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/TaggedTuple.hpp"
      12              : #include "DataStructures/Tensor/Tensor.hpp"
      13              : #include "Evolution/Systems/CurvedScalarWave/Tags.hpp"
      14              : #include "Options/Context.hpp"
      15              : #include "Options/String.hpp"
      16              : #include "PointwiseFunctions/AnalyticData/AnalyticData.hpp"
      17              : #include "PointwiseFunctions/InitialDataUtilities/InitialData.hpp"
      18              : #include "Utilities/TMPL.hpp"
      19              : 
      20              : namespace CurvedScalarWave::AnalyticData {
      21              : 
      22              : /*!
      23              :  * \brief Analytic initial data for a pure spherical harmonic in three
      24              :  * dimensions.
      25              :  *
      26              :  * \details The initial data is taken from \cite Scheel2003vs , Eqs. 4.1--4.3,
      27              :  * and sets the evolved variables of the scalar wave as follows:
      28              :  *
      29              :  * \f{align}
      30              :  * \Psi &= 0 \\
      31              :  * \Phi_i &= 0 \\
      32              :  * \Pi &= \Pi_0(r, \theta, \phi) =  e^{- (r - r_0)^2 / w^2} Y_{lm}(\theta,
      33              :  * \phi), \f}
      34              :  *
      35              :  * where \f$r_0\f$ is the radius of the profile and \f$w\f$ is its width. This
      36              :  * describes a pure spherical harmonic mode \f$Y_{lm}(\theta, \phi)\f$ truncated
      37              :  * by a circular Gaussian window function.
      38              :  *
      39              :  * When evolved, the scalar field \f$\Phi\f$ will briefly build up around the
      40              :  * radius \f$r_0\f$ and then disperse. This can be used to study the ringdown
      41              :  * behavior and late-time tails in different background spacetimes.
      42              :  */
      43              : 
      44            1 : class PureSphericalHarmonic : public evolution::initial_data::InitialData,
      45              :                               public MarkAsAnalyticData {
      46              :  public:
      47            0 :   struct Radius {
      48            0 :     using type = double;
      49            0 :     static constexpr Options::String help = {
      50              :         "The radius of the spherical harmonic profile"};
      51            0 :     static type lower_bound() { return 0.0; }
      52              :   };
      53              : 
      54            0 :   struct Width {
      55            0 :     using type = double;
      56            0 :     static constexpr Options::String help = {
      57              :         "The width of the spherical harmonic profile."};
      58            0 :     static type lower_bound() { return 0.0; }
      59              :   };
      60              : 
      61            0 :   struct Mode {
      62            0 :     using type = std::pair<size_t, int>;
      63            0 :     static constexpr Options::String help = {
      64              :         "The l-mode and m-mode of the spherical harmonic Ylm"};
      65              :   };
      66              : 
      67            0 :   using options = tmpl::list<Radius, Width, Mode>;
      68              : 
      69            0 :   static constexpr Options::String help = {
      70              :       "Initial data for a pure spherical harmonic mode truncated by a circular "
      71              :       "Gaussian window funtion. The expression is taken from Scheel(2003), "
      72              :       "equations 4.1-4.3."};
      73              : 
      74            0 :   PureSphericalHarmonic() = default;
      75              : 
      76            0 :   PureSphericalHarmonic(double radius, double width,
      77              :                         std::pair<size_t, int> mode,
      78              :                         const Options::Context& context = {});
      79            0 :   PureSphericalHarmonic(const PureSphericalHarmonic&) = default;
      80            0 :   PureSphericalHarmonic& operator=(const PureSphericalHarmonic&) = default;
      81            0 :   PureSphericalHarmonic(PureSphericalHarmonic&&) = default;
      82            0 :   PureSphericalHarmonic& operator=(PureSphericalHarmonic&&) = default;
      83            0 :   ~PureSphericalHarmonic() override = default;
      84              : 
      85            0 :   auto get_clone() const
      86              :       -> std::unique_ptr<evolution::initial_data::InitialData> override;
      87              : 
      88              :   /// \cond
      89              :   explicit PureSphericalHarmonic(CkMigrateMessage* msg);
      90              :   using PUP::able::register_constructor;
      91              :   WRAPPED_PUPable_decl_template(PureSphericalHarmonic);
      92              :   /// \endcond
      93              : 
      94            0 :   static constexpr size_t volume_dim = 3;
      95            0 :   using tags =
      96              :       tmpl::list<CurvedScalarWave::Tags::Psi, CurvedScalarWave::Tags::Pi,
      97              :                  CurvedScalarWave::Tags::Phi<3>>;
      98              : 
      99              :   /// Retrieve the evolution variables at spatial coordinates `x`
     100              :   tuples::TaggedTuple<CurvedScalarWave::Tags::Psi, CurvedScalarWave::Tags::Pi,
     101              :                       CurvedScalarWave::Tags::Phi<3>>
     102            1 :   variables(const tnsr::I<DataVector, 3>& x, tags /*meta*/) const;
     103              : 
     104              :   // NOLINTNEXTLINE(google-runtime-references)
     105            0 :   void pup(PUP::er& /*p*/) override;
     106              : 
     107              :  private:
     108            0 :   double radius_{std::numeric_limits<double>::signaling_NaN()};
     109            0 :   double width_sq_{std::numeric_limits<double>::signaling_NaN()};
     110            0 :   std::pair<size_t, int> mode_{std::numeric_limits<size_t>::signaling_NaN(),
     111              :                                std::numeric_limits<int>::signaling_NaN()};
     112              : 
     113            0 :   friend bool operator==(const PureSphericalHarmonic& lhs,
     114              :                          const PureSphericalHarmonic& rhs);
     115              : 
     116            0 :   friend bool operator!=(const PureSphericalHarmonic& lhs,
     117              :                          const PureSphericalHarmonic& rhs);
     118              : };
     119              : 
     120              : }  // namespace CurvedScalarWave::AnalyticData