The fluxes of the conservative variables. More...

#include <Fluxes.hpp>

Public Types
using	return_tags = implementation defined

using	argument_tags = implementation defined

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.

$\begin{aligned} F^{i} (\tilde{D}) = & \tilde{D} v_{t r}^{i} \\ F^{i} ({\tilde{Y}}_{e}) = & {\tilde{Y}}_{e} v_{t r}^{i} \\ F^{i} ({\tilde{S}}_{j}) = & {\tilde{S}}_{j} v_{t r}^{i} + \sqrt{γ} α (p + p_{m}) δ_{j}^{i} - \frac{B_{j} {\tilde{B}}^{i}}{W^{2}} - v_{j} {\tilde{B}}^{i} B^{m} v_{m} \\ F^{i} (\tilde{τ}) = & \tilde{τ} v_{t r}^{i} + \sqrt{γ} α (p + p_{m}) v^{i} - α {\tilde{B}}^{i} B^{m} v_{m} \\ F^{i} ({\tilde{B}}^{j}) = & {\tilde{B}}^{j} v_{t r}^{i} - v_{t r}^{j} {\tilde{B}}^{i} + α γ^{i j} \tilde{Φ} \\ F^{i} (\tilde{Φ}) = & α {\tilde{B}}^{i} - β^{i} \tilde{Φ} \end{aligned}$

where the conserved variables $\tilde{D}$ , ${\tilde{Y}}_{e}$ , ${\tilde{S}}_{i}$ , $\tilde{τ}$ , ${\tilde{B}}^{i}$ , and $\tilde{Φ}$ are a generalized mass-energy density, electron fraction, momentum density, specific internal energy density, magnetic field, and divergence cleaning field. Furthermore, $v_{t r}^{i} = α v^{i} - β^{i}$ is the transport velocity, $α$ is the lapse, $β^{i}$ is the shift, $γ$ is the determinant of the spatial metric $γ_{i j}$ , $Y_{e}$ 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 $p_{m} = \frac{1}{2} [{(B^{n} v_{n})}^{2} + B^{n} B_{n} / W^{2}]$ is the magnetic pressure.

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

src/Evolution/Systems/GrMhd/ValenciaDivClean/Fluxes.hpp

Public Types

Static Public Member Functions

Detailed Description