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convect_hdg.cc

Convection-diffusion equation by the hybrid discontinuous Galerkin method.

Convection-diffusion equation by the hybrid discontinuous Galerkin method

#include "rheolef.h"
using namespace rheolef;
using namespace std;
#include "rotating-hill-statio.h"
int main (int argc, char **argv) {
environment rheolef (argc,argv);
geo omega (argv[1]);
string approx = (argc > 2) ? argv[2] : "P1d";
Float nu = (argc > 3) ? atof(argv[3]) : 1e-2;
Float beta = (argc > 4) ? atof(argv[4]) : 1;
space Th (omega, approx, "vector"),
Xh (omega, approx),
Yh = Th*Xh,
Mh (omega["sides"], approx);
Mh.block("boundary");
space Wh(Mh.get_geo()["boundary"],approx);
size_t d = omega.dimension();
trial x(Yh);
trial lambda(Mh);
test y(Yh);
test mu(Mh);
integrate_option iopt;
iopt.invert = true;
form inv_a = integrate((1/nu)*dot(x[0],y[0]) + x[1]*div_h(y[0])
+ y[1]*div_h(x[0]) - phi::sigma(d,nu)*x[1]*y[1]
+ x[1]*dot(u(d),grad_h(y[1]))
- on_local_sides((beta+abs(dot(u(d),normal())))*x[1]*y[1]), iopt);
form b1 = integrate("internal_sides", (-dot(jump(x[0]),normal())
+ 2*(beta+abs(dot(u(d),normal())))*average(x[1])
- dot(u(d),normal())*jump(x[1]))*mu);
form b2 = integrate("internal_sides", (-dot(jump(x[0]),normal())
+ 2*(beta+abs(dot(u(d),normal())))*average(x[1]))*mu);
form c = integrate("internal_sides",
2*(beta+abs(dot(u(d),normal())))*lambda*mu);
field lh = integrate(omega, -f(d,nu)*y[1])
+ integrate("boundary", phi(d,nu)*(dot(y[0],normal())
- (beta+abs(dot(u(d),normal()))-dot(u(d),normal()))*y[1]));
field kh(Mh,0), lambda_h(Mh,0);
lambda_h["boundary"] = lazy_interpolate(Wh,phi(d,nu));
form s = c + b2*inv_a*trans(b1);
field rh = b2*(inv_a*lh) - kh;
problem p(s);
p.solve (rh, lambda_h);
field xh = inv_a*(lh - b1.trans_mult(lambda_h));
dout << catchmark("nu") << nu << endl
<< catchmark("phi") << xh[1]
<< catchmark("sigma") << xh[0]
<< catchmark("lambda") << lambda_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
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::invert
bool invert
Definition integrate_option.h:168
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-statio.h
f
Definition cavity_dg.h:29
lambda
Definition yield_slip_circle.h:34
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
u
Definition leveque.h:25