gh::BoundaryConditions::ConstraintPreservingBjorhus< Dim > Class Template Reference

Sets constraint preserving boundary conditions using the Bjorhus method. More...

#include <Bjorhus.hpp>

Classes
struct	TypeOptionTag

Public Types
using	options = implementation defined
using	dg_interior_evolved_variables_tags = implementation defined
using	dg_interior_temporary_tags = implementation defined
using	dg_interior_dt_vars_tags = implementation defined
using	dg_interior_deriv_vars_tags = implementation defined
using	dg_gridless_tags = implementation defined

Public Member Functions
	ConstraintPreservingBjorhus (detail::ConstraintPreservingBjorhusType type)
	ConstraintPreservingBjorhus (CkMigrateMessage *msg)
	WRAPPED_PUPable_decl_base_template (domain::BoundaryConditions::BoundaryCondition, ConstraintPreservingBjorhus)
auto	get_clone () const -> std::unique_ptr< domain::BoundaryConditions::BoundaryCondition > override
void	pup (PUP::er &p) override
std::optional< std::string >	dg_time_derivative (gsl::not_null< tnsr::aa< DataVector, Dim, Frame::Inertial > * > dt_spacetime_metric_correction, gsl::not_null< tnsr::aa< DataVector, Dim, Frame::Inertial > * > dt_pi_correction, gsl::not_null< tnsr::iaa< DataVector, Dim, Frame::Inertial > * > dt_phi_correction, const std::optional< tnsr::I< DataVector, Dim, Frame::Inertial > > &face_mesh_velocity, const tnsr::i< DataVector, Dim, Frame::Inertial > &normal_covector, const tnsr::I< DataVector, Dim, Frame::Inertial > &, 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 tnsr::I< DataVector, Dim, Frame::Inertial > &coords, const Scalar< DataVector > &gamma1, const Scalar< DataVector > &gamma2, const Scalar< DataVector > &lapse, const tnsr::I< DataVector, Dim, Frame::Inertial > &shift, const tnsr::AA< DataVector, Dim, Frame::Inertial > &inverse_spacetime_metric, const tnsr::A< DataVector, Dim, Frame::Inertial > &spacetime_unit_normal_vector, const tnsr::iaa< DataVector, Dim, Frame::Inertial > &three_index_constraint, const tnsr::a< DataVector, Dim, Frame::Inertial > &gauge_source, const tnsr::ab< DataVector, Dim, Frame::Inertial > &spacetime_deriv_gauge_source, const tnsr::aa< DataVector, Dim, Frame::Inertial > &logical_dt_spacetime_metric, const tnsr::aa< DataVector, Dim, Frame::Inertial > &logical_dt_pi, const tnsr::iaa< DataVector, Dim, Frame::Inertial > &logical_dt_phi, const tnsr::iaa< DataVector, Dim, Frame::Inertial > &d_spacetime_metric, const tnsr::iaa< DataVector, Dim, Frame::Inertial > &d_pi, const tnsr::ijaa< DataVector, Dim, Frame::Inertial > &d_phi) const
Public Member Functions inherited from gh::BoundaryConditions::BoundaryCondition< Dim >
	BoundaryCondition (BoundaryCondition &&)=default
BoundaryCondition &	operator= (BoundaryCondition &&)=default
	BoundaryCondition (const BoundaryCondition &)=default
BoundaryCondition &	operator= (const BoundaryCondition &)=default
	BoundaryCondition (CkMigrateMessage *msg)
void	pup (PUP::er &p) override
Public Member Functions inherited from domain::BoundaryConditions::BoundaryCondition
	BoundaryCondition (BoundaryCondition &&)=default
BoundaryCondition &	operator= (BoundaryCondition &&)=default
	BoundaryCondition (const BoundaryCondition &)=default
BoundaryCondition &	operator= (const BoundaryCondition &)=default
	BoundaryCondition (CkMigrateMessage *const msg)
	WRAPPED_PUPable_abstract (BoundaryCondition)
virtual auto	get_clone () const -> std::unique_ptr< BoundaryCondition >=0

Static Public Member Functions
static std::string	name ()

Static Public Attributes
static constexpr Options::String	help
static constexpr evolution::BoundaryConditions::Type	bc_type

Detailed Description

template<size_t Dim>
class gh::BoundaryConditions::ConstraintPreservingBjorhus< Dim >

Sets constraint preserving boundary conditions using the Bjorhus method.

