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CurvedScalarWave::TimeDerivative< Dim > Struct Template Reference

Compute the time derivative of the evolved variables of the first-order scalar wave system on a curved background. More...

#include <TimeDerivative.hpp>

Public Types

using temporary_tags = implementation defined
 
using argument_tags = implementation defined
 

Static Public Member Functions

static void apply (gsl::not_null< Scalar< DataVector > * > dt_psi, gsl::not_null< Scalar< DataVector > * > dt_pi, gsl::not_null< tnsr::i< DataVector, Dim, Frame::Inertial > * > dt_phi, gsl::not_null< Scalar< DataVector > * > result_lapse, gsl::not_null< tnsr::I< DataVector, Dim > * > result_shift, gsl::not_null< tnsr::II< DataVector, Dim > * > result_inverse_spatial_metric, gsl::not_null< Scalar< DataVector > * > result_gamma1, gsl::not_null< Scalar< DataVector > * > result_gamma2, const tnsr::i< DataVector, Dim > &d_psi, const tnsr::i< DataVector, Dim > &d_pi, const tnsr::ij< DataVector, Dim > &d_phi, const Scalar< DataVector > &pi, const tnsr::i< DataVector, Dim > &phi, const Scalar< DataVector > &lapse, const tnsr::I< DataVector, Dim > &shift, const tnsr::i< DataVector, Dim > &deriv_lapse, const tnsr::iJ< DataVector, Dim > &deriv_shift, const tnsr::II< DataVector, Dim > &upper_spatial_metric, const tnsr::I< DataVector, Dim > &trace_spatial_christoffel, const Scalar< DataVector > &trace_extrinsic_curvature, const Scalar< DataVector > &gamma1, const Scalar< DataVector > &gamma2)
 

Detailed Description

template<size_t Dim>
struct CurvedScalarWave::TimeDerivative< Dim >

Compute the time derivative of the evolved variables of the first-order scalar wave system on a curved background.

The evolution equations for the first-order scalar wave system are given by [93] :

(1)tΨ=αΠ+βkkΨ+γ1βk(kΨΦk)(2)tΠ=αKΠ+βiiΠ+αΓiΦi+γ1γ2βi(iΨΦi)αγijiΦjγijΦijα(3)tΦi=αiΠ+βkkΦi+γ2α(iΨΦi)Πiα+Φjiβj

where Ψ is the scalar field, Π is the conjugate momentum to Ψ, Φi=iΨ is an auxiliary variable, α is the lapse, βk is the shift, γij is the spatial metric, K is the trace of the extrinsic curvature, and Γi is the trace of the spatial Christoffel symbol of the second kind. γ1,γ2 are constraint damping parameters.


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