grmhd::ValenciaDivClean::ConservativeFromPrimitive Struct Reference

Compute the conservative variables from primitive variables. More...

#include <ConservativeFromPrimitive.hpp>

Public Types
using	return_tags = implementation defined
using	argument_tags = implementation defined

Static Public Member Functions
static void	apply (gsl::not_null< Scalar< DataVector > * > tilde_d, gsl::not_null< Scalar< DataVector > * > tilde_ye, gsl::not_null< Scalar< DataVector > * > tilde_tau, gsl::not_null< tnsr::i< DataVector, 3, Frame::Inertial > * > tilde_s, gsl::not_null< tnsr::I< DataVector, 3, Frame::Inertial > * > tilde_b, gsl::not_null< Scalar< DataVector > * > tilde_phi, const Scalar< DataVector > &rest_mass_density, const Scalar< DataVector > &electron_fraction, const Scalar< DataVector > &specific_internal_energy, 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, const Scalar< DataVector > &sqrt_det_spatial_metric, const tnsr::ii< DataVector, 3, Frame::Inertial > &spatial_metric, const Scalar< DataVector > &divergence_cleaning_field)

Detailed Description

Compute the conservative variables from primitive variables.

$$\begin{array}{rl}\tilde{D}=& \sqrt{\gamma }\rho W\\ {\tilde{Y}}_e=& \sqrt{\gamma }\rho Y_{e}W\\ {\tilde{S}}_i=& \sqrt{\gamma }(\rho h{W}^2{v}_i+B^m{B}_m{v}_i-B^m{v}_m{B}_i)\\ \tilde{\tau }=& \sqrt{\gamma }[\rho h{W}^2-p-\rho W-\frac{1}{2}(B^m{v}_m{)}^2+\frac{1}{2}{B}^m{B}_m(1+v^m{v}_m)]\\ {\tilde{B}}^i=& \sqrt{\gamma }{B}^i\\ \tilde{\mathrm{\Phi }}=& \sqrt{\gamma }\mathrm{\Phi }\end{array}$$

where the conserved variables $\tilde{D}$, ${\tilde{Y}}_e$, ${\tilde{S}}_i$, $\tilde{\tau }$, ${\tilde{B}}^i$, and $\tilde{\mathrm{\Phi }}$ are a generalized mass-energy density, electron fraction, momentum density, specific internal energy density, magnetic field, and divergence cleaning field. Furthermore $\gamma$ is the determinant of the spatial metric, $\rho$ is the rest mass density, $Y_e$ is the electron fraction, $W=1/\sqrt{1-v_i{v}^i}$ is the Lorentz factor, $h=1+ϵ+\frac{p}{\rho }$ is the specific enthalpy, $v^i$ is the spatial velocity, $ϵ$ is the specific internal energy, $p$ is the pressure, $B^i$ is the spatial magnetic field measured by an Eulerian observer, and $\mathrm{\Phi }$ is a divergence cleaning field.

The quantity $\tilde{\tau }$ is rewritten as in RelativisticEuler to avoid cancellation error in the non-relativistic limit:

$$(\rho h{W}^2-p-\rho W)⟶W^2[\rho (ϵ+v^2\frac{W}{W+1})+p{v}^2].$$

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

• src/Evolution/Systems/GrMhd/ValenciaDivClean/ConservativeFromPrimitive.hpp