convect_hdg.cc
Go to the documentation of this file.
#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"] = 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;
}
form
see the form page for the full documentation
rheolef::catchmark
see the catchmark page for the full documentation
Definition: catchmark.h:67
rheolef::dot
rheolef::std enable_if ::type dot const Expr1 expr1, const Expr2 expr2 dot(const Expr1 &expr1, const Expr2 &expr2)
dot(x,y): see the expression page for the full documentation
Definition: vec_expr_v2.h:415
field
see the field page for the full documentation
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:439
nu
Definition: nu.h:26
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:202
mkgeo_ball.f
f
Definition: mkgeo_ball.sh:221
phi
Float phi(const point &nu, Float a, Float b)
Definition: burgers_flux_godunov.icc:25
space
see the space page for the full documentation
mkgeo_ball.c
c
Definition: mkgeo_ball.sh:153
rheolef::div_h
std::enable_if< details::is_field_convertible< Expr >::value,details::field_expr_v2_nonlinear_terminal_field< typename Expr::scalar_type,typename Expr::memory_type,details::differentiate_option::divergence >>::type div_h(const Expr &expr)
div_h(uh): see the expression page for the full documentation
Definition: field_expr_terminal.h:1069
rheolef.h
rheolef - reference manual
p
Definition: sphere.icc:25
rheolef::integrate_option
see the integrate_option page for the full documentation
Definition: integrate_option.h:125
rheolef::on_local_sides
std::enable_if< details::is_field_expr_v2_variational_arg< Expr >::value,details::field_expr_quadrature_on_sides< Expr > >::type on_local_sides(const Expr &expr)
on_local_sides(expr): see the expression page for the full documentation
Definition: field_expr_quadrature.h:321
rheolef::interpolate
field_basic< T, M > interpolate(const space_basic< T, M > &V2h, const field_basic< T, M > &u1h)
see the interpolate page for the full documentation
Definition: interpolate.cc:233
main
int main(int argc, char **argv)
Definition: convect_hdg.cc:29
rheolef::environment
see the environment page for the full documentation
Definition: environment.h:115
lh
field lh(Float epsilon, Float t, const test &v)
Definition: burgers_diffusion_operators.icc:25
rheolef
This file is part of Rheolef.
Definition: compiler_eigen.h:37
rheolef::integrate_option::invert
bool invert
Definition: integrate_option.h:168
test
see the test page for the full documentation
problem
see the problem page for the full documentation
Float
see the Float page for the full documentation
mkgeo_ball.d
d
Definition: mkgeo_ball.sh:154
u
Float u(const point &x)
Definition: transmission_error.cc:26
rotating-hill-statio.h
phi::sigma
Float sigma
Definition: transport_dg_error.cc:27
mkgeo_contraction.mu
mu
Definition: mkgeo_contraction.sh:193
rheolef::grad_h
std::enable_if< details::is_field_convertible< Expr >::value,details::field_expr_v2_nonlinear_terminal_field< typename Expr::scalar_type,typename Expr::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:949
trial
see the test page for the full documentation
rheolef::dout
odiststream dout(cout)
see the diststream page for the full documentation
Definition: diststream.h:430
rheolef::trans
csr< T, sequential > trans(const csr< T, sequential > &a)
trans(a): see the form page for the full documentation
Definition: csr.h:455
rheolef::std
Definition: vec_expr_v2.h:391
geo
see the geo page for the full documentation
rk::beta
Float beta[][pmax+1]
Definition: runge_kutta_semiimplicit.icc:60
lambda
Definition: yield_slip_circle.h:34