CurvedScalarWave::Tags::ComputeLargestCharacteristicSpeed< SpatialDim > Struct Template Reference

Computes the largest magnitude of the characteristic speeds. More...

#include <Characteristics.hpp>

Public Types
using	argument_tags = implementation defined
using	return_type = double
using	base = LargestCharacteristicSpeed
Public Types inherited from CurvedScalarWave::Tags::LargestCharacteristicSpeed
using	type = double

Static Public Member Functions
static void	function (const gsl::not_null< double * > max_speed, const Scalar< DataVector > &gamma_1, const Scalar< DataVector > &lapse, const tnsr::I< DataVector, SpatialDim, Frame::Inertial > &shift, const tnsr::ii< DataVector, SpatialDim, Frame::Inertial > &spatial_metric)

Detailed Description

template<size_t SpatialDim>
struct CurvedScalarWave::Tags::ComputeLargestCharacteristicSpeed< SpatialDim >

Computes the largest magnitude of the characteristic speeds.

Details

Returns the magnitude of the largest characteristic speed along any direction at a given point in space, considering all characteristic fields. This is useful, for e.g., in computing the Courant factor. The coordinate characteristic speeds for this system are $\{-(1+{\gamma }_1)n_k{N}^k,-n_k{N}^k,-n_k{N}^k\pm N\}$. At any point in space, these are maximized when the normal vector is parallel to the shift vector, i.e. $n^j=N^j/\sqrt{N^i{N}_i}$, and $n_k{N}^k=g_{jk}{N}^j{N}^k/\sqrt{N^i{N}_i}=\sqrt{N^i{N}_i}=$ magnitude(shift, spatial_metric). The maximum characteristic speed is therefore calculated as $\mathrm{m}\mathrm{a}\mathrm{x}(|1+{\gamma }_1|\sqrt{{\mathrm{N}}^{\mathrm{i}}{\mathrm{N}}_{\mathrm{i}}},\sqrt{{\mathrm{N}}^{\mathrm{i}}{\mathrm{N}}_{\mathrm{i}}}+|\mathrm{N}|)$.

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

• src/Evolution/Systems/CurvedScalarWave/Characteristics.hpp