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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;
}
f
point f(const Float &u)
Definition burgers.icc:25
lh
field lh(Float epsilon, Float t, const test &v)
Definition burgers_diffusion_operators.icc:25
phi
Float phi(const point &nu, Float a, Float b)
Definition burgers_flux_godunov.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
u
point u(const point &x)
Definition diffusion_transport_tensor_exact.icc:25
main
int main()
Definition field2bb.cc:58
rheolef
This file is part of Rheolef.
Definition compiler_eigen.h:39
rheolef::div_h
std::enable_if< details::has_field_rdof_interface< Expr >::value, details::field_expr_v2_nonlinear_terminal_field< typenameExpr::scalar_type, typenameExpr::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:1088
rheolef::lazy_interpolate
field_basic< T, M > lazy_interpolate(const space_basic< T, M > &X2h, const field_basic< T, M > &u1h)
see the interpolate page for the full documentation
Definition field.h:871
rheolef::grad_h
std::enable_if< details::has_field_rdof_interface< Expr >::value, details::field_expr_v2_nonlinear_terminal_field< typenameExpr::scalar_type, typenameExpr::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:968
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:432
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:211
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:323
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::dot
rheolef::std::enable_if< details::is_vec_expr_v2_arg< Expr1 >::value &&details::is_vec_expr_v2_arg< Expr2 >::value, promote< Expr1::float_type, Expr2::float_type >::type > type dot const Expr1 expr1, const Expr2 expr2 dot(const Expr1 &expr1, const Expr2 &expr2)
Definition vec_expr_v2.h:415
std
STL namespace.
d
size_t d
Definition neumann-laplace-lambda.cc:28
rheolef.h
rheolef - reference manual
rotating-hill-statio.h
lambda
Definition yield_slip_circle.h:34
nu
Definition nu.h:26
p
Definition sphere.icc:25
phi::sigma
Float sigma
Definition transport_dg_error.cc:27