wave_speed_estimator.h

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//
// SPDX-License-Identifier: Apache-2.0
// [LANL Copyright Statement]
// Copyright (C) 2023 - 2026 by the ryujin authors
// Copyright (C) 2023 - 2024 by Triad National Security, LLC
//
 
#pragma once
 
#include <compile_time_options.h>
 
#include "hyperbolic_system.h"
 
#include <gpu.h>
#include <observer_pointer.h>
#include <simd.h>
 
#include <deal.II/base/point.h>
#include <deal.II/base/tensor.h>
 
// #define DEBUG_WAVE_SPEED_ESTIMATOR
 
namespace ryujin
{
  namespace ShallowWater
  {
    template <int dim,
              typename Number = double,
              typename MemorySpace = dealii::MemorySpace::Host>
    class WaveSpeedEstimatorView;
 
    template <typename ScalarNumber = double>
    class WaveSpeedEstimator : public dealii::ParameterAcceptor
    {
    public:
 
      WaveSpeedEstimator(const HyperbolicSystem &hyperbolic_system,
                         const std::string &subsection = "/WaveSpeedEstimator")
          : ParameterAcceptor(subsection)
          , hyperbolic_system_(&hyperbolic_system)
      {
      }
 
      template <int dim,
                typename Number,
                typename MemorySpace = dealii::MemorySpace::Host>
      auto view() const
      {
        return WaveSpeedEstimatorView<dim, Number, MemorySpace>{
            hyperbolic_system_->template view<dim, Number, MemorySpace>(),
            *this};
      }
 
    private:
 
 
      dealii::ObserverPointer<const HyperbolicSystem> hyperbolic_system_;
 
      template <int, typename, typename>
      friend class WaveSpeedEstimatorView;
 
    };
 
 
    template <int dim, typename Number, typename MemorySpace>
    class WaveSpeedEstimatorView
    {
    public:
      static_assert(
          std::is_same_v<MemorySpace, dealii::MemorySpace::Host> ||
              std::is_same_v<MemorySpace, dealii::MemorySpace::Default>,
          "Unexpected memory space");
 
 
      using View = HyperbolicSystemView<dim, Number, MemorySpace>;
 
      using ScalarNumber = typename View::ScalarNumber;
 
      using state_type = typename View::state_type;
 
      static constexpr unsigned int riemann_data_size = 3;
 
      using primitive_type = typename std::array<Number, riemann_data_size>;
 
      using PrecomputedVectorView = typename View::PrecomputedVectorView;
 
 
 
      WaveSpeedEstimatorView(const View &view,
                             const WaveSpeedEstimator<ScalarNumber> & /*wse*/)
          : view_(view)
      {
      }
 
      DEAL_II_HOST_DEVICE Number
      compute(const primitive_type &riemann_data_i,
              const primitive_type &riemann_data_j) const;
 
      DEAL_II_HOST_DEVICE Number
      compute(const PrecomputedVectorView &pv,
              const state_type &U_i,
              const state_type &U_j,
              const unsigned int i,
              const unsigned int *js,
              const dealii::Tensor<1, dim, Number> &n_ij) const;
 
    protected:
 
 
      DEAL_II_HOST_DEVICE Number f(const primitive_type &primitive_state,
                                   const Number &h_star) const;
 
      DEAL_II_HOST_DEVICE Number phi(const primitive_type &riemann_data_i,
                                     const primitive_type &riemann_data_j,
                                     const Number &h) const;
 
      DEAL_II_HOST_DEVICE Number lambda1_minus(
          const primitive_type &riemann_data, const Number h_star) const;
 
      DEAL_II_HOST_DEVICE Number lambda3_plus(
          const primitive_type &riemann_data, const Number h_star) const;
 
      DEAL_II_HOST_DEVICE Number
      compute_lambda(const primitive_type &riemann_data_i,
                     const primitive_type &riemann_data_j,
                     const Number h_star) const;
 
    public:
      DEAL_II_HOST_DEVICE Number
      compute_h_star(const primitive_type &riemann_data_i,
                     const primitive_type &riemann_data_j) const;
 
    protected:
      DEAL_II_HOST_DEVICE primitive_type
      riemann_data_from_state(const state_type &U,
                              const dealii::Tensor<1, dim, Number> &n_ij) const;
 
    private:
 
 
      const View view_;
 
    };
 
