SpECTRE
v2024.04.12
|
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< hydro::Tags::SpatialVelocity< DataVector, Dim >, hydro::Tags::SpecificInternalEnergy< DataVector > > |
using | dg_package_data_volume_tags = tmpl::list< hydro::Tags::EquationOfState< false, 2 > > |
using | dg_boundary_terms_volume_tags = tmpl::list<> |
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 | |
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 |
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 [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. \(n_i^{\text{ext}}=-n_i^{\text{int}}\).
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.
dg_boundary_terms
function returns \(G - F_\text{int}\)
|
overridevirtual |
|
staticconstexpr |