The fluxes of the conservative variables. More...

#include <Fluxes.hpp>

Public Types
using	return_tags
using	argument_tags

Static Public Member Functions

static void apply (gsl::not_null< tnsr::I< DataVector, 3, Frame::Inertial > * > tilde_d_flux, gsl::not_null< tnsr::I< DataVector, 3, Frame::Inertial > * > tilde_ye_flux, gsl::not_null< tnsr::I< DataVector, 3, Frame::Inertial > * > tilde_tau_flux, gsl::not_null< tnsr::Ij< DataVector, 3, Frame::Inertial > * > tilde_s_flux, gsl::not_null< tnsr::IJ< DataVector, 3, Frame::Inertial > * > tilde_b_flux, gsl::not_null< tnsr::I< DataVector, 3, Frame::Inertial > * > tilde_phi_flux, const Scalar< DataVector > &tilde_d, const Scalar< DataVector > &tilde_ye, const Scalar< DataVector > &tilde_tau, const tnsr::i< DataVector, 3, Frame::Inertial > &tilde_s, const tnsr::I< DataVector, 3, Frame::Inertial > &tilde_b, const Scalar< DataVector > &tilde_phi, const Scalar< DataVector > &lapse, const tnsr::I< DataVector, 3, Frame::Inertial > &shift, const Scalar< DataVector > &sqrt_det_spatial_metric, const tnsr::ii< DataVector, 3, Frame::Inertial > &spatial_metric, const tnsr::II< DataVector, 3, Frame::Inertial > &inv_spatial_metric, const Scalar< DataVector > &pressure, const tnsr::I< DataVector, 3, Frame::Inertial > &spatial_velocity, const Scalar< DataVector > &lorentz_factor, const tnsr::I< DataVector, 3, Frame::Inertial > &magnetic_field)

Detailed Description

The fluxes of the conservative variables.

\begin{align*}F^i({\tilde D}) = &~ {\tilde D} v^i_{tr} \\ F^i({\tilde Y}_e) = &~ {\tilde Y}_e v^i_{tr} \\ F^i({\tilde S}_j) = &~ {\tilde S}_j v^i_{tr} + \sqrt{\gamma} \alpha \left( p + p_m \right) \delta^i_j - \frac{B_j {\tilde B}^i}{W^2} - v_j {\tilde B}^i B^m v_m\\ F^i({\tilde \tau}) = &~ {\tilde \tau} v^i_{tr} + \sqrt{\gamma} \alpha \left( p + p_m \right) v^i - \alpha {\tilde B}^i B^m v_m \\ F^i({\tilde B}^j) = &~ {\tilde B}^j v^i_{tr} - \alpha v^j {\tilde B}^i + \alpha \gamma^{ij} {\tilde \Phi} \\ F^i({\tilde \Phi}) = &~ \alpha {\tilde B^i} - \beta^i {\tilde \Phi} \end{align*}

where the conserved variables \({\tilde D}\), \({\tilde Y}_e\), \({\tilde S}_i\), \({\tilde \tau}\), \({\tilde B}^i\), and \({\tilde \Phi}\) are a generalized mass-energy density, electron fraction, momentum density, specific internal energy density, magnetic field, and divergence cleaning field. Furthermore, \(v^i_{tr} = \alpha v^i - \beta^i\) is the transport velocity, \(\alpha\) is the lapse, \(\beta^i\) is the shift, \(\gamma\) is the determinant of the spatial metric \(\gamma_{ij}\), \(Y_e\) is the electron fraction, \(v^i\) is the spatial velocity, \(B^i\) is the spatial magnetic field measured by an Eulerian observer, \(p\) is the fluid pressure, and \(p_m = \frac{1}{2} \left[ \left( B^n v_n \right)^2 + B^n B_n / W^2 \right]\) is the magnetic pressure.

Member Typedef Documentation

◆ argument_tags

using grmhd::ValenciaDivClean::ComputeFluxes::argument_tags

Initial value:

 
      tmpl::list<grmhd::ValenciaDivClean::Tags::TildeD,
                 grmhd::ValenciaDivClean::Tags::TildeYe,
                 grmhd::ValenciaDivClean::Tags::TildeTau,
                 grmhd::ValenciaDivClean::Tags::TildeS<>,
                 grmhd::ValenciaDivClean::Tags::TildeB<>,
                 grmhd::ValenciaDivClean::Tags::TildePhi,
                 gr::Tags::Lapse<DataVector>, gr::Tags::Shift<DataVector, 3>,
                 gr::Tags::SqrtDetSpatialMetric<DataVector>,
                 gr::Tags::SpatialMetric<DataVector, 3>,
                 gr::Tags::InverseSpatialMetric<DataVector, 3>,
                 hydro::Tags::Pressure<DataVector>,
                 hydro::Tags::SpatialVelocity<DataVector, 3>,
                 hydro::Tags::LorentzFactor<DataVector>,
                 hydro::Tags::MagneticField<DataVector, 3>>

◆ return_tags

using grmhd::ValenciaDivClean::ComputeFluxes::return_tags