limiter.h

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//
// SPDX-License-Identifier: Apache-2.0
// [LANL Copyright Statement]
// Copyright (C) 2023 - 2024 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 <multicomponent_vector.h>
#include <newton.h>
 
namespace ryujin
{
  namespace ShallowWater
  {
    template <typename ScalarNumber = double>
    class LimiterParameters : public dealii::ParameterAcceptor
    {
    public:
      LimiterParameters(const std::string &subsection = "/Limiter")
          : ParameterAcceptor(subsection)
      {
        iterations_ = 2;
        add_parameter(
            "iterations", iterations_, "Number of limiter iterations");
 
        if constexpr (std::is_same_v<ScalarNumber, double>)
          newton_tolerance_ = 1.e-10;
        else
          newton_tolerance_ = 1.e-4;
        add_parameter("newton tolerance",
                      newton_tolerance_,
                      "Tolerance for the quadratic newton stopping criterion");
 
        newton_max_iterations_ = 2;
        add_parameter("newton max iterations",
                      newton_max_iterations_,
                      "Maximal number of quadratic newton iterations performed "
                      "during limiting");
 
        relaxation_factor_ = ScalarNumber(1.);
        add_parameter("relaxation factor",
                      relaxation_factor_,
                      "Factor for scaling the relaxation window with r_i = "
                      "factor * (m_i/|Omega|)^(1.5/d).");
      }
 
      ACCESSOR_READ_ONLY(iterations);
      ACCESSOR_READ_ONLY(newton_tolerance);
      ACCESSOR_READ_ONLY(newton_max_iterations);
      ACCESSOR_READ_ONLY(relaxation_factor);
 
    private:
      unsigned int iterations_;
      ScalarNumber newton_tolerance_;
      unsigned int newton_max_iterations_;
      ScalarNumber relaxation_factor_;
    };
 
 
    template <int dim, typename Number = double>
    class Limiter
    {
    public:
 
      using View = HyperbolicSystemView<dim, Number>;
 
      using ScalarNumber = typename View::ScalarNumber;
 
      static constexpr auto problem_dimension = View::problem_dimension;
 
      using state_type = typename View::state_type;
 
      using flux_contribution_type = typename View::flux_contribution_type;
 
      using precomputed_type = typename View::precomputed_type;
 
      using PrecomputedVector = typename View::PrecomputedVector;
 
      using Parameters = LimiterParameters<ScalarNumber>;
 
 
      static constexpr unsigned int n_bounds = 3;
 
      using Bounds = std::array<Number, n_bounds>;
 
      Limiter(const HyperbolicSystem &hyperbolic_system,
              const Parameters &parameters,
              const PrecomputedVector &precomputed_values)
          : hyperbolic_system(hyperbolic_system)
          , parameters(parameters)
          , precomputed_values(precomputed_values)
      {
      }
 
      Bounds projection_bounds_from_state(const unsigned int i,
                                          const state_type &U_i) const;
 
      Bounds combine_bounds(const Bounds &bounds_left,
                            const Bounds &bounds_right) const;
 
      Bounds fully_relax_bounds(const Bounds &bounds, const Number &hd) const;
 
 
 
      void reset(const unsigned int i,
                 const state_type &U_i,
                 const flux_contribution_type &flux_i);
 
      void accumulate(const state_type &U_j,
                      const state_type &U_star_ij,
                      const state_type &U_star_ji,
                      const dealii::Tensor<1, dim, Number> &scaled_c_ij,
                      const state_type &affine_shift);
 
      Bounds bounds(const Number hd_i) const;
 
      //*}
 
      std::tuple<Number, bool> limit(const Bounds &bounds,
                                     const state_type &U,
                                     const state_type &P,
                                     const Number t_min = Number(0.),
                                     const Number t_max = Number(1.)) const;
 
    private:
 
 
      const HyperbolicSystem &hyperbolic_system;
      const Parameters &parameters;
      const PrecomputedVector &precomputed_values;
 
      state_type U_i;
 
      Bounds bounds_;
 
      /* for relaxation */
 
      Number h_relaxation_numerator;
      Number v2_relaxation_numerator;
      Number relaxation_denominator;
 
    };
 
