Rheolef  7.2
an efficient C++ finite element environment
 
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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);
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);
}
}
field lh(Float epsilon, Float t, const test &v)
see the Float page for the full documentation
see the branch page for the full documentation
see the characteristic 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
void set_family(family_type type)
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.
STL namespace.
rheolef - reference manual
Convection-diffusion equation – the rotating hill benchmark.
Definition nu.h:26
Definition sphere.icc:25
Definition phi.h:25
Definition leveque.h:25