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             : #include <limits>
       8             : #include <pup.h>
       9             : #include <utility>
      10             : 
      11             : #include "DataStructures/Tensor/Tensor.hpp"
      12             : #include "Evolution/Systems/CurvedScalarWave/Tags.hpp"
      13             : #include "Options/Context.hpp"
      14             : #include "Options/String.hpp"
      15             : #include "PointwiseFunctions/AnalyticData/AnalyticData.hpp"
      16             : #include "Utilities/TMPL.hpp"
      17             : #include "Utilities/TaggedTuple.hpp"
      18             : 
      19             : namespace CurvedScalarWave::AnalyticData {
      20             : 
      21             : /*!
      22             :  * \brief Analytic initial data for a pure spherical harmonic in three
      23             :  * dimensions.
      24             :  *
      25             :  * \details The initial data is taken from \cite Scheel2003vs , Eqs. 4.1--4.3,
      26             :  * and sets the evolved variables of the scalar wave as follows:
      27             :  *
      28             :  * \f{align}
      29             :  * \Psi &= 0 \\
      30             :  * \Phi_i &= 0 \\
      31             :  * \Pi &= \Pi_0(r, \theta, \phi) =  e^{- (r - r_0)^2 / w^2} Y_{lm}(\theta,
      32             :  * \phi), \f}
      33             :  *
      34             :  * where \f$r_0\f$ is the radius of the profile and \f$w\f$ is its width. This
      35             :  * describes a pure spherical harmonic mode \f$Y_{lm}(\theta, \phi)\f$ truncated
      36             :  * by a circular Gaussian window function.
      37             :  *
      38             :  * When evolved, the scalar field \f$\Phi\f$ will briefly build up around the
      39             :  * radius \f$r_0\f$ and then disperse. This can be used to study the ringdown
      40             :  * behavior and late-time tails in different background spacetimes.
      41             :  */
      42             : 
      43           1 : class PureSphericalHarmonic : public MarkAsAnalyticData {
      44             :  public:
      45           0 :   struct Radius {
      46           0 :     using type = double;
      47           0 :     static constexpr Options::String help = {
      48             :         "The radius of the spherical harmonic profile"};
      49           0 :     static type lower_bound() { return 0.0; }
      50             :   };
      51             : 
      52           0 :   struct Width {
      53           0 :     using type = double;
      54           0 :     static constexpr Options::String help = {
      55             :         "The width of the spherical harmonic profile."};
      56           0 :     static type lower_bound() { return 0.0; }
      57             :   };
      58             : 
      59           0 :   struct Mode {
      60           0 :     using type = std::pair<size_t, int>;
      61           0 :     static constexpr Options::String help = {
      62             :         "The l-mode and m-mode of the spherical harmonic Ylm"};
      63             :   };
      64             : 
      65           0 :   using options = tmpl::list<Radius, Width, Mode>;
      66             : 
      67           0 :   static constexpr Options::String help = {
      68             :       "Initial data for a pure spherical harmonic mode truncated by a circular "
      69             :       "Gaussian window funtion. The expression is taken from Scheel(2003), "
      70             :       "equations 4.1-4.3."};
      71             : 
      72           0 :   PureSphericalHarmonic() = default;
      73             : 
      74           0 :   PureSphericalHarmonic(double radius, double width,
      75             :                         std::pair<size_t, int> mode,
      76             :                         const Options::Context& context = {});
      77             : 
      78           0 :   static constexpr size_t volume_dim = 3;
      79           0 :   using tags =
      80             :       tmpl::list<CurvedScalarWave::Tags::Psi, CurvedScalarWave::Tags::Pi,
      81             :                  CurvedScalarWave::Tags::Phi<3>>;
      82             : 
      83             :   /// Retrieve the evolution variables at spatial coordinates `x`
      84             :   tuples::TaggedTuple<CurvedScalarWave::Tags::Psi, CurvedScalarWave::Tags::Pi,
      85             :                       CurvedScalarWave::Tags::Phi<3>>
      86           1 :   variables(const tnsr::I<DataVector, 3>& x, tags /*meta*/) const;
      87             : 
      88             :   // NOLINTNEXTLINE(google-runtime-references)
      89           0 :   void pup(PUP::er& /*p*/);
      90             : 
      91             :  private:
      92           0 :   double radius_{std::numeric_limits<double>::signaling_NaN()};
      93           0 :   double width_sq_{std::numeric_limits<double>::signaling_NaN()};
      94           0 :   std::pair<size_t, int> mode_{std::numeric_limits<size_t>::signaling_NaN(),
      95             :                                std::numeric_limits<int>::signaling_NaN()};
      96             : 
      97           0 :   friend bool operator==(const PureSphericalHarmonic& lhs,
      98             :                          const PureSphericalHarmonic& rhs);
      99             : 
     100           0 :   friend bool operator!=(const PureSphericalHarmonic& lhs,
     101             :                          const PureSphericalHarmonic& rhs);
     102             : };
     103             : 
     104             : }  // namespace CurvedScalarWave::AnalyticData