NewtonianEuler::BoundaryCorrections::Hll< Dim > Class Template Reference

An HLL (Harten-Lax-van Leer) Riemann solver for NewtonianEuler system. More...

#include <Hll.hpp>

Classes
struct	LargestIngoingCharSpeed
struct	LargestOutgoingCharSpeed

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_primitive_tags = implementation defined
using	dg_package_data_volume_tags = implementation defined
using	dg_boundary_terms_volume_tags = implementation defined
Public Types inherited from NewtonianEuler::BoundaryCorrections::BoundaryCorrection< Dim >
using	creatable_classes = implementation defined

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< Dim > >	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_largest_outgoing_char_speed, gsl::not_null< Scalar< DataVector > * > packaged_largest_ingoing_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 > &largest_outgoing_char_speed_int, const Scalar< DataVector > &largest_ingoing_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 > &largest_outgoing_char_speed_ext, const Scalar< DataVector > &largest_ingoing_char_speed_ext, dg::Formulation dg_formulation) const
Public Member Functions inherited from NewtonianEuler::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 Attributes
static constexpr Options::String	help

Detailed Description

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

An HLL (Harten-Lax-van Leer) Riemann solver for NewtonianEuler system.

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 [89]

$$\begin{array}{r}{G}_{\text{HLL}}=\frac{{\lambda }_{\text{max}}{F}_{\text{int}}+{\lambda }_{\text{min}}{F}_{\text{ext}}}{{\lambda }_{\text{max}}-{\lambda }_{\text{min}}}-\frac{{\lambda }_{\text{min}}{\lambda }_{\text{max}}}{{\lambda }_{\text{max}}-{\lambda }_{\text{min}}}(U_{\text{int}}-U_{\text{ext}})\end{array}$$

where "int" and "ext" stand for interior and exterior. ${\lambda }_{\text{min}}$ and ${\lambda }_{\text{max}}$ are defined as

$$\begin{array}{rl}{\lambda }_{\text{min}}& =\text{min}({\lambda }_{\text{int}}^{-},-{\lambda }_{\text{ext}}^{+},0)\\ {\lambda }_{\text{max}}& =\text{max}({\lambda }_{\text{int}}^{+},-{\lambda }_{\text{ext}}^{-},0)\end{array}$$

where ${\lambda }^{+}$ ( ${\lambda }^{-}$) is the largest characteristic speed in the outgoing (ingoing) direction. Note the minus signs in front of ${\lambda }_{\text{ext}}^{\pm }$, 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. $n_i^{\text{ext}}=-n_i^{\text{int}}$.

For the NewtonianEuler system, ${\lambda }^{\pm }$ are given as

$$\begin{array}{r}{\lambda }^{\pm }=v^i{n}_i\pm c_s\end{array}$$

where $v^i$ is the spatial velocity and $c_s$ the sound speed.

Note

• In the strong form the dg_boundary_terms function returns $G-F_{\text{int}}$
• 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

Member Function Documentation

get_clone()

template<size_t Dim>

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

overridevirtual

Implements NewtonianEuler::BoundaryCorrections::BoundaryCorrection< Dim >.

Member Data Documentation

help

template<size_t Dim>

constexpr Options::String NewtonianEuler::BoundaryCorrections::Hll< Dim >::help

staticconstexpr

Initial value:

= {
      "Computes the HLL 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/Hll.hpp