Line data    Source code

       1            0 : // Distributed under the MIT License.
       2              : // See LICENSE.txt for details.
       3              : 
       4              : #pragma once
       5              : 
       6              : #include "DataStructures/DataVector.hpp"
       7              : #include "DataStructures/Tensor/Tensor.hpp"
       8              : #include "Utilities/Gsl.hpp"
       9              : 
      10              : namespace grmhd::GhValenciaDivClean {
      11              : 
      12              : /*!
      13              :  * \brief Add in the trace-reversed stress-energy source term to the \f$\Pi\f$
      14              :  * evolved variable of the Generalized Harmonic system.
      15              :  *
      16              :  * \details The only stress energy source term in the Generalized Harmonic
      17              :  * evolution equations is in the equation for \f$\Pi_{a b}\f$:
      18              :  *
      19              :  * \f[
      20              :  * \partial_t \Pi_{ab} + \text{(spatial derivative terms)} =
      21              :  * \text{(GH source terms)}
      22              :  * - 16 \pi \alpha (T_{ab} - \frac{1}{2} g_{a b} T^c{}_c)
      23              :  * \f]
      24              :  *
      25              :  * (note that this function takes as argument the trace-reversed stress energy
      26              :  * tensor)
      27              :  *
      28              :  * This function adds that contribution to the existing value of `dt_pi`. The
      29              :  * spacetime terms in the GH equation should be computed before passing the
      30              :  * `dt_pi` to this function for updating.
      31              :  *
      32              :  * \see `gh::TimeDerivative` for details about the spacetime
      33              :  * part of the time derivative calculation.
      34              :  */
      35            1 : void add_stress_energy_term_to_dt_pi(
      36              :     gsl::not_null<tnsr::aa<DataVector, 3>*> dt_pi,
      37              :     const tnsr::aa<DataVector, 3>& trace_reversed_stress_energy,
      38              :     const Scalar<DataVector>& lapse);
      39              : 
      40              : /*!
      41              :  * \brief Calculate the trace-reversed stress-energy tensor \f$(T_{\mu \nu} -
      42              :  * 1/2 g_{\mu \nu} g^{\lambda \sigma} T_{\lambda \sigma}) \f$ associated with
      43              :  * the matter part of the GRMHD system.
      44              :  *
      45              :  * \details The stress energy tensor is needed to compute the backreaction of
      46              :  * the matter to the spacetime degrees of freedom. The stress energy is
      47              :  * calculated as described in \cite Moesta2013dna :
      48              :  *
      49              :  * \f[
      50              :  * T_{\mu \nu} = \rho h^* u_\mu u_\nu + p^* g_{\mu \nu} - b_\mu b_\nu,
      51              :  * \f]
      52              :  *
      53              :  * where \f$u_\mu\f$ is the four-velocity, \f$\rho\f$ is the rest mass density,
      54              :  * \f$h^*\f$ is the magnetically modified enthalpy, \f$p^*\f$ is the
      55              :  * magnetically modified pressure, and \f$b_{\mu}\f$ is the comoving magnetic
      56              :  * field (note that we deviate from the notation of \cite Moesta2013dna by
      57              :  * denoting the pressure with a lower-case \f$p\f$ instead of an upper-case
      58              :  * \f$P\f$).
      59              :  *
      60              :  * The spatial components of the four velocity \f$u_\mu\f$ are
      61              :  *
      62              :  * \f[
      63              :  * u_i = W v_i,
      64              :  * \f]
      65              :  *
      66              :  * and the time component is
      67              :  *
      68              :  * \f[
      69              :  * u_0 = - \alpha W + \beta^i u_i.
      70              :  * \f].
      71              :  *
      72              :  * The magnetically modified enthalpy is
      73              :  *
      74              :  * \f[
      75              :  * h^* = 1 + \epsilon + (p + b^2) / \rho.
      76              :  * \f]
      77              :  *
      78              :  * The magnetically modified pressure is
      79              :  *
      80              :  * \f[
      81              :  * p^* = p + b^2 / 2.
      82              :  * \f]
      83              :  *
      84              :  *
      85              :  * The comoving magnetic field is computed via
      86              :  *
      87              :  * \f{align}{
      88              :  * b_i &= B_i / W + v_i W v^k B_k\\
      89              :  * b_0 &= - \alpha W v^i B_i + \beta^i b_i
      90              :  * \f}
      91              :  *
      92              :  * Therefore, the trace-reversed stress energy simplifies to
      93              :  *
      94              :  * \f[
      95              :  * (T_{\mu \nu} - \frac{1}{2} g_{\mu \nu} g^{\lambda \sigma} T_{\lambda \sigma})
      96              :  * = \rho h^* u_\mu u_\nu  + \left(\frac{1}{2} \rho h^* - p\right) g_{\mu \nu}
      97              :  *  - b_\mu b_\nu
      98              :  * \f]
      99              :  */
     100            1 : void trace_reversed_stress_energy(
     101              :     gsl::not_null<tnsr::aa<DataVector, 3>*> stress_energy,
     102              :     gsl::not_null<tnsr::a<DataVector, 3>*> four_velocity_one_form_buffer,
     103              :     gsl::not_null<tnsr::a<DataVector, 3>*>
     104              :         comoving_magnetic_field_one_form_buffer,
     105              :     const Scalar<DataVector>& rest_mass_density,
     106              :     const tnsr::i<DataVector, 3, Frame::Inertial>& spatial_velocity_one_form,
     107              :     const tnsr::i<DataVector, 3, Frame::Inertial>& magnetic_field_one_form,
     108              :     const Scalar<DataVector>& magnetic_field_squared,
     109              :     const Scalar<DataVector>& magnetic_field_dot_spatial_velocity,
     110              :     const Scalar<DataVector>& lorentz_factor,
     111              :     const Scalar<DataVector>& one_over_w_squared,
     112              :     const Scalar<DataVector>& pressure,
     113              :     const Scalar<DataVector>& specific_internal_energy,
     114              :     const tnsr::aa<DataVector, 3, Frame::Inertial>& spacetime_metric,
     115              :     const tnsr::I<DataVector, 3, Frame::Inertial>& shift,
     116              :     const Scalar<DataVector>& lapse);
     117              : }  // namespace grmhd::GhValenciaDivClean