ForceFree::BoundaryCorrections::Rusanov Class Reference

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

#include <Rusanov.hpp>

Public Types
using	options = tmpl::list<>
using	dg_package_field_tags
using	dg_package_data_temporary_tags
using	dg_package_data_primitive_tags = tmpl::list<>
using	dg_package_data_volume_tags = tmpl::list<>
using	dg_boundary_terms_volume_tags = tmpl::list<>

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 >	get_clone () const override
Public Member Functions inherited from evolution::BoundaryCorrection
	BoundaryCorrection (const BoundaryCorrection &)=default
BoundaryCorrection &	operator= (const BoundaryCorrection &)=default
	BoundaryCorrection (BoundaryCorrection &&)=default
BoundaryCorrection &	operator= (BoundaryCorrection &&)=default
	BoundaryCorrection (CkMigrateMessage *msg)

Static Public Member Functions
static double	dg_package_data (gsl::not_null< tnsr::I< DataVector, 3, Frame::Inertial > * > packaged_tilde_e, gsl::not_null< tnsr::I< DataVector, 3, Frame::Inertial > * > packaged_tilde_b, gsl::not_null< Scalar< DataVector > * > packaged_tilde_psi, gsl::not_null< Scalar< DataVector > * > packaged_tilde_phi, gsl::not_null< Scalar< DataVector > * > packaged_tilde_q, gsl::not_null< tnsr::I< DataVector, 3, Frame::Inertial > * > packaged_normal_dot_flux_tilde_e, gsl::not_null< tnsr::I< DataVector, 3, Frame::Inertial > * > packaged_normal_dot_flux_tilde_b, gsl::not_null< Scalar< DataVector > * > packaged_normal_dot_flux_tilde_psi, gsl::not_null< Scalar< DataVector > * > packaged_normal_dot_flux_tilde_phi, gsl::not_null< Scalar< DataVector > * > packaged_normal_dot_flux_tilde_q, gsl::not_null< Scalar< DataVector > * > packaged_abs_char_speed, const tnsr::I< DataVector, 3, Frame::Inertial > &tilde_e, const tnsr::I< DataVector, 3, Frame::Inertial > &tilde_b, const Scalar< DataVector > &tilde_psi, const Scalar< DataVector > &tilde_phi, const Scalar< DataVector > &tilde_q, const tnsr::IJ< DataVector, 3, Frame::Inertial > &flux_tilde_e, const tnsr::IJ< DataVector, 3, Frame::Inertial > &flux_tilde_b, const tnsr::I< DataVector, 3, Frame::Inertial > &flux_tilde_psi, const tnsr::I< DataVector, 3, Frame::Inertial > &flux_tilde_phi, const tnsr::I< DataVector, 3, Frame::Inertial > &flux_tilde_q, const Scalar< DataVector > &lapse, const tnsr::I< DataVector, 3, Frame::Inertial > &shift, const tnsr::i< DataVector, 3, Frame::Inertial > &normal_covector, const tnsr::I< DataVector, 3, Frame::Inertial > &normal_vector, const std::optional< tnsr::I< DataVector, 3, Frame::Inertial > > &, const std::optional< Scalar< DataVector > > &normal_dot_mesh_velocity)
static void	dg_boundary_terms (gsl::not_null< tnsr::I< DataVector, 3, Frame::Inertial > * > boundary_correction_tilde_e, gsl::not_null< tnsr::I< DataVector, 3, Frame::Inertial > * > boundary_correction_tilde_b, gsl::not_null< Scalar< DataVector > * > boundary_correction_tilde_psi, gsl::not_null< Scalar< DataVector > * > boundary_correction_tilde_phi, gsl::not_null< Scalar< DataVector > * > boundary_correction_tilde_q, const tnsr::I< DataVector, 3, Frame::Inertial > &tilde_e_int, const tnsr::I< DataVector, 3, Frame::Inertial > &tilde_b_int, const Scalar< DataVector > &tilde_psi_int, const Scalar< DataVector > &tilde_phi_int, const Scalar< DataVector > &tilde_q_int, const tnsr::I< DataVector, 3, Frame::Inertial > &normal_dot_flux_tilde_e_int, const tnsr::I< DataVector, 3, Frame::Inertial > &normal_dot_flux_tilde_b_int, const Scalar< DataVector > &normal_dot_flux_tilde_psi_int, const Scalar< DataVector > &normal_dot_flux_tilde_phi_int, const Scalar< DataVector > &normal_dot_flux_tilde_q_int, const Scalar< DataVector > &abs_char_speed_int, const tnsr::I< DataVector, 3, Frame::Inertial > &tilde_e_ext, const tnsr::I< DataVector, 3, Frame::Inertial > &tilde_b_ext, const Scalar< DataVector > &tilde_psi_ext, const Scalar< DataVector > &tilde_phi_ext, const Scalar< DataVector > &tilde_q_ext, const tnsr::I< DataVector, 3, Frame::Inertial > &normal_dot_flux_tilde_e_ext, const tnsr::I< DataVector, 3, Frame::Inertial > &normal_dot_flux_tilde_b_ext, const Scalar< DataVector > &normal_dot_flux_tilde_psi_ext, const Scalar< DataVector > &normal_dot_flux_tilde_phi_ext, const Scalar< DataVector > &normal_dot_flux_tilde_q_ext, const Scalar< DataVector > &abs_char_speed_ext, dg::Formulation dg_formulation)

Static Public Attributes
static constexpr Options::String	help

Detailed Description

A Rusanov/local Lax-Friedrichs Riemann solver.

Let \(U\) be the evolved variables, \(F^i\) 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 GRFFE system the largest characteristic speeds \(\lambda\) of our interest are given as

\begin{align*} \lambda_{\pm} = -\beta^i n_i \pm \alpha. \end{align*}

which correspond to fast mode waves.

Note

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

Member Typedef Documentation

dg_package_data_temporary_tags

using ForceFree::BoundaryCorrections::Rusanov::dg_package_data_temporary_tags

Initial value:

 
      tmpl::list<gr::Tags::Lapse<DataVector>, gr::Tags::Shift<DataVector, 3>>

dg_package_field_tags

using ForceFree::BoundaryCorrections::Rusanov::dg_package_field_tags

Initial value:

 
      tmpl::list<Tags::TildeE, Tags::TildeB, Tags::TildePsi, Tags::TildePhi,
                 Tags::TildeQ, ::Tags::NormalDotFlux<Tags::TildeE>,
                 ::Tags::NormalDotFlux<Tags::TildeB>,
                 ::Tags::NormalDotFlux<Tags::TildePsi>,
                 ::Tags::NormalDotFlux<Tags::TildePhi>,
                 ::Tags::NormalDotFlux<Tags::TildeQ>, AbsCharSpeed>

Member Function Documentation

get_clone()

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

overridevirtual

Implements evolution::BoundaryCorrection.

Member Data Documentation

help

Options::String ForceFree::BoundaryCorrections::Rusanov::help

staticconstexpr

Initial value:

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

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

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