Line data    Source code

       1           0 : // Distributed under the MIT License.
       2             : // See LICENSE.txt for details.
       3             : 
       4             : #pragma once
       5             : 
       6             : #include <cstddef>
       7             : 
       8             : #include "DataStructures/Tensor/TypeAliases.hpp"
       9             : #include "Evolution/Systems/RelativisticEuler/Valencia/TagsDeclarations.hpp"
      10             : #include "PointwiseFunctions/GeneralRelativity/TagsDeclarations.hpp"
      11             : #include "PointwiseFunctions/Hydro/EquationsOfState/EquationOfState.hpp"
      12             : #include "PointwiseFunctions/Hydro/TagsDeclarations.hpp"
      13             : #include "Utilities/TMPL.hpp"
      14             : 
      15             : /// \cond
      16             : class DataVector;
      17             : 
      18             : namespace gsl {
      19             : template <typename T>
      20             : class not_null;
      21             : }  // namespace gsl
      22             : /// \endcond
      23             : 
      24             : // IWYU pragma: no_forward_declare EquationsOfState::EquationOfState
      25             : 
      26             : namespace RelativisticEuler {
      27             : namespace Valencia {
      28             : 
      29             : /*!
      30             :  * \brief Compute the primitive variables from the conservative variables
      31             :  *
      32             :  * For the Valencia formulation of the Relativistic Euler system, the conversion
      33             :  * of the evolved conserved variables to the primitive variables cannot
      34             :  * be expressed in closed analytic form and requires a root find.  We use
      35             :  * the method from [Appendix C of Galeazzi \em et \em al, PRD 88, 064009 (2013)]
      36             :  * (https://journals.aps.org/prd/abstract/10.1103/PhysRevD.88.064009).  The
      37             :  * method finds the root of \f[ f(z) = z - \frac{r}{h(z)} \f] where
      38             :  * \f{align*}
      39             :  * r = & \frac{\sqrt{\gamma^{mn} {\tilde S}_m {\tilde S}_n}}{\tilde D} \\
      40             :  * h(z) = & [1+ \epsilon(z)][1 + a(z)] \\
      41             :  * \epsilon(z) = & W(z) q - z r + \frac{z^2}{1 + W(z)} \\
      42             :  * W(z) = & \sqrt{1 + z^2} \\
      43             :  * q = & \frac{\tilde \tau}{\tilde D} \\
      44             :  * a(z) = & \frac{p}{\rho(z) [1 + \epsilon(z)]} \\
      45             :  * \rho(z) = & \frac{\tilde D}{\sqrt{\gamma} W(z)}
      46             :  * \f}
      47             :  * and where the conserved variables \f${\tilde D}\f$, \f${\tilde S}_i\f$, and
      48             :  * \f${\tilde \tau}\f$ are a generalized mass-energy density, momentum density,
      49             :  * and specific internal energy density as measured by an Eulerian observer,
      50             :  * \f$\gamma\f$ and \f$\gamma^{mn}\f$ are the determinant and inverse of the
      51             :  * spatial metric \f$\gamma_{mn}\f$, \f$\rho\f$ is the rest mass density, \f$W =
      52             :  * 1/\sqrt{1 - \gamma_{mn} v^m v^n}\f$ is the Lorentz factor, \f$h = 1 +
      53             :  * \epsilon + \frac{p}{\rho}\f$ is the specific enthalpy, \f$v^i\f$ is the
      54             :  * spatial velocity, \f$\epsilon\f$ is the specific internal energy, and \f$p\f$
      55             :  * is the pressure.  The pressure is determined from the equation of state.
      56             :  * Finally, once \f$z\f$ is found, the spatial velocity is given by \f[ v^i =
      57             :  * \frac{{\tilde S}^i}{{\tilde D} W(z) h(z)} \f]
      58             :  *
      59             :  * \todo The method also will make corrections if physical bounds are violated,
      60             :  * see the paper for details.
      61             :  */
      62             : template <size_t Dim>
      63           1 : struct PrimitiveFromConservative {
      64           0 :   using return_tags =
      65             :       tmpl::list<hydro::Tags::RestMassDensity<DataVector>,
      66             :                  hydro::Tags::SpecificInternalEnergy<DataVector>,
      67             :                  hydro::Tags::LorentzFactor<DataVector>,
      68             :                  hydro::Tags::SpecificEnthalpy<DataVector>,
      69             :                  hydro::Tags::Pressure<DataVector>,
      70             :                  hydro::Tags::SpatialVelocity<DataVector, Dim>>;
      71             : 
      72           0 :   using argument_tags =
      73             :       tmpl::list<RelativisticEuler::Valencia::Tags::TildeD,
      74             :                  RelativisticEuler::Valencia::Tags::TildeTau,
      75             :                  RelativisticEuler::Valencia::Tags::TildeS<Dim>,
      76             :                  gr::Tags::InverseSpatialMetric<DataVector, Dim>,
      77             :                  gr::Tags::SqrtDetSpatialMetric<DataVector>,
      78             :                  hydro::Tags::EquationOfStateBase>;
      79             : 
      80             :   template <size_t ThermodynamicDim>
      81           0 :   static void apply(
      82             :       gsl::not_null<Scalar<DataVector>*> rest_mass_density,
      83             :       gsl::not_null<Scalar<DataVector>*> specific_internal_energy,
      84             :       gsl::not_null<Scalar<DataVector>*> lorentz_factor,
      85             :       gsl::not_null<Scalar<DataVector>*> specific_enthalpy,
      86             :       gsl::not_null<Scalar<DataVector>*> pressure,
      87             :       gsl::not_null<tnsr::I<DataVector, Dim, Frame::Inertial>*>
      88             :           spatial_velocity,
      89             :       const Scalar<DataVector>& tilde_d, const Scalar<DataVector>& tilde_tau,
      90             :       const tnsr::i<DataVector, Dim, Frame::Inertial>& tilde_s,
      91             :       const tnsr::II<DataVector, Dim, Frame::Inertial>& inv_spatial_metric,
      92             :       const Scalar<DataVector>& sqrt_det_spatial_metric,
      93             :       const EquationsOfState::EquationOfState<true, ThermodynamicDim>&
      94             :           equation_of_state);
      95             : };
      96             : }  // namespace Valencia
      97             : }  // namespace RelativisticEuler