|
|
| ConstraintPreservingBjorhus (detail::ConstraintPreservingBjorhusType type, std::optional< std::unique_ptr<::MathFunction< 1, Frame::Inertial > > > incoming_wave_profile=std::nullopt) |
|
| 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, double time=std::numeric_limits< double >::signaling_NaN()) const |
|
| 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) |
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 [132] . 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 [132]). 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 [181] . 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 \(\Psi_4\) and \(\Psi_0\). Here we use Eq. (68) of [132] 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.
An optional injected incoming-wave contribution can be specified through IncomingWaveProfile. The injected strain-rate tensor is
\[ \dot{h}_{ab} = \dot{f}(t)
\left(\hat{x}_a \hat{x}_b + \hat{y}_a \hat{y}_b - 2 \hat{z}_a
\hat{z}_b\right),
\]
where the configured profile is interpreted directly as \(\dot{f}(t)\) and \(\hat{x}_a\), \(\hat{y}_a\) and \(\hat{z}_a\) are the components of the coordinate basis vectors. This formula is taken from [132]. It should be considered an approximate perturbation rather than an exact gravitational wave which would have to be constructed at null-infinity. Note that the profile of the injected wave is specified at the outer boundary and its amplitude should be adjusted according to the usual 1/r scaling.
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_corrections_dt_v_psi(), Bjorhus::constraint_preserving_corrections_dt_v_zero(), Bjorhus::constraint_preserving_gauge_corrections_dt_v_minus(), and Bjorhus::constraint_preserving_gauge_physical_corrections_dt_v_minus() for the further details on implementation.
- Note
- These boundary conditions assume a spherical outer boundary.