Sets boundary conditions for the elements abutting the worldtube using a combination of constraint-preserving boundary conditions and the local solution evolved inside the worldtube. More...

#include <Worldtube.hpp>

Public Types
using	options = tmpl::list<>
using	dg_interior_temporary_tags
using	dg_gridless_tags
using	dg_interior_evolved_variables_tags
using	dg_interior_dt_vars_tags = tmpl::list<::Tags::dt<Tags::Psi>>
using	dg_interior_deriv_vars_tags

Public Member Functions
	Worldtube (CkMigrateMessage *msg)
	WRAPPED_PUPable_decl_base_template (domain::BoundaryConditions::BoundaryCondition, Worldtube)
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< Scalar< DataVector > * > dt_psi_correction, gsl::not_null< Scalar< DataVector > * > dt_pi_correction, gsl::not_null< tnsr::i< DataVector, Dim, Frame::Inertial > * > dt_phi_correction, const std::optional< tnsr::I< DataVector, Dim > > &face_mesh_velocity, const tnsr::i< DataVector, Dim > &normal_covector, const tnsr::I< DataVector, Dim > &normal_vector, const Scalar< DataVector > &, const Scalar< DataVector > &, const tnsr::i< DataVector, Dim > &phi, const Scalar< DataVector > &lapse, const tnsr::I< DataVector, Dim > &shift, const tnsr::II< DataVector, Dim, Frame::Inertial > &, const Scalar< DataVector > &gamma1, const Scalar< DataVector > &gamma2, const Scalar< DataVector > &, const tnsr::i< DataVector, Dim > &d_psi, const tnsr::ij< DataVector, Dim > &d_phi, const Variables< tmpl::list< Tags::Psi, Tags::Pi, Tags::Phi< Dim > > > &) const
std::optional< std::string >	dg_ghost (const gsl::not_null< Scalar< DataVector > * > psi, const gsl::not_null< Scalar< DataVector > * > pi, const gsl::not_null< tnsr::i< DataVector, Dim, Frame::Inertial > * > phi, const gsl::not_null< Scalar< DataVector > * > lapse, const gsl::not_null< tnsr::I< DataVector, Dim, Frame::Inertial > * > shift, const gsl::not_null< Scalar< DataVector > * > gamma1, const gsl::not_null< Scalar< DataVector > * > gamma2, const gsl::not_null< tnsr::II< DataVector, Dim, Frame::Inertial > * > inverse_spatial_metric, const std::optional< tnsr::I< DataVector, Dim, Frame::Inertial > > &, const tnsr::i< DataVector, Dim, Frame::Inertial > &normal_covector, const tnsr::I< DataVector, Dim, Frame::Inertial > &normal_vector, const Scalar< DataVector > &psi_interior, const Scalar< DataVector > &pi_interior, const tnsr::i< DataVector, Dim > &phi_interior, const Scalar< DataVector > &lapse_interior, const tnsr::I< DataVector, Dim, Frame::Inertial > &shift_interior, const tnsr::II< DataVector, Dim, Frame::Inertial > &inverse_spatial_metric_interior, const Scalar< DataVector > &gamma1_interior, const Scalar< DataVector > &gamma2_interior, const Scalar< DataVector > &, const tnsr::i< DataVector, Dim > &d_psi, const tnsr::ij< DataVector, Dim > &, const Variables< tmpl::list< Tags::Psi, Tags::Pi, Tags::Phi< Dim > > > &worldtube_vars) const
Public Member Functions inherited from CurvedScalarWave::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)

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

Detailed Description

template<size_t Dim>
class CurvedScalarWave::BoundaryConditions::Worldtube< Dim >

Sets boundary conditions for the elements abutting the worldtube using a combination of constraint-preserving boundary conditions and the local solution evolved inside the worldtube.

Details

After extensive experimentation we found this set of boundary conditions to be optimal. They are formulated in terms of characteristic fields.

