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

#include <PrimitiveFromConservative.hpp>

Public Types
using	return_tags = tmpl::list< hydro::Tags::RestMassDensity< DataVector >, hydro::Tags::ElectronFraction< DataVector >, hydro::Tags::SpecificInternalEnergy< DataVector >, hydro::Tags::SpatialVelocity< DataVector, 3 >, hydro::Tags::MagneticField< DataVector, 3 >, hydro::Tags::DivergenceCleaningField< DataVector >, hydro::Tags::LorentzFactor< DataVector >, hydro::Tags::Pressure< DataVector >, hydro::Tags::Temperature< DataVector > >

using	argument_tags = 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::SpatialMetric< DataVector, 3 >, gr::Tags::InverseSpatialMetric< DataVector, 3 >, gr::Tags::SqrtDetSpatialMetric< DataVector >, hydro::Tags::GrmhdEquationOfState, grmhd::ValenciaDivClean::Tags::PrimitiveFromConservativeOptions >

Static Public Member Functions
template<bool EnforcePhysicality = true>
static bool	apply (gsl::not_null< Scalar< DataVector > * > rest_mass_density, gsl::not_null< Scalar< DataVector > * > electron_fraction, gsl::not_null< Scalar< DataVector > * > specific_internal_energy, gsl::not_null< tnsr::I< DataVector, 3, Frame::Inertial > * > spatial_velocity, gsl::not_null< tnsr::I< DataVector, 3, Frame::Inertial > * > magnetic_field, gsl::not_null< Scalar< DataVector > * > divergence_cleaning_field, gsl::not_null< Scalar< DataVector > * > lorentz_factor, gsl::not_null< Scalar< DataVector > * > pressure, gsl::not_null< Scalar< DataVector > * > temperature, 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 tnsr::ii< DataVector, 3, Frame::Inertial > &spatial_metric, const tnsr::II< DataVector, 3, Frame::Inertial > &inv_spatial_metric, const Scalar< DataVector > &sqrt_det_spatial_metric, const EquationsOfState::EquationOfState< true, 3 > &equation_of_state, const grmhd::ValenciaDivClean::PrimitiveFromConservativeOptions &primitive_from_conservative_options)

Detailed Description

template<typename OrderedListOfPrimitiveRecoverySchemes, bool ErrorOnFailure = true>
struct grmhd::ValenciaDivClean::PrimitiveFromConservative< OrderedListOfPrimitiveRecoverySchemes, ErrorOnFailure >

Compute the primitive variables from the conservative variables.

For the Valencia formulation of the GRMHD system with divergence cleaning, the conversion of the evolved conserved variables to the primitive variables cannot be expressed in closed analytic form and requires a root find.

[Siegel {et al}, The Astrophysical Journal 859:71(2018)] (http://iopscience.iop.org/article/10.3847/1538-4357/aabcc5/meta) compares several inversion methods.

If ErrorOnFailure is false then the returned bool will be false if recovery failed and true if it succeeded.

If EnforcePhysicality is false then the hydrodynamic inversion will return with an error if the input conservatives are unphysical, i.e., if no solution exits. The exact behavior is governed by ErrorOnFailure.

Note: Here, we outline the algebra for computing the spatial velocity \( v^i \):

We start from definition of the momentum density \( S_i \):

\[ \begin{aligned} S_i &= (\rho h)^* W^2 v_i - \alpha b^0 b_i \\ &= \left(\rho h + \frac{B^2}{W^2} + (v \cdot B)^2\right) W^2 v_i - \alpha \left(\frac{W}{\alpha}(v \cdot B)\right) \left(\frac{B_i}{W} + (v \cdot B) W v_i\right) \\ &= \left(\rho h + \frac{B^2}{W^2}\right) W^2 v_i - (v \cdot B) B_i \end{aligned} \]

From the above, we obtain:

\[ \begin{aligned} S^i &= \left(\rho h + \frac{B^2}{W^2}\right) W^2 v^i - (v \cdot B) B^i \\ S \cdot B &= \left(\rho h + \frac{B^2}{W^2}\right) W^2 (v \cdot B) - (v \cdot B) B^2 \\ &= \rho h W^2 (v \cdot B) \\ v^i &= \frac{1}{\sqrt{\gamma} (\rho h W^2 + B^2)} \tilde{S}^i + \frac{S \cdot B}{\rho h W^2 (\rho h W^2 + B^2)} B^i \end{aligned} \]

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

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

Public Types

Static Public Member Functions

Detailed Description