grmhd::ValenciaDivClean::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
using	dg_package_data_volume_tags
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< Scalar< DataVector > * > packaged_tilde_d, gsl::not_null< Scalar< DataVector > * > packaged_tilde_ye, gsl::not_null< Scalar< DataVector > * > packaged_tilde_tau, gsl::not_null< tnsr::i< DataVector, 3, Frame::Inertial > * > packaged_tilde_s, gsl::not_null< tnsr::I< DataVector, 3, Frame::Inertial > * > packaged_tilde_b, gsl::not_null< Scalar< DataVector > * > packaged_tilde_phi, gsl::not_null< Scalar< DataVector > * > packaged_normal_dot_flux_tilde_d, gsl::not_null< Scalar< DataVector > * > packaged_normal_dot_flux_tilde_ye, gsl::not_null< Scalar< DataVector > * > packaged_normal_dot_flux_tilde_tau, gsl::not_null< tnsr::i< DataVector, 3, Frame::Inertial > * > packaged_normal_dot_flux_tilde_s, 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_phi, gsl::not_null< Scalar< DataVector > * > packaged_abs_char_speed, const Scalar< DataVector > &tilde_d, const Scalar< DataVector > &tilde_ye, const Scalar< DataVector > &tilde_tau, const tnsr::i< DataVector, 3, Frame::Inertial > &tilde_s, const tnsr::I< DataVector, 3, Frame::Inertial > &tilde_b, const Scalar< DataVector > &tilde_phi, const tnsr::I< DataVector, 3, Frame::Inertial > &flux_tilde_d, const tnsr::I< DataVector, 3, Frame::Inertial > &flux_tilde_ye, const tnsr::I< DataVector, 3, Frame::Inertial > &flux_tilde_tau, const tnsr::Ij< DataVector, 3, Frame::Inertial > &flux_tilde_s, const tnsr::IJ< DataVector, 3, Frame::Inertial > &flux_tilde_b, const tnsr::I< DataVector, 3, Frame::Inertial > &flux_tilde_phi, const Scalar< DataVector > &lapse, const tnsr::I< DataVector, 3, Frame::Inertial > &shift, const tnsr::i< DataVector, 3, Frame::Inertial > &, const Scalar< DataVector > &, const Scalar< DataVector > &, const Scalar< DataVector > &, const tnsr::I< DataVector, 3, Frame::Inertial > &, 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, const EquationsOfState::EquationOfState< true, 3 > &)
static void	dg_boundary_terms (gsl::not_null< Scalar< DataVector > * > boundary_correction_tilde_d, gsl::not_null< Scalar< DataVector > * > boundary_correction_tilde_ye, gsl::not_null< Scalar< DataVector > * > boundary_correction_tilde_tau, gsl::not_null< tnsr::i< DataVector, 3, Frame::Inertial > * > boundary_correction_tilde_s, gsl::not_null< tnsr::I< DataVector, 3, Frame::Inertial > * > boundary_correction_tilde_b, gsl::not_null< Scalar< DataVector > * > boundary_correction_tilde_phi, const Scalar< DataVector > &tilde_d_int, const Scalar< DataVector > &tilde_ye_int, const Scalar< DataVector > &tilde_tau_int, const tnsr::i< DataVector, 3, Frame::Inertial > &tilde_s_int, const tnsr::I< DataVector, 3, Frame::Inertial > &tilde_b_int, const Scalar< DataVector > &tilde_phi_int, const Scalar< DataVector > &normal_dot_flux_tilde_d_int, const Scalar< DataVector > &normal_dot_flux_tilde_ye_int, const Scalar< DataVector > &normal_dot_flux_tilde_tau_int, const tnsr::i< DataVector, 3, Frame::Inertial > &normal_dot_flux_tilde_s_int, const tnsr::I< DataVector, 3, Frame::Inertial > &normal_dot_flux_tilde_b_int, const Scalar< DataVector > &normal_dot_flux_tilde_phi_int, const Scalar< DataVector > &abs_char_speed_int, const Scalar< DataVector > &tilde_d_ext, const Scalar< DataVector > &tilde_ye_ext, const Scalar< DataVector > &tilde_tau_ext, const tnsr::i< DataVector, 3, Frame::Inertial > &tilde_s_ext, const tnsr::I< DataVector, 3, Frame::Inertial > &tilde_b_ext, const Scalar< DataVector > &tilde_phi_ext, const Scalar< DataVector > &normal_dot_flux_tilde_d_ext, const Scalar< DataVector > &normal_dot_flux_tilde_ye_ext, const Scalar< DataVector > &normal_dot_flux_tilde_tau_ext, const tnsr::i< DataVector, 3, Frame::Inertial > &normal_dot_flux_tilde_s_ext, const tnsr::I< DataVector, 3, Frame::Inertial > &normal_dot_flux_tilde_b_ext, const Scalar< DataVector > &normal_dot_flux_tilde_phi_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 state vector of 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 set of characteristic/signal speeds. 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. \(n_i^{\text{ext}}=-n_i^{\text{int}}\). The characteristic/signal speeds are given in the documentation for grmhd::ValenciaDivClean::characteristic_speeds(). Since the fluid is travelling slower than the speed of light, the speeds we are interested in are

