|
SpECTRE
v2024.04.12
|
The fluxes of the conservative variables. More...
#include <Fluxes.hpp>
Public Types | |
| using | return_tags = tmpl::list<::Tags::Flux< RelativisticEuler::Valencia::Tags::TildeD, tmpl::size_t< Dim >, Frame::Inertial >, ::Tags::Flux< RelativisticEuler::Valencia::Tags::TildeTau, tmpl::size_t< Dim >, Frame::Inertial >, ::Tags::Flux< RelativisticEuler::Valencia::Tags::TildeS< Dim >, tmpl::size_t< Dim >, Frame::Inertial > > |
| using | argument_tags = tmpl::list< RelativisticEuler::Valencia::Tags::TildeD, RelativisticEuler::Valencia::Tags::TildeTau, RelativisticEuler::Valencia::Tags::TildeS< Dim >, gr::Tags::Lapse< DataVector >, gr::Tags::Shift< DataVector, Dim >, gr::Tags::SqrtDetSpatialMetric< DataVector >, hydro::Tags::Pressure< DataVector >, hydro::Tags::SpatialVelocity< DataVector, Dim > > |
Static Public Member Functions | |
| static void | apply (gsl::not_null< tnsr::I< DataVector, Dim, Frame::Inertial > * > tilde_d_flux, gsl::not_null< tnsr::I< DataVector, Dim, Frame::Inertial > * > tilde_tau_flux, gsl::not_null< tnsr::Ij< DataVector, Dim, Frame::Inertial > * > tilde_s_flux, const Scalar< DataVector > &tilde_d, const Scalar< DataVector > &tilde_tau, const tnsr::i< DataVector, Dim, Frame::Inertial > &tilde_s, const Scalar< DataVector > &lapse, const tnsr::I< DataVector, Dim, Frame::Inertial > &shift, const Scalar< DataVector > &sqrt_det_spatial_metric, const Scalar< DataVector > &pressure, const tnsr::I< DataVector, Dim, Frame::Inertial > &spatial_velocity) |
The fluxes of the conservative variables.
\begin{align*} F^i({\tilde D}) = &~ {\tilde D} v^i_{tr} \\ F^i({\tilde S}_j) = &~ {\tilde S}_j v^i_{tr} + \sqrt{\gamma} \alpha p \delta^i_j \\ F^i({\tilde \tau}) = &~ {\tilde \tau} v^i_{tr} + \sqrt{\gamma} \alpha p v^i \end{align*}
where the conservative variables \({\tilde D}\), \({\tilde S}_i\), and \({\tilde \tau}\) are a generalized mass-energy density, momentum density, and specific internal energy density as measured by an Eulerian observer, \(v^i_{tr} = \alpha v^i - \beta^i\) is the transport velocity, \(\alpha\) is the lapse, \(\beta^i\) is the shift, \(v^i\) is the spatial velocity, \(\gamma\) is the determinant of the spatial metric, and \(p\) is the pressure.