SpECTRE Documentation Coverage Report
Current view: top level - PointwiseFunctions/GeneralRelativity/GeneralizedHarmonic - TimeDerivOfSpatialMetric.hpp Hit Total Coverage
Commit: 664546099c4dbf27a1b708fac45e39c82dd743d2 Lines: 3 8 37.5 %
Date: 2024-04-19 16:28:01
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          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/DataBox/Prefixes.hpp"
       9             : #include "DataStructures/DataBox/Tag.hpp"
      10             : #include "DataStructures/DataVector.hpp"
      11             : #include "DataStructures/Tensor/Tensor.hpp"
      12             : #include "Evolution/Systems/GeneralizedHarmonic/Tags.hpp"
      13             : #include "NumericalAlgorithms/LinearOperators/PartialDerivatives.hpp"
      14             : #include "PointwiseFunctions/GeneralRelativity/Tags.hpp"
      15             : #include "Utilities/ContainerHelpers.hpp"
      16             : #include "Utilities/Gsl.hpp"
      17             : #include "Utilities/TMPL.hpp"
      18             : 
      19             : // IWYU pragma: no_forward_declare Tags::deriv
      20             : 
      21             : /// \cond
      22             : namespace domain {
      23             : namespace Tags {
      24             : template <size_t Dim, typename Frame>
      25             : struct Coordinates;
      26             : }  // namespace Tags
      27             : }  // namespace domain
      28             : class DataVector;
      29             : template <typename X, typename Symm, typename IndexList>
      30             : class Tensor;
      31             : /// \endcond
      32             : 
      33             : namespace gh {
      34             : /// @{
      35             : /*!
      36             :  * \ingroup GeneralRelativityGroup
      37             :  * \brief Computes time derivative of the spatial metric.
      38             :  *
      39             :  * \details Let the generalized harmonic conjugate momentum and spatial
      40             :  * derivative variables be \f$\Pi_{ab} = -n^c \partial_c g_{ab} \f$ and
      41             :  * \f$\Phi_{iab} = \partial_i g_{ab} \f$. As \f$ n_i \equiv 0 \f$. The time
      42             :  * derivative of the spatial metric is given by the time derivative of the
      43             :  * spatial sector of the spacetime metric, i.e.
      44             :  * \f$ \partial_0 \gamma_{ij} = \partial_0 g_{ij} \f$.
      45             :  *
      46             :  * To compute the latter, we use the evolution equation for \f$ g_{ij} \f$,
      47             :  * c.f. eq.(35) of \cite Lindblom2005qh (with \f$\gamma_1 = -1\f$):
      48             :  *
      49             :  * \f[
      50             :  * \partial_0 g_{ab} = - \alpha \Pi_{ab} + \beta^k \Phi_{kab}
      51             :  * \f]
      52             :  */
      53             : template <typename DataType, size_t SpatialDim, typename Frame>
      54           1 : void time_deriv_of_spatial_metric(
      55             :     gsl::not_null<tnsr::ii<DataType, SpatialDim, Frame>*> dt_spatial_metric,
      56             :     const Scalar<DataType>& lapse,
      57             :     const tnsr::I<DataType, SpatialDim, Frame>& shift,
      58             :     const tnsr::iaa<DataType, SpatialDim, Frame>& phi,
      59             :     const tnsr::aa<DataType, SpatialDim, Frame>& pi);
      60             : 
      61             : template <typename DataType, size_t SpatialDim, typename Frame>
      62           1 : tnsr::ii<DataType, SpatialDim, Frame> time_deriv_of_spatial_metric(
      63             :     const Scalar<DataType>& lapse,
      64             :     const tnsr::I<DataType, SpatialDim, Frame>& shift,
      65             :     const tnsr::iaa<DataType, SpatialDim, Frame>& phi,
      66             :     const tnsr::aa<DataType, SpatialDim, Frame>& pi);
      67             : /// @}
      68             : 
      69             : namespace Tags {
      70             : /*!
      71             :  * \brief Compute item to get time derivative of the spatial metric from
      72             :  *        generalized harmonic and geometric variables
      73             :  *
      74             :  * \details See `time_deriv_of_spatial_metric()`. Can be retrieved using
      75             :  * `gr::Tags::SpatialMetric` wrapped in `Tags::dt`.
      76             :  */
      77             : template <size_t SpatialDim, typename Frame>
      78           1 : struct TimeDerivSpatialMetricCompute
      79             :     : ::Tags::dt<gr::Tags::SpatialMetric<DataVector, SpatialDim, Frame>>,
      80             :       db::ComputeTag {
      81           0 :   using argument_tags =
      82             :       tmpl::list<gr::Tags::Lapse<DataVector>,
      83             :                  gr::Tags::Shift<DataVector, SpatialDim, Frame>,
      84             :                  Phi<DataVector, SpatialDim, Frame>,
      85             :                  Pi<DataVector, SpatialDim, Frame>>;
      86             : 
      87           0 :   using return_type = tnsr::ii<DataVector, SpatialDim, Frame>;
      88             : 
      89           0 :   static constexpr auto function = static_cast<void (*)(
      90             :       gsl::not_null<tnsr::ii<DataVector, SpatialDim, Frame>*>,
      91             :       const Scalar<DataVector>&, const tnsr::I<DataVector, SpatialDim, Frame>&,
      92             :       const tnsr::iaa<DataVector, SpatialDim, Frame>&,
      93             :       const tnsr::aa<DataVector, SpatialDim, Frame>&)>(
      94             :       &time_deriv_of_spatial_metric<DataVector, SpatialDim, Frame>);
      95             : 
      96           0 :   using base =
      97             :       ::Tags::dt<gr::Tags::SpatialMetric<DataVector, SpatialDim, Frame>>;
      98             : };
      99             : }  // namespace Tags
     100             : }  // namespace gh

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