 
    /*
     * -------------------------------------------------------------------------
     * Inline definitions
     * -------------------------------------------------------------------------
     */
 
 
    template <int dim, typename Number, typename MemorySpace>
    DEAL_II_HOST_DEVICE_ALWAYS_INLINE Number
    WaveSpeedEstimatorView<dim, Number, MemorySpace>::compute(
        const primitive_type &riemann_data_i,
        const primitive_type &riemann_data_j) const
    {
      const Number h_star = compute_h_star(riemann_data_i, riemann_data_j);
 
      const Number lambda_max =
          compute_lambda(riemann_data_i, riemann_data_j, h_star);
 
      return lambda_max;
    }
 
 
    template <int dim, typename Number, typename MemorySpace>
    DEAL_II_HOST_DEVICE_ALWAYS_INLINE Number
    WaveSpeedEstimatorView<dim, Number, MemorySpace>::compute(
        const PrecomputedVectorView & /*pv*/,
        const state_type &U_i,
        const state_type &U_j,
        const unsigned int /*i*/,
        const unsigned int * /*js*/,
        const dealii::Tensor<1, dim, Number> &n_ij) const
    {
      const auto riemann_data_i = riemann_data_from_state(U_i, n_ij);
      const auto riemann_data_j = riemann_data_from_state(U_j, n_ij);
      return compute(riemann_data_i, riemann_data_j);
    }
 
 
    template <int dim, typename Number, typename MemorySpace>
    DEAL_II_HOST_DEVICE_ALWAYS_INLINE Number
    WaveSpeedEstimatorView<dim, Number, MemorySpace>::f(
        const primitive_type &riemann_data_Z, const Number &h) const
    {
      const ScalarNumber gravity = view_.gravity();
 
      const auto &[h_Z, u_Z, a_Z] = riemann_data_Z;
 
      const auto left_value = ScalarNumber(2.) * (std::sqrt(gravity * h) - a_Z);
 
      const Number radicand =
          ScalarNumber(0.5) * gravity * (h + h_Z) / (h * h_Z);
      const Number right_value = (h - h_Z) * std::sqrt(radicand);
 
      return ryujin::compare_and_apply_mask<
          dealii::SIMDComparison::less_than_or_equal>(
          h, h_Z, left_value, right_value);
    }
 
 
    template <int dim, typename Number, typename MemorySpace>
    DEAL_II_HOST_DEVICE_ALWAYS_INLINE Number
    WaveSpeedEstimatorView<dim, Number, MemorySpace>::phi(
        const primitive_type &riemann_data_i,
        const primitive_type &riemann_data_j,
        const Number &h) const
    {
      const Number &u_i = riemann_data_i[1];
      const Number &u_j = riemann_data_j[1];
 
#ifdef DEBUG_WAVE_SPEED_ESTIMATOR
      std::cout << "f_L --> " << f(riemann_data_i, h) << std::endl;
      std::cout << "f_R --> " << f(riemann_data_j, h) << std::endl;
#endif
      return f(riemann_data_i, h) + f(riemann_data_j, h) + u_j - u_i;
    }
 
 
    template <int dim, typename Number, typename MemorySpace>
    DEAL_II_HOST_DEVICE_ALWAYS_INLINE Number
    WaveSpeedEstimatorView<dim, Number, MemorySpace>::lambda1_minus(
        const primitive_type &riemann_data, const Number h_star) const
    {
      const auto &[h, u, a] = riemann_data;
 
      const Number factor = positive_part((h_star - h) / h);
      const Number half_factor = ScalarNumber(0.5) * factor;
 
      return u - a * std::sqrt((ScalarNumber(1.) + half_factor) *
                               (ScalarNumber(1.) + factor));
    }
 
 
    template <int dim, typename Number, typename MemorySpace>
    DEAL_II_HOST_DEVICE_ALWAYS_INLINE Number
    WaveSpeedEstimatorView<dim, Number, MemorySpace>::lambda3_plus(
        const primitive_type &riemann_data, const Number h_star) const
    {
      const auto &[h, u, a] = riemann_data;
 
      const Number factor = positive_part((h_star - h) / h);
      const Number half_factor = ScalarNumber(0.5) * factor;
 
      return u + a * std::sqrt((ScalarNumber(1.) + half_factor) *
                               (ScalarNumber(1.) + factor));
    }
 
 
    template <int dim, typename Number, typename MemorySpace>
    DEAL_II_HOST_DEVICE_ALWAYS_INLINE Number
    WaveSpeedEstimatorView<dim, Number, MemorySpace>::compute_lambda(
        const primitive_type &riemann_data_i,
        const primitive_type &riemann_data_j,
        const Number h_star) const
    {
      const Number lambda1 = lambda1_minus(riemann_data_i, h_star);
      const Number lambda3 = lambda3_plus(riemann_data_j, h_star);
 
      return std::max(negative_part(lambda1), positive_part(lambda3));
    }
 
 
    template <int dim, typename Number, typename MemorySpace>
    DEAL_II_HOST_DEVICE_ALWAYS_INLINE Number
    WaveSpeedEstimatorView<dim, Number, MemorySpace>::compute_h_star(
        const primitive_type &riemann_data_i,
        const primitive_type &riemann_data_j) const
    {
      const ScalarNumber gravity = view_.gravity();
      const auto gravity_inverse = ScalarNumber(1.) / gravity;
 
      const auto &[h_i, u_i, a_i] = riemann_data_i;
      const auto &[h_j, u_j, a_j] = riemann_data_j;
 
      const Number h_min = std::min(h_i, h_j);
      const Number h_max = std::max(h_i, h_j);
 
