Computes the upwind multipenalty boundary correction for scalar wave in curved spacetime. More...

#include <UpwindPenalty.hpp>

Public Types
using	options = tmpl::list<>

using	dg_package_field_tags = tmpl::list< Tags::VPsi, Tags::VZero< Dim >, Tags::VPlus, Tags::VMinus, Tags::ConstraintGamma2, ::Tags::Normalized< domain::Tags::UnnormalizedFaceNormal< Dim, Frame::Inertial > >, CharSpeedsTensor >

using	dg_package_data_temporary_tags = tmpl::list< gr::Tags::Lapse< DataVector >, gr::Tags::Shift< DataVector, Dim >, Tags::ConstraintGamma1, Tags::ConstraintGamma2 >

using	dg_package_data_volume_tags = tmpl::list<>

using	dg_boundary_terms_volume_tags = tmpl::list<>

Public Types inherited from CurvedScalarWave::BoundaryCorrections::BoundaryCorrection< Dim >
using	creatable_classes = tmpl::list< UpwindPenalty< Dim > >

Public Member Functions
	UpwindPenalty (const UpwindPenalty &)=default

UpwindPenalty &	operator= (const UpwindPenalty &)=default

	UpwindPenalty (UpwindPenalty &&)=default

UpwindPenalty &	operator= (UpwindPenalty &&)=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_v_psi, gsl::not_null< tnsr::i< DataVector, Dim, Frame::Inertial > * > packaged_v_zero, gsl::not_null< Scalar< DataVector > * > packaged_v_plus, gsl::not_null< Scalar< DataVector > * > packaged_v_minus, gsl::not_null< Scalar< DataVector > * > packaged_gamma2, gsl::not_null< tnsr::i< DataVector, Dim, Frame::Inertial > * > packaged_interface_unit_normal, gsl::not_null< tnsr::a< DataVector, 3, Frame::Inertial > * > packaged_char_speeds, const Scalar< DataVector > &psi, const Scalar< DataVector > &pi, const tnsr::i< DataVector, Dim, Frame::Inertial > &phi, const Scalar< DataVector > &lapse, const tnsr::I< DataVector, Dim, Frame::Inertial > &shift, const Scalar< DataVector > &constraint_gamma1, const Scalar< DataVector > &constraint_gamma2, const tnsr::i< DataVector, Dim, Frame::Inertial > &interface_unit_normal, const tnsr::I< DataVector, Dim, Frame::Inertial > &interface_unit_normal_vector, const std::optional< tnsr::I< DataVector, Dim, Frame::Inertial > > &, const std::optional< Scalar< DataVector > > &normal_dot_mesh_velocity) const

void	dg_boundary_terms (gsl::not_null< Scalar< DataVector > * > psi_boundary_correction, gsl::not_null< Scalar< DataVector > * > pi_boundary_correction, gsl::not_null< tnsr::i< DataVector, Dim, Frame::Inertial > * > phi_boundary_correction, const Scalar< DataVector > &v_psi_int, const tnsr::i< DataVector, Dim, Frame::Inertial > &v_zero_int, const Scalar< DataVector > &v_plus_int, const Scalar< DataVector > &v_minus_int, const Scalar< DataVector > &gamma2_int, const tnsr::i< DataVector, Dim, Frame::Inertial > &interface_unit_normal_int, const tnsr::a< DataVector, 3, Frame::Inertial > &char_speeds_int, const Scalar< DataVector > &v_psi_ext, const tnsr::i< DataVector, Dim, Frame::Inertial > &v_zero_ext, const Scalar< DataVector > &v_plus_ext, const Scalar< DataVector > &v_minus_ext, const Scalar< DataVector > &gamma2_ext, const tnsr::i< DataVector, Dim, Frame::Inertial > &interface_unit_normal_ext, const tnsr::a< DataVector, 3, Frame::Inertial > &char_speeds_ext, dg::Formulation) const

Public Member Functions inherited from CurvedScalarWave::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

Detailed Description

template<size_t Dim>
class CurvedScalarWave::BoundaryCorrections::UpwindPenalty< Dim >

Computes the upwind multipenalty boundary correction for scalar wave in curved spacetime.

Details

This implements the upwind multipenalty boundary correction term. The general form is given by:

\[ G = T^{\rm ext}\Lambda^{\rm ext,-} {T^{\rm ext}}^{-1} U^{\rm ext} + T^{\rm int}\Lambda^{\rm int,+} {T^{\rm int}}^{-1} U^{\rm int} = T^{\rm ext}\Lambda^{\rm ext,-} V^{\rm ext} + T^{\rm int}\Lambda^{\rm int,+} V^{\rm int}, \]

where

\(G\) is a vector of numerical upwind fluxes dotted with the interface normal for all evolved variables;
\(U\) is a vector of all evolved variables;
\(T\) is a matrix whose columns are the eigenvectors of the characteristic matrix for the evolution system. It maps the evolved variables to characteristic variables \(V\), s.t. \(V := T^{-1}\cdot U\); and
\(\Lambda^\pm\) are diagonal matrices containing positive / negative eigenvalues of \(T\) as its diagonal elements, with the rest set to \( 0\).

The superscripts \({\rm int}\) and \({\rm ext}\) indicate that the corresponding variable at the element interface comes from the interior or exterior of the element. Exterior of the element is naturally the interior of its neighboring element. The sign of characteristic speeds indicate the direction of propagation of the corresponding characteristic field with respect to the interface normal that the field has been computed along, with negative speeds indicating incoming characteristics, and positive speeds indicating outgoing characteristics. The expressions implemented here differ from Eq.(63) of [182] as that boundary term does not consistently treat both sides of the interface on the same footing. Unlike in [182], in code the interface normal vector on the interior side and the one on the exterior side point in opposite directions, and the characteristic speeds end up having different signs. This class therefore computes:

\[ G = T^{\rm ext}w_{\rm ext} V^{\rm ext} - T^{\rm int}w_{\rm int} V^{\rm int}, \]

with weights \(w_{\rm ext} = -\Theta(\Lambda^{\rm ext})\cdot\Lambda^{\rm ext}\), and \(w_{\rm int} = \Theta(-\Lambda^{\rm int})\cdot\Lambda^{\rm int}\), where \(\Theta\) is the Heaviside function centered at zero, \(\Lambda = \Lambda^+ + \Lambda^-\), and the dot operator \((\cdot)\) indicates an element-wise product.

Member Function Documentation

◆ get_clone()

template<size_t Dim>

std::unique_ptr< BoundaryCorrection< Dim > > CurvedScalarWave::BoundaryCorrections::UpwindPenalty< Dim >::get_clone ( ) const

overridevirtual

Implements CurvedScalarWave::BoundaryCorrections::BoundaryCorrection< Dim >.

Member Data Documentation

◆ help

template<size_t Dim>

constexpr Options::String CurvedScalarWave::BoundaryCorrections::UpwindPenalty< Dim >::help

staticconstexpr

Initial value:

= {
      "Computes the UpwindPenalty boundary correction term for the scalar wave "
      "system in curved spacetime."}

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

src/Evolution/Systems/CurvedScalarWave/BoundaryCorrections/UpwindPenalty.hpp

Public Types

Public Member Functions