ScalarAdvection::BoundaryCorrections::Rusanov< Dim > Class Template Reference

A Rusanov/local Lax-Friedrichs Riemann solver. More...

#include <Rusanov.hpp>

Public Types
using	options = tmpl::list<>
using	dg_package_field_tags = tmpl::list< Tags::U, ::Tags::NormalDotFlux< Tags::U >, AbsCharSpeed >
using	dg_package_data_temporary_tags = tmpl::list< Tags::VelocityField< Dim > >
using	dg_package_data_volume_tags = tmpl::list<>
using	dg_boundary_terms_volume_tags = tmpl::list<>
Public Types inherited from ScalarAdvection::BoundaryCorrections::BoundaryCorrection< Dim >
using	creatable_classes = tmpl::list< Rusanov< Dim > >

Public Member Functions
	Rusanov (const Rusanov &)=default
Rusanov &	operator= (const Rusanov &)=default
	Rusanov (Rusanov &&)=default
Rusanov &	operator= (Rusanov &&)=default
void	pup (PUP::er &p) override
std::unique_ptr< BoundaryCorrection< Dim > >	get_clone () const override
Public Member Functions inherited from ScalarAdvection::BoundaryCorrections::BoundaryCorrection< Dim >
	BoundaryCorrection (const BoundaryCorrection &)=default
BoundaryCorrection &	operator= (const BoundaryCorrection &)=default
	BoundaryCorrection (BoundaryCorrection &&)=default
BoundaryCorrection &	operator= (BoundaryCorrection &&)=default
virtual std::unique_ptr< BoundaryCorrection< Dim > >	get_clone () const =0

Static Public Member Functions
static double	dg_package_data (gsl::not_null< Scalar< DataVector > * > packaged_u, gsl::not_null< Scalar< DataVector > * > packaged_normal_dot_flux_u, gsl::not_null< Scalar< DataVector > * > packaged_abs_char_speed, const Scalar< DataVector > &u, const tnsr::I< DataVector, Dim, Frame::Inertial > &flux_u, const tnsr::I< DataVector, Dim, Frame::Inertial > &velocity_field, const tnsr::i< DataVector, Dim, Frame::Inertial > &normal_covector, const std::optional< tnsr::I< DataVector, Dim, Frame::Inertial > > &mesh_velocity, const std::optional< Scalar< DataVector > > &normal_dot_mesh_velocity)
static void	dg_boundary_terms (gsl::not_null< Scalar< DataVector > * > boundary_correction_u, const Scalar< DataVector > &u_int, const Scalar< DataVector > &normal_dot_flux_u_int, const Scalar< DataVector > &abs_char_speed_int, const Scalar< DataVector > &u_ext, const Scalar< DataVector > &normal_dot_flux_u_ext, const Scalar< DataVector > &abs_char_speed_ext, dg::Formulation dg_formulation)

Static Public Attributes
static constexpr Options::String	help

Detailed Description

template<size_t Dim>
class ScalarAdvection::BoundaryCorrections::Rusanov< Dim >

A Rusanov/local Lax-Friedrichs Riemann solver.

Let \(U\) be the evolved scalar variable, \(F^i\) the corresponding fluxes, and \(n_i\) be the outward directed unit normal to the interface. Denoting \(F := n_i F^i\), the Rusanov boundary correction is

\begin{align*} G_\text{Rusanov} = \frac{F_\text{int} - F_\text{ext}}{2} - \frac{\text{max}\left(|\lambda_\text{int}|, |\lambda_\text{ext}|\right)}{2} \left(U_\text{ext} - U_\text{int}\right), \end{align*}

where "int" and "ext" stand for interior and exterior, and \(\lambda\) is the characteristic/signal speed. The minus sign in front of the \(F_{\text{ext}}\) is necessary because the outward directed normal of the neighboring element has the opposite sign, i.e. \(n_i^{\text{ext}}=-n_i^{\text{int}}\).

For the ScalarAdvection system, \(\lambda\) is given as

\begin{align*} \lambda = |v| = \sqrt{v^iv_i} \end{align*}

where \(v^i\) is the advection velocity field.

Note

In the strong form the dg_boundary_terms function returns \(G - F_\text{int}\)

Member Function Documentation

get_clone()

template<size_t Dim>

std::unique_ptr< BoundaryCorrection< Dim > > ScalarAdvection::BoundaryCorrections::Rusanov< Dim >::get_clone ( ) const

overridevirtual

Implements ScalarAdvection::BoundaryCorrections::BoundaryCorrection< Dim >.

Member Data Documentation

help

template<size_t Dim>

constexpr Options::String ScalarAdvection::BoundaryCorrections::Rusanov< Dim >::help

staticconstexpr

Initial value:

= {
      "Computes the Rusanov or local Lax-Friedrichs boundary correction term "
      "for the ScalarAdvection system."}

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The documentation for this class was generated from the following file:

• src/Evolution/Systems/ScalarAdvection/BoundaryCorrections/Rusanov.hpp