Classes | Public Types | Public Member Functions | Static Public Attributes | List of all members
NewtonianEuler::BoundaryCorrections::Hll< Dim > Class Template Referencefinal

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

#include <Hll.hpp>

Classes

struct  LargestIngoingCharSpeed
 
struct  LargestOutgoingCharSpeed
 

Public Types

using options = tmpl::list<>
 
using dg_package_field_tags = tmpl::list< Tags::MassDensityCons, Tags::MomentumDensity< Dim >, Tags::EnergyDensity, ::Tags::NormalDotFlux< Tags::MassDensityCons >, ::Tags::NormalDotFlux< Tags::MomentumDensity< Dim > >, ::Tags::NormalDotFlux< Tags::EnergyDensity >, LargestOutgoingCharSpeed, LargestIngoingCharSpeed >
 
using dg_package_data_temporary_tags = tmpl::list<>
 
using dg_package_data_primitive_tags = tmpl::list< NewtonianEuler::Tags::Velocity< DataVector, Dim >, NewtonianEuler::Tags::SpecificInternalEnergy< DataVector > >
 
using dg_package_data_volume_tags = tmpl::list< hydro::Tags::EquationOfStateBase >
 
- Public Types inherited from NewtonianEuler::BoundaryCorrections::BoundaryCorrection< Dim >
using creatable_classes = tmpl::list< Hll< Dim >, Hllc< Dim >, Rusanov< Dim > >
 

Public Member Functions

 Hll (const Hll &)=default
 
Hlloperator= (const Hll &)=default
 
 Hll (Hll &&)=default
 
Hlloperator= (Hll &&)=default
 
void pup (PUP::er &p) override
 
std::unique_ptr< BoundaryCorrection< Dim > > get_clone () const noexcept override
 
template<size_t ThermodynamicDim>
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, ThermodynamicDim > &equation_of_state) const noexcept
 
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 noexcept
 
- Public Member Functions inherited from NewtonianEuler::BoundaryCorrections::BoundaryCorrection< Dim >
 BoundaryCorrection (const BoundaryCorrection &)=default
 
BoundaryCorrectionoperator= (const BoundaryCorrection &)=default
 
 BoundaryCorrection (BoundaryCorrection &&)=default
 
BoundaryCorrectionoperator= (BoundaryCorrection &&)=default
 

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 [51]

\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. \(n_i^{\text{ext}}=-n_i^{\text{int}}\).

For the NewtonianEuler system, \(\lambda^\pm\) are given as

\begin{align*} \lambda^\pm = v^in_i \pm c_s \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 \(G - F_\text{int}\)
  • 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 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."}

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