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| Rusanov (const Rusanov &)=default |
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Rusanov & | operator= (const Rusanov &)=default |
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| Rusanov (Rusanov &&)=default |
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Rusanov & | operator= (Rusanov &&)=default |
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void | pup (PUP::er &p) override |
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std::unique_ptr< BoundaryCorrection< Dim > > | get_clone () const override |
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template<size_t ThermodynamicDim> |
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, Dim, Frame::Inertial > * > packaged_tilde_s, 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, Dim, Frame::Inertial > * > packaged_normal_dot_flux_tilde_s, gsl::not_null< Scalar< DataVector > * > packaged_abs_char_speed, const Scalar< DataVector > &tilde_d, const Scalar< DataVector > &tilde_tau, const tnsr::i< DataVector, Dim, Frame::Inertial > &tilde_s, const tnsr::I< DataVector, Dim, Frame::Inertial > &flux_tilde_d, const tnsr::I< DataVector, Dim, Frame::Inertial > &flux_tilde_tau, const tnsr::Ij< DataVector, Dim, Frame::Inertial > &flux_tilde_s, const Scalar< DataVector > &lapse, const tnsr::I< DataVector, Dim, Frame::Inertial > &shift, const tnsr::ii< DataVector, Dim, Frame::Inertial > &spatial_metric, const Scalar< DataVector > &rest_mass_density, const Scalar< DataVector > &specific_internal_energy, const Scalar< DataVector > &specific_enthalpy, const tnsr::I< DataVector, Dim, Frame::Inertial > &spatial_velocity, const tnsr::i< DataVector, Dim, Frame::Inertial > &normal_covector, const tnsr::I< DataVector, Dim, Frame::Inertial > &normal_vector, const std::optional< tnsr::I< DataVector, Dim, Frame::Inertial > > &, const std::optional< Scalar< DataVector > > &normal_dot_mesh_velocity, const EquationsOfState::EquationOfState< true, ThermodynamicDim > &equation_of_state) const |
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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, Dim, Frame::Inertial > * > boundary_correction_tilde_s, const Scalar< DataVector > &tilde_d_int, const Scalar< DataVector > &tilde_tau_int, const tnsr::i< DataVector, Dim, Frame::Inertial > &tilde_s_int, const Scalar< DataVector > &normal_dot_flux_tilde_d_int, const Scalar< DataVector > &normal_dot_flux_tilde_tau_int, const tnsr::i< DataVector, Dim, Frame::Inertial > &normal_dot_flux_tilde_s_int, const Scalar< DataVector > &abs_char_speed_int, const Scalar< DataVector > &tilde_d_ext, const Scalar< DataVector > &tilde_tau_ext, const tnsr::i< DataVector, Dim, Frame::Inertial > &tilde_s_ext, const Scalar< DataVector > &normal_dot_flux_tilde_d_ext, const Scalar< DataVector > &normal_dot_flux_tilde_tau_ext, const tnsr::i< DataVector, Dim, Frame::Inertial > &normal_dot_flux_tilde_s_ext, const Scalar< DataVector > &abs_char_speed_ext, dg::Formulation dg_formulation) const |
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| BoundaryCorrection (const BoundaryCorrection &)=default |
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BoundaryCorrection & | operator= (const BoundaryCorrection &)=default |
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| BoundaryCorrection (BoundaryCorrection &&)=default |
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BoundaryCorrection & | operator= (BoundaryCorrection &&)=default |
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virtual std::unique_ptr< BoundaryCorrection< Dim > > | get_clone () const =0 |
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template<size_t Dim>
class RelativisticEuler::Valencia::BoundaryCorrections::Rusanov< Dim >
A Rusanov/local Lax-Friedrichs Riemann solver.
Let \(U\) be the state vector of evolved variables, \(F^i\) the corresponding fluxes, and \(n_i\) be the outward directed unit normal to the interface. Denoting \(F := n_i F^i\), the Rusanov boundary correction is
\begin{align*} G_\text{Rusanov} = \frac{F_\text{int} - F_\text{ext}}{2} - \frac{\text{max}\left(\{|\lambda_\text{int}|\}, \{|\lambda_\text{ext}|\}\right)}{2} \left(U_\text{ext} - U_\text{int}\right), \end{align*}
where "int" and "ext" stand for interior and exterior, and \(\{|\lambda|\}\) is the set of characteristic/signal speeds. The minus sign in front of the \(F_{\text{ext}}\) is necessary 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 expressions are listed in the documentation of characteristic_speeds
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- Note
- In the strong form the
dg_boundary_terms
function returns \(G - F_\text{int}\)