#ifdef DEBUG_WAVE_SPEED_ESTIMATOR
      std::cout << h_min << "  <- h_min/max ->  " << h_max << std::endl;
#endif
 
      const Number a_min = std::sqrt(gravity * h_min);
      const Number a_max = std::sqrt(gravity * h_max);
 
#ifdef DEBUG_WAVE_SPEED_ESTIMATOR
      std::cout << a_min << "  <- a_min/max ->  " << a_max << std::endl;
#endif
 
      const Number sqrt_two = std::sqrt(ScalarNumber(2.));
 
      /* x0 = (2 sqrt(2) - 1)^2 */
      const Number x0 = Number(9.) - ScalarNumber(4.) * sqrt_two;
 
      const Number phi_value_min =
          phi(riemann_data_i, riemann_data_j, x0 * h_min);
#ifdef DEBUG_WAVE_SPEED_ESTIMATOR
      std::cout << "phi_value_min ->" << phi_value_min << std::endl;
#endif
 
      const Number phi_value_max =
          phi(riemann_data_i, riemann_data_j, x0 * h_max);
#ifdef DEBUG_WAVE_SPEED_ESTIMATOR
      std::cout << "phi_value_max ->" << phi_value_max << std::endl;
#endif
 
      /* We compute the three h_star quantities */
 
      Number tmp;
 
      /* Double rarefaction case (h_star left): */
 
      tmp = positive_part(u_i - u_j + ScalarNumber(2.) * (a_i + a_j));
      const Number h_star_left =
          ScalarNumber(0.0625) * gravity_inverse * tmp * tmp;
 
#ifdef DEBUG_WAVE_SPEED_ESTIMATOR
      std::cout << "left: " << h_star_left << std::endl;
#endif
 
      /* Double modified shock (h_star middle): */
 
      tmp = Number(1.) + sqrt_two * (u_i - u_j) / (a_min + a_max);
      const Number h_star_middle = std::sqrt(h_min * h_max) * tmp;
 
#ifdef DEBUG_WAVE_SPEED_ESTIMATOR
      std::cout << "middle: " << h_star_middle << std::endl;
#endif
 
      /* Expansion and modified shock (h_star right): */
 
      const auto left_radicand =
          ScalarNumber(3.) * h_min +
          ScalarNumber(2.) * sqrt_two * std::sqrt(h_min * h_max);
 
      const auto right_radicand =
          sqrt_two * std::sqrt(gravity_inverse * h_min) * (u_i - u_j);
 
      tmp = std::sqrt(positive_part(left_radicand + right_radicand));
      tmp -= sqrt_two * std::sqrt(h_min);
 
      const Number h_star_right = tmp * tmp;
 
#ifdef DEBUG_WAVE_SPEED_ESTIMATOR
      std::cout << "right: " << h_star_right << std::endl;
#endif
 
      /* Finally define h_star */
 
      Number h_star = ryujin::compare_and_apply_mask<
          dealii::SIMDComparison::less_than_or_equal>(
          Number(0.), phi_value_min, h_star_left, h_star_right);
 
      h_star =
          ryujin::compare_and_apply_mask<dealii::SIMDComparison::less_than>(
              phi_value_max, Number(0.), h_star_middle, h_star);
 
      return h_star;
    }
 
 
    template <int dim, typename Number, typename MemorySpace>
    DEAL_II_HOST_DEVICE_ALWAYS_INLINE auto
    WaveSpeedEstimatorView<dim, Number, MemorySpace>::riemann_data_from_state(
        const state_type &U, const dealii::Tensor<1, dim, Number> &n_ij) const
        -> primitive_type
    {
      const Number h = view_.water_depth_sharp(U);
      const Number gravity = view_.gravity();
 
      const auto velocity = view_.momentum(U) / h;
      const auto projected_velocity = n_ij * velocity;
      const auto a = std::sqrt(h * gravity);
 
      return {{h, projected_velocity, a}};
    }
  } // namespace ShallowWater
} // namespace ryujin