Computes the generalized harmonic upwind multipenalty boundary correction using the averaged fields across the interface. More...
#include <AveragedUpwindPenalty.hpp>
Classes | |
| struct | MeshVelocity |
Public Types | |
| using | options = tmpl::list<> |
| using | dg_package_field_tags = tmpl::list< gr::Tags::SpacetimeMetric< DataVector, Dim >, gh::Tags::Pi< DataVector, Dim >, gh::Tags::Phi< DataVector, Dim >, gh::Tags::ConstraintGamma1, gh::Tags::ConstraintGamma2, domain::Tags::UnnormalizedFaceNormal< Dim >, MeshVelocity > |
| using | dg_package_data_temporary_tags = tmpl::list< gh::Tags::ConstraintGamma1, gh::Tags::ConstraintGamma2, gr::Tags::Lapse< DataVector >, gr::Tags::Shift< DataVector, Dim > > |
| using | dg_package_data_primitive_tags = tmpl::list<> |
| using | dg_package_data_volume_tags = tmpl::list<> |
| using | dg_boundary_terms_volume_tags = tmpl::list<> |
Public Member Functions | |
| AveragedUpwindPenalty (const AveragedUpwindPenalty &)=default | |
| AveragedUpwindPenalty & | operator= (const AveragedUpwindPenalty &)=default |
| AveragedUpwindPenalty (AveragedUpwindPenalty &&)=default | |
| AveragedUpwindPenalty & | operator= (AveragedUpwindPenalty &&)=default |
| void | pup (PUP::er &p) override |
| std::unique_ptr< BoundaryCorrection > | get_clone () const override |
| double | dg_package_data (gsl::not_null< tnsr::aa< DataVector, Dim, Frame::Inertial > * > packaged_spacetime_metric, gsl::not_null< tnsr::aa< DataVector, Dim, Frame::Inertial > * > packaged_pi, gsl::not_null< tnsr::iaa< DataVector, Dim, Frame::Inertial > * > packaged_phi, gsl::not_null< Scalar< DataVector > * > packaged_constraint_gamma1, gsl::not_null< Scalar< DataVector > * > packaged_constraint_gamma2, gsl::not_null< tnsr::i< DataVector, Dim, Frame::Inertial > * > packaged_normal, gsl::not_null< tnsr::I< DataVector, Dim, Frame::Inertial > * > packaged_mesh_velocity, const tnsr::aa< DataVector, Dim, Frame::Inertial > &spacetime_metric, const tnsr::aa< DataVector, Dim, Frame::Inertial > &pi, const tnsr::iaa< DataVector, Dim, Frame::Inertial > &phi, const Scalar< DataVector > &constraint_gamma1, const Scalar< DataVector > &constraint_gamma2, const Scalar< DataVector > &lapse, const tnsr::I< DataVector, Dim > &shift, 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 > > &mesh_velocity, const std::optional< Scalar< DataVector > > &normal_dot_mesh_velocity) const |
| void | dg_boundary_terms (gsl::not_null< tnsr::aa< DataVector, Dim, Frame::Inertial > * > boundary_correction_spacetime_metric, gsl::not_null< tnsr::aa< DataVector, Dim, Frame::Inertial > * > boundary_correction_pi, gsl::not_null< tnsr::iaa< DataVector, Dim, Frame::Inertial > * > boundary_correction_phi, const tnsr::aa< DataVector, Dim, Frame::Inertial > &spacetime_metric_int, const tnsr::aa< DataVector, Dim, Frame::Inertial > &pi_int, const tnsr::iaa< DataVector, Dim, Frame::Inertial > &phi_int, const Scalar< DataVector > &constraint_gamma1_int, const Scalar< DataVector > &constraint_gamma2_int, const tnsr::i< DataVector, Dim, Frame::Inertial > &normal_int, const tnsr::I< DataVector, Dim, Frame::Inertial > &mesh_velocity_int, const tnsr::aa< DataVector, Dim, Frame::Inertial > &spacetime_metric_ext, const tnsr::aa< DataVector, Dim, Frame::Inertial > &pi_ext, const tnsr::iaa< DataVector, Dim, Frame::Inertial > &phi_ext, const Scalar< DataVector > &constraint_gamma1_ext, const Scalar< DataVector > &constraint_gamma2_ext, const tnsr::i< DataVector, Dim, Frame::Inertial > &normal_ext, const tnsr::I< DataVector, Dim, Frame::Inertial > &mesh_velocity_ext, dg::Formulation dg_formulation) const |
 Public Member Functions inherited from evolution::BoundaryCorrection | |
| BoundaryCorrection (const BoundaryCorrection &)=default | |
| BoundaryCorrection & | operator= (const BoundaryCorrection &)=default |
| BoundaryCorrection (BoundaryCorrection &&)=default | |
| BoundaryCorrection & | operator= (BoundaryCorrection &&)=default |
| BoundaryCorrection (CkMigrateMessage *msg) | |
| virtual std::unique_ptr< BoundaryCorrection > | get_clone () const =0 |
Static Public Attributes | |
| static constexpr Options::String | help |
Detailed Description
class gh::BoundaryCorrections::AveragedUpwindPenalty< Dim >
Computes the generalized harmonic upwind multipenalty boundary correction using the averaged fields across the interface.
