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