- HINT: decrease delta_t");
if (!strip || n == n_max) dout << event (t, phi_h[0]);
for (size_t i = min(p,pn+1); i >= 1; i--)
phi_h[i] = phi_h[i-1];
}
derr << endl;
}
bdf.icc
BDF(p) backward differentiation formula – coefficients.
lh
field lh(Float epsilon, Float t, const test &v)
Definition burgers_diffusion_operators.icc:25
Float
see the Float page for the full documentation
branch
see the branch page for the full documentation
field
see the field page for the full documentation
form
see the form page for the full documentation
geo
see the geo page for the full documentation
problem
see the problem page for the full documentation
rheolef::environment
see the environment page for the full documentation
Definition environment.h:121
space
see the space page for the full documentation
test
see the test page for the full documentation
trial
see the test page for the full documentation
main
int main()
Definition field2bb.cc:58
check_macro
check_macro(expr1.have_homogeneous_space(Xh1), "dual(expr1,expr2); expr1 should have homogeneous space. HINT: use dual(interpolate(Xh, expr1),expr2)")
bdf::alpha
Float alpha[pmax+1][pmax+1]
Definition bdf.icc:28
bdf::pmax
constexpr size_t pmax
Definition bdf.icc:26
rheolef
This file is part of Rheolef.
Definition compiler_eigen.h:39
rheolef::lazy_interpolate
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
rheolef::grad_h
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
Definition field_expr_terminal.h:968
rheolef::normal
details::field_expr_v2_nonlinear_terminal_function< details::normal_pseudo_function< Float > > normal()
normal: see the expression page for the full documentation
Definition field_expr_terminal.h:432
rheolef::integrate
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
rheolef::dot
rheolef::std enable_if ::type dot const Expr1 expr1, const Expr2 expr2 dot(const Expr1 &expr1, const Expr2 &expr2)
Definition vec_expr_v2.h:415
std
STL namespace.
rheolef.h
rheolef - reference manual
p
Definition sphere.icc:25
phi0
Definition leveque.h:37
phi_exact
Definition transport_dg2.h:30
phi
Definition phi.h:25
u
Definition leveque.h:25
u::period
static Float period()
Definition leveque.h:32
zalesak.h
The Zalesak slotted disk benchmark – the exact solution.