The correction is given by
\begin{equation} D_\beta = T^{-1}_{\beta\hat{\beta}}(u^{\text{avg}}) \Lambda^-_{\hat{\beta}\hat{\alpha}}(u^{\text{avg}}) T_{\hat{\alpha}\alpha}(u^{\text{avg}}) \Delta u_\alpha, \end{equation}
where \(u_\alpha\) are the evolved fields, \(\Lambda^-\) is the diagonal matrix of incoming characteristic speeds, \(T_{\hat{\alpha}\alpha}\) transforms from evolved to characteristic fields, and \(\Delta u_\alpha = u_\alpha^{\text{ext}} - u_\alpha^{\text{int}}\) is the discontinuity in the evolved fields. All factors except the boundary discontinuity are calculated using the averaged of the internal and external evolved fields:
\begin{equation} u^{\text{avg}} = \frac{u^{\text{int}} + u^{\text{ext}}}{2}. \end{equation}
For the first-order generalized harmonic system the correction is:
\begin{align} D_{g_{ab}} &= \lambda_{v^g}^- \Delta g_{ab} \\ D_{\Pi_{ab}} &= \left(\lambda_{v^g}^- - \frac{\lambda_{v^+}^- + \lambda_{v^-}^-}{2}\right) \gamma_2 \Delta g_{ab} + \frac{\lambda_{v^+}^- + \lambda_{v^-}^-}{2} \Delta \Pi_{ab} + \frac{\lambda_{v^+}^- - \lambda_{v^-}^-}{2} n^j \Delta \Phi_{jab} \\ D_{\Phi_{iab}} &= \lambda_{v^0}^- (\delta_i^j - n_i n^j) \Delta \Phi_{jab} + \frac{\lambda_{v^+}^- - \lambda_{v^-}^-}{2} n_i (\Delta \Pi_{ab} - \gamma_2 \Delta g_{ab}) + \frac{\lambda_{v^+}^- + \lambda_{v^-}^-}{2} n_i n^j \Delta \Phi_{jab}. \end{align}
In the above expressions, the outgoing face normal \(n_i\) is normalized using the average metric from the two sides. Quantities such as \(\gamma_2\) that should analytically be the same on both sides of the interface are also averaged, as they can differ because of truncation errors during projection.
The characteristic speeds are given by
\begin{align} \lambda_{v^g} &= - (1 + \gamma_1) (\beta^i + v^i_g) n_i, \\ \lambda_{v^0} &= - (\beta^i + v^i_g) n_i, \\ \lambda_{v^\pm} &= \pm \alpha - (\beta^i + v^i_g) n_i, \end{align}
where \(v_g^i\) is the mesh velocity, with the incoming speeds
\begin{equation} \lambda^-_{\hat{\alpha}} = \begin{cases} \lambda_{\hat{\alpha}} & \lambda_{\hat{\alpha}} < 0 \\ 0 & \text{otherwise.} \end{cases} \end{equation}
Member Function Documentation
◆ get_clone()
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overridevirtual |
Implements evolution::BoundaryCorrection.
Member Data Documentation
◆ help
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staticconstexpr |
The documentation for this class was generated from the following file:
- src/Evolution/Systems/GeneralizedHarmonic/BoundaryCorrections/AveragedUpwindPenalty.hpp