Convection-diffusion equation by the hybrid discontinuous Galerkin method.
int main (
int argc,
char **argv) {
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();
form inv_a = integrate((1/
nu)*dot(x[0],y[0]) + x[1]*div_h(y[0])
+ 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);
+ 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 xh = inv_a*(
lh - b1.trans_mult(lambda_h));
}
field lh(Float epsilon, Float t, const test &v)
see the Float page for the full documentation
see the field 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
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
This file is part of Rheolef.
rheolef - reference manual