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/DataBox/Tag.hpp"
       7             : #include "DataStructures/Tensor/Tensor.hpp"
       8             : 
       9             : /// \cond
      10             : class DataVector;
      11             : /// \endcond
      12             : 
      13             : namespace domain::Tags {
      14             : 
      15             : /*!
      16             :  * \brief The determinant of the induced Jacobian on a surface
      17             :  *
      18             :  * The surface Jacobian determinant on a surface \f$\Sigma\f$ with constant
      19             :  * logical coordinate \f$\xi^i\f$ is:
      20             :  *
      21             :  * \f{equation}
      22             :  * J^\Sigma = J \sqrt{\gamma^{jk} (J^{-1})^i_j (J^{-1})^i_k}
      23             :  * \f}
      24             :  *
      25             :  * where \f$J^i_j = \partial x^i / \xi^j\f$ is the volume Jacobian with
      26             :  * determinant \f$J\f$ and inverse \f$(J^{-1})^i_j = \partial \xi^i / \partial
      27             :  * x^j\f$. Note that the square root in the expression above is the magnitude of
      28             :  * the unnormalized face normal, where \f$\gamma^{jk}\f$ is the inverse spatial
      29             :  * metric.
      30             :  */
      31             : template <typename SourceFrame, typename TargetFrame>
      32           1 : struct DetSurfaceJacobian : db::SimpleTag {
      33           0 :   using type = Scalar<DataVector>;
      34             : };
      35             : 
      36             : }  // namespace domain::Tags