NewtonianEuler::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
using	dg_package_data_temporary_tags = tmpl::list<>
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
double	dg_package_data (gsl::not_null< Scalar< DataVector > * > packaged_mass_density, gsl::not_null< tnsr::I< DataVector, Dim, Frame::Inertial > * > packaged_momentum_density, gsl::not_null< Scalar< DataVector > * > packaged_energy_density, gsl::not_null< Scalar< DataVector > * > packaged_normal_dot_flux_mass_density, gsl::not_null< tnsr::I< DataVector, Dim, Frame::Inertial > * > packaged_normal_dot_flux_momentum_density, gsl::not_null< Scalar< DataVector > * > packaged_normal_dot_flux_energy_density, gsl::not_null< Scalar< DataVector > * > packaged_abs_char_speed, const Scalar< DataVector > &mass_density, const tnsr::I< DataVector, Dim, Frame::Inertial > &momentum_density, const Scalar< DataVector > &energy_density, const tnsr::I< DataVector, Dim, Frame::Inertial > &flux_mass_density, const tnsr::IJ< DataVector, Dim, Frame::Inertial > &flux_momentum_density, const tnsr::I< DataVector, Dim, Frame::Inertial > &flux_energy_density, const tnsr::I< DataVector, Dim, Frame::Inertial > &velocity, const Scalar< DataVector > &specific_internal_energy, const tnsr::i< DataVector, Dim, Frame::Inertial > &normal_covector, const std::optional< tnsr::I< DataVector, Dim, Frame::Inertial > > &, const std::optional< Scalar< DataVector > > &normal_dot_mesh_velocity, const EquationsOfState::EquationOfState< false, 2 > &equation_of_state) const
void	dg_boundary_terms (gsl::not_null< Scalar< DataVector > * > boundary_correction_mass_density, gsl::not_null< tnsr::I< DataVector, Dim, Frame::Inertial > * > boundary_correction_momentum_density, gsl::not_null< Scalar< DataVector > * > boundary_correction_energy_density, const Scalar< DataVector > &mass_density_int, const tnsr::I< DataVector, Dim, Frame::Inertial > &momentum_density_int, const Scalar< DataVector > &energy_density_int, const Scalar< DataVector > &normal_dot_flux_mass_density_int, const tnsr::I< DataVector, Dim, Frame::Inertial > &normal_dot_flux_momentum_density_int, const Scalar< DataVector > &normal_dot_flux_energy_density_int, const Scalar< DataVector > &abs_char_speed_int, const Scalar< DataVector > &mass_density_ext, const tnsr::I< DataVector, Dim, Frame::Inertial > &momentum_density_ext, const Scalar< DataVector > &energy_density_ext, const Scalar< DataVector > &normal_dot_flux_mass_density_ext, const tnsr::I< DataVector, Dim, Frame::Inertial > &normal_dot_flux_momentum_density_ext, const Scalar< DataVector > &normal_dot_flux_energy_density_ext, const Scalar< DataVector > &abs_char_speed_ext, dg::Formulation dg_formulation) const
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 Attributes
static constexpr Options::String	help

Detailed Description

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

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 by:

\begin{align*}\lambda_{\pm}&=v^i n_i \pm c_s, \\ \lambda_v&=v^i n_i \end{align*}

where \(v^i\) is the spatial velocity and \(c_s\) the sound speed.

Note

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

Member Typedef Documentation

dg_package_data_primitive_tags

template<size_t Dim>

using NewtonianEuler::BoundaryCorrections::Rusanov< Dim >::dg_package_data_primitive_tags

Initial value:

 
      tmpl::list<hydro::Tags::SpatialVelocity<DataVector, Dim>,
                 hydro::Tags::SpecificInternalEnergy<DataVector>>

dg_package_data_volume_tags

template<size_t Dim>

using NewtonianEuler::BoundaryCorrections::Rusanov< Dim >::dg_package_data_volume_tags

Initial value:

 
      tmpl::list<hydro::Tags::EquationOfState<false, 2>>

dg_package_field_tags

template<size_t Dim>

using NewtonianEuler::BoundaryCorrections::Rusanov< Dim >::dg_package_field_tags

Initial value:

 
      tmpl::list<Tags::MassDensityCons, Tags::MomentumDensity<Dim>,
                 Tags::EnergyDensity,
                 ::Tags::NormalDotFlux<Tags::MassDensityCons>,
                 ::Tags::NormalDotFlux<Tags::MomentumDensity<Dim>>,
                 ::Tags::NormalDotFlux<Tags::EnergyDensity>, AbsCharSpeed>

Member Function Documentation

get_clone()

template<size_t Dim>

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

overridevirtual

Implements evolution::BoundaryCorrection.

Member Data Documentation

help

template<size_t Dim>

Options::String NewtonianEuler::BoundaryCorrections::Rusanov< Dim >::help

staticconstexpr

Initial value:

= {
      "Computes the Rusanov or local Lax-Friedrichs boundary correction term "
      "for the Newtonian Euler/hydrodynamics system."}

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

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