Rheolef  7.2
an efficient C++ finite element environment
inertia_cks.icc

The inertia term of the Navier-Stokes equation with the discontinuous Galerkin method – Cockburn, Kanschat & Schotzau variant

integrate_option iopt = integrate_option())
{
return
integrate (- dot(trans(grad_h(v))*w,u) - 0.5*div_h(v)*dot(u,w), iopt)
+ integrate ("internal_sides",
dot(average(u),normal())*dot(jump(v),average(w))
+ 0.5*dot(jump(v),normal())
*(dot(average(u),average(w)) + 0.25*dot(jump(u),jump(w))), iopt)
+ integrate ("boundary", 0.5*dot(v,normal())*dot(u,w), iopt);
}
integrate_option iopt = integrate_option())
{
return integrate("boundary", -dot(g(),normal())*dot(g(),v), iopt);
}
u_exact g
see the field page for the full documentation
see the form page for the full documentation
see the test page for the full documentation
see the test page for the full documentation
form inertia(field w, trial u, test v, integrate_option iopt=integrate_option())
Definition: inertia_cks.icc:25
field inertia_fix_rhs(test v, integrate_option iopt=integrate_option())
Definition: inertia_cks.icc:36
rheolef::details::is_vec dot
std::enable_if< details::has_field_rdof_interface< 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
csr< T, sequential > trans(const csr< T, sequential > &a)
trans(a): see the form page for the full documentation
Definition: csr.h:455
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
std::enable_if< details::has_field_rdof_interface< 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
details::field_expr_v2_nonlinear_terminal_function< details::normal_pseudo_function< Float > > normal()
normal: see the expression page for the full documentation
Definition: leveque.h:25