initial_state_paraboloid.h

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//
// SPDX-License-Identifier: Apache-2.0
// [LANL Copyright Statement]
// Copyright (C) 2022 - 2025 by the ryujin authors
// Copyright (C) 2023 - 2024 by Triad National Security, LLC
//
 
#pragma once
 
#include <compile_time_options.h>
 
#include <initial_state_library.h>
 
namespace ryujin
{
  namespace ShallowWaterInitialStates
  {
    template <typename Description, int dim, typename Number>
    class Paraboloid : public InitialState<Description, dim, Number>
    {
    public:
      using HyperbolicSystem = typename Description::HyperbolicSystem;
      using View = typename HyperbolicSystem::template View<dim, Number>;
      using state_type = typename View::state_type;
 
      Paraboloid(const HyperbolicSystem &hyperbolic_system,
                 const std::string subsection)
          : InitialState<Description, dim, Number>("paraboloid", subsection)
          , hyperbolic_system_(hyperbolic_system)
      {
        a_ = 1.;
        this->add_parameter(
            "free surface radius", a_, "Radius of the circular free surface");
 
        h_0_ = 0.1;
        this->add_parameter(
            "water height", h_0_, "Water height at central point");
 
        if constexpr (dim == 1) {
 
          length_ = 10000.;
          this->add_parameter(
              "paraboloid length", length_, "Length of 1D paraboloid");
 
          B_ = 2.;
          this->add_parameter("speed", B_, "The 1D paraboloid speed");
 
        } else {
          eta_ = 0.5;
          this->add_parameter("eta", eta_, "The eta parameter");
        }
      }
 
      state_type compute(const dealii::Point<dim> &point, Number t) final
      {
        const auto view = hyperbolic_system_.template view<dim, Number>();
 
        /* Common quantities */
        const auto z = compute_bathymetry(point);
        const auto g = view.gravity();
        const Number omega = std::sqrt(2. * g * h_0_) / a_;
        const Number &x = point[0];
 
        /* Initialize primitive variables */
        Number h, v_x, v_y = 0.;
 
        /* Define slightly different profiles for each dimension */
 
        if constexpr (dim == 1) {
 
          const Number k = view.manning_friction_coefficient();
          const Number p = std::sqrt(8. * g * h_0_) / a_;
          const Number s = std::sqrt(p * p - k * k) / 2.;
 
          auto term1 =
              (a_ * a_ * B_ * B_) / (8. * g * g * h_0_) * std::exp(-k * t);
          term1 *= (1. / 4. * k * k - s * s) * std::cos(2. * s * t) -
                   s * k * sin(2. * s * t);
 
          const auto term2 = -(B_ * B_ / (4. * g)) * std::exp(-k * t);
 
          auto term3 = -(B_ / g) * std::exp(-1. / 2. * k * t);
          term3 *= (s * std::cos(s * t) + 1. / 2. * k * std::sin(s * t)) *
                   (point[0] - 1. / 2. * length_);
 
          auto htilde = h_0_ - compute_bathymetry(point);
          htilde += term1 + term2 + term3;
 
          h = std::max(htilde, Number(0.));
          v_x = B_ * std::exp(-1. / 2. * k * t) * std::sin(s * t);
 
          return state_type{{h, h * v_x}};
        } else if constexpr (dim == 2) {
 
          const Number &y = point[1];
 
          const Number elevation =
              eta_ * h_0_ / (a_ * a_) *
              (2. * x * std::cos(omega * t) + 2. * y * std::sin(omega * t));
 
          h = std::max(elevation - z, Number(0.));
          v_x = -eta_ * omega * std::sin(omega * t);
          v_y = eta_ * omega * std::cos(omega * t);
 
          return state_type{{h, h * v_x, h * v_y}};
 
        } else {
          AssertThrow(false, dealii::ExcNotImplemented());
          __builtin_trap();
        }
      }
 
 
      auto initial_precomputations(const dealii::Point<dim> &point) ->
          typename InitialState<Description, dim, Number>::
              initial_precomputed_type final
      {
        /* Compute bathymetry: */
        return {compute_bathymetry(point)};
      }
 
    private:
      const HyperbolicSystem &hyperbolic_system_;
 
      DEAL_II_ALWAYS_INLINE inline Number
      compute_bathymetry(const dealii::Point<dim> &point) const
      {
        if constexpr (dim == 1)
          return h_0_ / (a_ * a_) * std::pow(point[0] - 0.5 * length_, 2);
        else
          return -h_0_ * (Number(1.) - point.norm_square() / (a_ * a_));
      }
 
      Number a_;
      Number h_0_;
      Number eta_;
      Number length_;
      Number B_;
    };
 
  } // namespace ShallowWaterInitialStates
} // namespace ryujin