Boundary conditions for \(w^0_\psi\) \(w^0_i\) are formulated by demanding that there are no constraint violations flowing into the numerical domain and are formulated as corrections to the time derivative of the evolved variables directly. The derivation is described in ConstraintPreservingSphericalRadiation .

Boundary conditions for \(\w^-\) are formulated by evaluating the analytical solution of the worldtube at the grid points of each element abutting the worldtube. The data is updated and saved to CurvedScalarWave::Worldtube::Tags::WorldtubeSolution each time step. It is then treated like a ghost field and applied with the chosen numerical flux. So far only the upwind flux has been tried.

We tried several other combinations such as setting all fields from the worldtube solution but found that this caused major constraint violations to flow out of the worldtube.

Note: We found that, depending on the worldtube size, a fairly high value for \(\gamma_2\) of ca. 10 is required near the worldtube to ensure a stable evolution when using these boundary conditions.

Member Typedef Documentation

◆ dg_gridless_tags

template<size_t Dim>

using CurvedScalarWave::BoundaryConditions::Worldtube< Dim >::dg_gridless_tags

Initial value:

tmpl::list<CurvedScalarWave::Worldtube::Tags::WorldtubeSolution<Dim>>

◆ dg_interior_deriv_vars_tags

template<size_t Dim>

using CurvedScalarWave::BoundaryConditions::Worldtube< Dim >::dg_interior_deriv_vars_tags

Initial value:

 tmpl::list<
      ::Tags::deriv<Tags::Psi, tmpl::size_t<Dim>, Frame::Inertial>,
      ::Tags::deriv<Tags::Phi<Dim>, tmpl::size_t<Dim>, Frame::Inertial>>

◆ dg_interior_evolved_variables_tags

template<size_t Dim>

using CurvedScalarWave::BoundaryConditions::Worldtube< Dim >::dg_interior_evolved_variables_tags

Initial value:

tmpl::list<Tags::Psi, Tags::Pi, Tags::Phi<Dim>>

◆ dg_interior_temporary_tags

template<size_t Dim>

using CurvedScalarWave::BoundaryConditions::Worldtube< Dim >::dg_interior_temporary_tags

Initial value:

 
      tmpl::list<gr::Tags::Lapse<DataVector>, gr::Tags::Shift<DataVector, Dim>,
                 gr::Tags::InverseSpatialMetric<DataVector, Dim>,
                 Tags::ConstraintGamma1, Tags::ConstraintGamma2>

Member Function Documentation

◆ get_clone()

template<size_t Dim>

auto CurvedScalarWave::BoundaryConditions::Worldtube< Dim >::get_clone ( ) const -> std::unique_ptr< domain::BoundaryConditions::BoundaryCondition >

overridevirtual

Implements domain::BoundaryConditions::BoundaryCondition.

Member Data Documentation

◆ bc_type

template<size_t Dim>

evolution::BoundaryConditions::Type CurvedScalarWave::BoundaryConditions::Worldtube< Dim >::bc_type

staticconstexpr

Initial value:

=

evolution::BoundaryConditions::Type::GhostAndTimeDerivative

◆ help

template<size_t Dim>

Options::String CurvedScalarWave::BoundaryConditions::Worldtube< Dim >::help

staticconstexpr

Initial value:

{
      "Boundary conditions set by the worldtube. w^- will be set by the "
      "internal worldtube solution, w^psi and w^0_i are fixed by constraint "
      "preserving boundary conditions on the time derivative."}

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

src/Evolution/Systems/CurvedScalarWave/BoundaryConditions/Worldtube.hpp

Public Types

Public Member Functions

Static Public Attributes

Detailed Description

Details

Member Typedef Documentation

◆ dg_gridless_tags

◆ dg_interior_deriv_vars_tags

◆ dg_interior_evolved_variables_tags

◆ dg_interior_temporary_tags

Member Function Documentation

◆ get_clone()

Member Data Documentation

◆ bc_type

◆ help