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convect2.cc

Convection-diffusion equation by BDF2 scheme and the method of characteristics.

Convection-diffusion equation by BDF2 scheme and the method of characteristics

// mkgeo_grid -e 1000 -a -2 -b 2 > line2.geo
// ./convect line2 1e-3 5 > line2.branch
// ./convect2 line2 1e-3 5 > line22.branch
// (./convect_error < line2.branch > line2-cmp.branch) 2>&1|g -v trace |g -v load |tee cv.gdat
// (./convect_error < line22.branch > line22-cmp.branch) 2>&1|g -v trace |g -v load |tee cv2.gdat
#include "rheolef.h"
using namespace rheolef;
using namespace std;
#include "rotating-hill.h"
int main (int argc, char **argv) {
environment rheolef (argc,argv);
geo omega (argv[1]);
string approx = (argc > 2) ? argv[2] : "P1";
Float nu = (argc > 3) ? atof(argv[3]) : 1e-2;
size_t n_max = (argc > 4) ? atoi(argv[4]) : 50;
size_t d = omega.dimension();
Float delta_t = 2*acos(-1.)/n_max;
space Vh (omega, approx, "vector");
field uh = lazy_interpolate (Vh, u(d));
space Xh (omega, approx);
Xh.block ("boundary");
field phi_h = lazy_interpolate (Xh, phi(d,nu,0));
field phi_h_prec = lazy_interpolate (Xh, phi(d,nu,0));
characteristic X1 ( -delta_t*uh);
characteristic X2 (-2*delta_t*uh);
integrate_option iopt;
iopt.set_family (integrate_option::gauss_lobatto);
iopt.set_order (Xh.degree());
trial varphi (Xh); test psi (Xh);
branch event ("t","phi");
dout << catchmark("nu") << nu << endl
<< event (0, phi_h);
for (size_t n = 1; n <= n_max; n++) {
Float t = n*delta_t;
Float alpha = Float(1.5) + delta_t*phi::sigma(d,nu,t);
Float beta = delta_t*nu;
form c = integrate (alpha*varphi*psi + beta*dot(grad(varphi),grad(psi)), iopt);
field lh = integrate (omega, (2*compose(phi_h, X1) - 0.5*compose(phi_h_prec, X2))*psi, iopt);
phi_h_prec = phi_h;
problem p (c);
p.solve (lh, phi_h);
dout << event (t, phi_h);
}
}
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
characteristic
see the characteristic 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::catchmark
see the catchmark page for the full documentation
Definition catchmark.h:67
rheolef::environment
see the environment page for the full documentation
Definition environment.h:121
rheolef::integrate_option
see the integrate_option page for the full documentation
Definition integrate_option.h:125
rheolef::integrate_option::set_family
void set_family(family_type type)
Definition integrate_option.h:260
rheolef::integrate_option::set_order
void set_order(size_t r)
Definition integrate_option.h:254
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
rheolef
This file is part of Rheolef.
Definition compiler_eigen.h:39
std
STL namespace.
d
size_t d
Definition neumann-laplace-lambda.cc:28
rheolef.h
rheolef - reference manual
rotating-hill.h
Convection-diffusion equation – the rotating hill benchmark.
nu
Definition nu.h:26
p
Definition sphere.icc:25
phi
Definition phi.h:25
phi::sigma
Float sigma
Definition transport_dg_error.cc:27
psi
Definition interpolate_RTk_polynom.icc:34
u
Definition leveque.h:25