Details

Boundary conditions for the generalized harmonic evolution system can be divided in to three parts, constraint-preserving, physical and gauge boundary conditions.

The generalized harmonic (GH) evolution system is a first-order reduction of Einstein equations brought about by the imposition of GH gauge. This introduces constraints on the free (evolved) variables in addition to the standard Hamiltonian and momentum constraints. The constraint-preserving portion of the boundary conditions is designed to prevent the influx of constraint violations from external faces of the evolution domain, by damping them away on a controlled and short time-scale. These conditions are imposed as corrections to the characteristic projections of the right-hand-sides of the GH evolution equations (i.e. using Bjorhus' method [23]), as written down in Eq. (63) - (65) of [127] . In addition to these equations, the fourth projection is simply frozen in the unlikely case its coordinate speed becomes negative, i.e. $d_t{u}^{\hat{1}+}{}_{ab}=0$ (in the notation of [127]). The gauge degrees of freedom are controlled by imposing a Sommerfeld-type condition ( $L=0$ member of the hierarchy derived in [17]) that allow gauge perturbations to pass through the boundary without strong reflections. These assume a spherical outer boundary, and can be written down as in Eq. (25) of [173] . Finally, the physical boundary conditions control the influx of inward propagating gravitational-wave solutions from the external boundaries. These are derived by considering the evolution system of the Weyl curvature tensor, and controlling the inward propagating characteristics of the system that are proportional to the Newman-Penrose curvature spinor components ${\mathrm{\Psi }}_4$ and ${\mathrm{\Psi }}_0$. Here we use Eq. (68) of [127] to disallow any incoming waves. It is to be noted that all the above conditions are also imposed on characteristic modes with speeds exactly zero.

This class provides two choices of combinations of the above corrections:

• ConstraintPreserving : this imposes the constraint-preserving and gauge-controlling corrections;
• ConstraintPreservingPhysical : this additionally restricts the influx of any physical gravitational waves from the outer boundary, in addition to preventing the influx of constraint violations and gauge perturbations.

We refer to Bjorhus::constraint_preserving_bjorhus_corrections_dt_v_psi(), Bjorhus::constraint_preserving_bjorhus_corrections_dt_v_zero(), Bjorhus::constraint_preserving_bjorhus_corrections_dt_v_minus(), and Bjorhus::constraint_preserving_physical_bjorhus_corrections_dt_v_minus() for the further details on implementation.

Note

These boundary conditions assume a spherical outer boundary. Also, we do not yet have an option to inject incoming gravitational waves at the outer boundary.

Member Function Documentation

get_clone()

template<size_t Dim>

auto gh::BoundaryConditions::ConstraintPreservingBjorhus< Dim >::get_clone ( ) const -> std::unique_ptr< domain::BoundaryConditions::BoundaryCondition >

overridevirtual

Implements domain::BoundaryConditions::BoundaryCondition.

Member Data Documentation

bc_type

template<size_t Dim>

constexpr evolution::BoundaryConditions::Type gh::BoundaryConditions::ConstraintPreservingBjorhus< Dim >::bc_type

staticconstexpr

Initial value:

=
      evolution::BoundaryConditions::Type::TimeDerivative

help

template<size_t Dim>

constexpr Options::String gh::BoundaryConditions::ConstraintPreservingBjorhus< Dim >::help

staticconstexpr

Initial value:

{
      "ConstraintPreservingBjorhus boundary conditions setting the value of the"
      "time derivatives of the spacetime metric, Phi and Pi to expressions that"
      "prevent the influx of constraint violations and reflections."}

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

• src/Evolution/Systems/GeneralizedHarmonic/BoundaryConditions/Bjorhus.hpp