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 "NumericalAlgorithms/LinearOperators/PartialDerivatives.hpp"
      11             : #include "PointwiseFunctions/GeneralRelativity/TagsDeclarations.hpp"
      12             : #include "PointwiseFunctions/Hydro/TagsDeclarations.hpp"
      13             : #include "Utilities/TMPL.hpp"
      14             : 
      15             : // IWYU pragma: no_forward_declare Tensor
      16             : 
      17             : /// \cond
      18             : class DataVector;
      19             : 
      20             : namespace gsl {
      21             : template <typename T>
      22             : class not_null;
      23             : }  // namespace gsl
      24             : 
      25             : namespace Tags {
      26             : template <typename>
      27             : struct Source;
      28             : }  // namespace Tags
      29             : /// \endcond
      30             : 
      31             : namespace RelativisticEuler {
      32             : namespace Valencia {
      33             : 
      34             : /*!
      35             :  * \brief Compute the source terms for the flux-conservative Valencia
      36             :  * formulation of the relativistic Euler system.
      37             :  *
      38             :  *
      39             :  * A flux-conservative system has the generic form:
      40             :  * \f[
      41             :  * \partial_t U_i + \partial_m F^m(U_i) = S(U_i)
      42             :  * \f]
      43             :  *
      44             :  * where \f$F^a()\f$ denotes the flux of a conserved variable \f$U_i\f$ and
      45             :  * \f$S()\f$ denotes the source term for the conserved variable.
      46             :  *
      47             :  * For the Valencia formulation:
      48             :  * \f{align*}
      49             :  * S({\tilde D}) = & 0\\
      50             :  * S({\tilde S}_i) = & \frac{1}{2} \alpha {\tilde S}^{mn} \partial_i \gamma_{mn}
      51             :  * + {\tilde S}_m \partial_i \beta^m - ({\tilde D} + {\tilde \tau}) \partial_i
      52             :  * \alpha \\ S({\tilde \tau}) = & \alpha {\tilde S}^{mn} K_{mn}
      53             :  * - {\tilde S}^m \partial_m \alpha
      54             :  * \f}
      55             :  *
      56             :  * where
      57             :  * \f{align*}
      58             :  * {\tilde S}^i = & {\tilde S}_m \gamma^{im} \\
      59             :  * {\tilde S}^{ij} = & {\tilde S}^i v^j + \sqrt{\gamma} p \gamma^{ij}
      60             :  * \f}
      61             :  * where \f${\tilde D}\f$, \f${\tilde S}_i\f$, and \f${\tilde \tau}\f$ are a
      62             :  * generalized mass-energy density, momentum density, and specific internal
      63             :  * energy density as measured by an Eulerian observer, \f$\gamma\f$ is the
      64             :  * determinant of the spatial metric \f$\gamma_{ij}\f$, \f$\rho\f$ is the rest
      65             :  * mass density, \f$W\f$ is the Lorentz factor, \f$h\f$ is the specific
      66             :  * enthalpy, \f$v^i\f$ is the spatial velocity, \f$p\f$ is the pressure,
      67             :  * \f$\alpha\f$ is the lapse, \f$\beta^i\f$ is the shift, and \f$K_{ij}\f$ is
      68             :  * the extrinsic curvature.
      69             :  */
      70             : template <size_t Dim>
      71           1 : struct ComputeSources {
      72           0 :   using return_tags = tmpl::list<
      73             :       ::Tags::Source<RelativisticEuler::Valencia::Tags::TildeTau>,
      74             :       ::Tags::Source<RelativisticEuler::Valencia::Tags::TildeS<Dim>>>;
      75             : 
      76           0 :   using argument_tags =
      77             :       tmpl::list<RelativisticEuler::Valencia::Tags::TildeD,
      78             :                  RelativisticEuler::Valencia::Tags::TildeTau,
      79             :                  RelativisticEuler::Valencia::Tags::TildeS<Dim>,
      80             :                  hydro::Tags::SpatialVelocity<DataVector, Dim>,
      81             :                  hydro::Tags::Pressure<DataVector>, gr::Tags::Lapse<DataVector>,
      82             :                  ::Tags::deriv<gr::Tags::Lapse<DataVector>, tmpl::size_t<Dim>,
      83             :                                Frame::Inertial>,
      84             :                  ::Tags::deriv<gr::Tags::Shift<DataVector, Dim>,
      85             :                                tmpl::size_t<Dim>, Frame::Inertial>,
      86             :                  ::Tags::deriv<gr::Tags::SpatialMetric<DataVector, Dim>,
      87             :                                tmpl::size_t<Dim>, Frame::Inertial>,
      88             :                  gr::Tags::InverseSpatialMetric<DataVector, Dim>,
      89             :                  gr::Tags::SqrtDetSpatialMetric<DataVector>,
      90             :                  gr::Tags::ExtrinsicCurvature<DataVector, Dim>>;
      91             : 
      92           0 :   static void apply(
      93             :       gsl::not_null<Scalar<DataVector>*> source_tilde_tau,
      94             :       gsl::not_null<tnsr::i<DataVector, Dim, Frame::Inertial>*> source_tilde_s,
      95             :       const Scalar<DataVector>& tilde_d, const Scalar<DataVector>& tilde_tau,
      96             :       const tnsr::i<DataVector, Dim, Frame::Inertial>& tilde_s,
      97             :       const tnsr::I<DataVector, Dim, Frame::Inertial>& spatial_velocity,
      98             :       const Scalar<DataVector>& pressure, const Scalar<DataVector>& lapse,
      99             :       const tnsr::i<DataVector, Dim, Frame::Inertial>& d_lapse,
     100             :       const tnsr::iJ<DataVector, Dim, Frame::Inertial>& d_shift,
     101             :       const tnsr::ijj<DataVector, Dim, Frame::Inertial>& d_spatial_metric,
     102             :       const tnsr::II<DataVector, Dim, Frame::Inertial>& inv_spatial_metric,
     103             :       const Scalar<DataVector>& sqrt_det_spatial_metric,
     104             :       const tnsr::ii<DataVector, Dim, Frame::Inertial>& extrinsic_curvature);
     105             : };
     106             : }  // namespace Valencia
     107             : }  // namespace RelativisticEuler