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::TildeTau, Tags::TildeS< Frame::Inertial >, Tags::TildeB< Frame::Inertial >, Tags::TildePhi, ::Tags::NormalDotFlux< Tags::TildeD >, ::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< 3, Frame::Inertial, DataVector > > |
| using | dg_package_data_primitive_tags = tmpl::list<> |
| using | dg_package_data_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 noexcept 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 |
Static Public Member Functions | |
| static double | dg_package_data (gsl::not_null< Scalar< DataVector > * > packaged_tilde_d, 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_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_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_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) noexcept |
| static void | dg_boundary_terms (gsl::not_null< Scalar< DataVector > * > boundary_correction_tilde_d, 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_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_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_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_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) noexcept |
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 [54]
\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_termsfunction 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.
- In the strong form the
Member Function Documentation
◆ get_clone()
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overridevirtualnoexcept |
Member Data Documentation
◆ help
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staticconstexpr |