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

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

#include <Rusanov.hpp>

Public Types
using	options = implementation defined
using	dg_package_field_tags = implementation defined
using	dg_package_data_temporary_tags = implementation defined
using	dg_package_data_volume_tags = implementation defined
using	dg_boundary_terms_volume_tags = implementation defined
Public Types inherited from ScalarAdvection::BoundaryCorrections::BoundaryCorrection< Dim >
using	creatable_classes = implementation defined

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

$$\begin{array}{r}{G}_{\text{Rusanov}}=\frac{F_{\text{int}}-F_{\text{ext}}}{2}-\frac{\text{max}(|{\lambda }_{\text{int}}|,|{\lambda }_{\text{ext}}|)}{2}(U_{\text{ext}}-U_{\text{int}}),\end{array}$$

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

$$\begin{array}{r}\lambda =|v|=\sqrt{v^i{v}_i}\end{array}$$

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