inertia.h

The inertia term of the Navier-Stokes equation with the discontinuous Galerkin method – di Pietro & Ern variant

template<class W, class U, class V>
form inertia (W w, U u, V v,
integrate_option iopt = integrate_option())
{
return
integrate (dot(grad_h(u)*w,v) + 0.5*div_h(w)*dot(u,v), iopt)
+ integrate ("boundary", - 0.5*dot(w,normal())*dot(u,v), iopt)
+ integrate ("internal_sides",
- dot(average(w),normal())*dot(jump(u),average(v))
- 0.5*dot(jump(w),normal())
*(dot(average(u),average(v)) + 0.25*dot(jump(u),jump(v))), iopt);
}
field inertia_fix_rhs (test v,
integrate_option iopt = integrate_option())
{
return integrate("boundary", - 0.5*dot(g(),normal())*dot(g(),v), iopt);
}
g
u_exact g
Definition: burgers_diffusion_exact.h:33
form
see the form page for the full documentation
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
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
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
inertia
form inertia(W w, U u, V v, integrate_option iopt=integrate_option())
Definition: inertia.h:26
test
see the test page for the full documentation
u
Definition: leveque.h:25
inertia_fix_rhs
field inertia_fix_rhs(test v, integrate_option iopt=integrate_option())
Definition: inertia.h:37
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
rheolef::details::dot
rheolef::details::is_vec dot