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

which correspond to the divergence cleaning field.

Note

• In the strong form the dg_boundary_terms function returns \(G - F_\text{int}\)
• It may be possible to use the slower speeds for the magnetic field and fluid part of the system in order to make the flux less dissipative for those variables.

Member Typedef Documentation

dg_package_data_primitive_tags

using grmhd::ValenciaDivClean::BoundaryCorrections::Rusanov::dg_package_data_primitive_tags

Initial value:

 
      tmpl::list<hydro::Tags::RestMassDensity<DataVector>,
                 hydro::Tags::ElectronFraction<DataVector>,
                 hydro::Tags::Temperature<DataVector>,
                 hydro::Tags::SpatialVelocity<DataVector, 3>>

dg_package_data_temporary_tags

using grmhd::ValenciaDivClean::BoundaryCorrections::Rusanov::dg_package_data_temporary_tags

Initial value:

 tmpl::list<
      gr::Tags::Lapse<DataVector>, gr::Tags::Shift<DataVector, 3>,
      hydro::Tags::SpatialVelocityOneForm<DataVector, 3, Frame::Inertial>>

dg_package_data_volume_tags

using grmhd::ValenciaDivClean::BoundaryCorrections::Rusanov::dg_package_data_volume_tags

Initial value:

 
      tmpl::list<hydro::Tags::GrmhdEquationOfState>

dg_package_field_tags

using grmhd::ValenciaDivClean::BoundaryCorrections::Rusanov::dg_package_field_tags

Initial value:

 
      tmpl::list<Tags::TildeD, Tags::TildeYe, Tags::TildeTau,
                 Tags::TildeS<Frame::Inertial>, Tags::TildeB<Frame::Inertial>,
                 Tags::TildePhi, ::Tags::NormalDotFlux<Tags::TildeD>,
                 ::Tags::NormalDotFlux<Tags::TildeYe>,
                 ::Tags::NormalDotFlux<Tags::TildeTau>,
                 ::Tags::NormalDotFlux<Tags::TildeS<Frame::Inertial>>,
                 ::Tags::NormalDotFlux<Tags::TildeB<Frame::Inertial>>,
                 ::Tags::NormalDotFlux<Tags::TildePhi>, AbsCharSpeed>

Member Function Documentation

get_clone()

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

overridevirtual

Implements evolution::BoundaryCorrection.

Member Data Documentation

help

Options::String grmhd::ValenciaDivClean::BoundaryCorrections::Rusanov::help

staticconstexpr

Initial value:

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

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

• src/Evolution/Systems/GrMhd/ValenciaDivClean/BoundaryCorrections/Rusanov.hpp