grmhd::ValenciaDivClean::BoundaryCorrections::Hll Class Reference

An HLL Riemann solver. More...

#include <Hll.hpp>

Classes
struct	LargestIngoingCharSpeed
struct	LargestOutgoingCharSpeed

Public Types
using	options = tmpl::list<>
using	dg_package_field_tags = 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 >, LargestOutgoingCharSpeed, LargestIngoingCharSpeed >
using	dg_package_data_temporary_tags = tmpl::list< gr::Tags::Lapse< DataVector >, gr::Tags::Shift< DataVector, 3 > >
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 Types inherited from grmhd::ValenciaDivClean::BoundaryCorrections::BoundaryCorrection
using	creatable_classes = tmpl::list< Hll, Rusanov >

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

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_largest_outgoing_char_speed, gsl::not_null< Scalar< DataVector > * > packaged_largest_ingoing_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 > &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< 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 > &largest_outgoing_char_speed_int, const Scalar< DataVector > &largest_ingoing_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 > &largest_outgoing_char_speed_ext, const Scalar< DataVector > &largest_ingoing_char_speed_ext, dg::Formulation dg_formulation)

Static Public Attributes
static constexpr Options::String	help

Detailed Description

An HLL Riemann solver.

Let \(U\) be the evolved variable, \(F^i\) the flux, and \(n_i\) be the outward directed unit normal to the interface. Denoting \(F := n_i F^i\), the HLL boundary correction is [82]

\begin{align*} G_\text{HLL} = \frac{\lambda_\text{max} F_\text{int} + \lambda_\text{min} F_\text{ext}}{\lambda_\text{max} - \lambda_\text{min}} - \frac{\lambda_\text{min}\lambda_\text{max}}{\lambda_\text{max} - \lambda_\text{min}} \left(U_\text{int} - U_\text{ext}\right) \end{align*}

where "int" and "ext" stand for interior and exterior. \(\lambda_\text{min}\) and \(\lambda_\text{max}\) are defined as

\begin{align*} \lambda_\text{min} &= \text{min}\left(\lambda^{-}_\text{int},-\lambda^{+}_\text{ext}, 0\right) \\ \lambda_\text{max} &= \text{max}\left(\lambda^{+}_\text{int},-\lambda^{-}_\text{ext}, 0\right) \end{align*}

where \(\lambda^{+}\) ( \(\lambda^{-}\)) is the largest characteristic speed in the outgoing (ingoing) direction. Note the minus signs in front of \(\lambda^{\pm}_\text{ext}\), which is because an outgoing speed w.r.t. the neighboring element is an ingoing speed w.r.t. the local element, and vice versa. Similarly, the \(F_{\text{ext}}\) term in \(G_\text{HLL}\) has a positive sign 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 \(G - F_\text{int}\)
• For either \(\lambda_\text{min} = 0\) or \(\lambda_\text{max} = 0\) (i.e. all characteristics move in the same direction) the HLL boundary correction reduces to pure upwinding.
• Some references use \(S\) instead of \(\lambda\) for the signal/characteristic speeds
• 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 Function Documentation

get_clone()

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

overridevirtual

Implements grmhd::ValenciaDivClean::BoundaryCorrections::BoundaryCorrection.

Member Data Documentation

help

constexpr Options::String grmhd::ValenciaDivClean::BoundaryCorrections::Hll::help

staticconstexpr

Initial value:

= {
      "Computes the HLL 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/Hll.hpp