 
    /*
     * -------------------------------------------------------------------------
     * Inline definitions
     * -------------------------------------------------------------------------
     */
 
 
    template <int dim, typename Number>
    DEAL_II_ALWAYS_INLINE inline auto
    Limiter<dim, Number>::projection_bounds_from_state(
        const unsigned int /*i*/, const state_type &U_i) const -> Bounds
    {
      const auto view = hyperbolic_system.view<dim, Number>();
      const auto h_i = view.water_depth(U_i);
      const auto v_i =
          view.momentum(U_i) * view.inverse_water_depth_mollified(U_i);
      const auto v2_i = v_i.norm_square();
 
      return {/*h_min*/ h_i, /*h_max*/ h_i, /*v2_max*/ v2_i};
    }
 
 
    template <int dim, typename Number>
    DEAL_II_ALWAYS_INLINE inline auto
    Limiter<dim, Number>::combine_bounds(const Bounds &bounds_l,
                                         const Bounds &bounds_r) const -> Bounds
    {
      const auto &[h_min_l, h_max_l, v2_max_l] = bounds_l;
      const auto &[h_min_r, h_max_r, v2_max_r] = bounds_r;
 
      return {std::min(h_min_l, h_min_r),
              std::max(h_max_l, h_max_r),
              std::max(v2_max_l, v2_max_r)};
    }
 
 
    template <int dim, typename Number>
    DEAL_II_ALWAYS_INLINE inline auto
    Limiter<dim, Number>::fully_relax_bounds(const Bounds &bounds,
                                             const Number &hd) const -> Bounds
    {
      auto relaxed_bounds = bounds;
      auto &[h_min, h_max, v2_max] = relaxed_bounds;
 
      /* Use r = factor * (m_i / |Omega|) ^ (1.5 / d): */
 
      Number r = std::sqrt(hd);                              // in 3D: ^ 3/6
      if constexpr (dim == 2)                                //
        r = dealii::Utilities::fixed_power<3>(std::sqrt(r)); // in 2D: ^ 3/4
      else if constexpr (dim == 1)                           //
        r = dealii::Utilities::fixed_power<3>(r);            // in 1D: ^ 3/2
      r *= parameters.relaxation_factor();
 
      constexpr ScalarNumber eps = std::numeric_limits<ScalarNumber>::epsilon();
      h_min *= std::max((Number(1.) - r), Number(eps));
      h_max *= (Number(1.) + r);
      v2_max *= (Number(1.) + r);
 
      return relaxed_bounds;
    }
 
 
    template <int dim, typename Number>
    DEAL_II_ALWAYS_INLINE inline void
    Limiter<dim, Number>::reset(unsigned int /*i*/,
                                const state_type &new_U_i,
                                const flux_contribution_type & /*new_flux_i*/)
    {
      U_i = new_U_i;
 
      auto &[h_min, h_max, v2_max] = bounds_;
 
      h_min = Number(std::numeric_limits<ScalarNumber>::max());
      h_max = Number(0.);
      v2_max = Number(0.);
 
      h_relaxation_numerator = Number(0.);
      v2_relaxation_numerator = Number(0.);
      relaxation_denominator = Number(0.);
    }
 
 
    template <int dim, typename Number>
    DEAL_II_ALWAYS_INLINE inline void Limiter<dim, Number>::accumulate(
        const state_type &U_j,
        const state_type &U_star_ij,
        const state_type &U_star_ji,
        const dealii::Tensor<1, dim, Number> &scaled_c_ij,
        const state_type &affine_shift)
    {
      const auto view = hyperbolic_system.view<dim, Number>();
 
      /* The bar states: */
 
      const auto f_star_ij = view.f(U_star_ij);
      const auto f_star_ji = view.f(U_star_ji);
 
      /* bar state shifted by an affine shift: */
      const auto U_ij_bar =
          ScalarNumber(0.5) *
              (U_star_ij + U_star_ji +
               contract(add(f_star_ij, -f_star_ji), scaled_c_ij)) +
          affine_shift;
 
      /* Bounds: */
 
      auto &[h_min, h_max, v2_max] = bounds_;
 
      const auto h_bar_ij = view.water_depth(U_ij_bar);
      h_min = std::min(h_min, h_bar_ij);
      h_max = std::max(h_max, h_bar_ij);
 
      const auto v_bar_ij = view.momentum(U_ij_bar) *
                            view.inverse_water_depth_mollified(U_ij_bar);
      const auto v2_bar_ij = v_bar_ij.norm_square();
      v2_max = std::max(v2_max, v2_bar_ij);
 
      /* Relaxation: */
 
      /* Use a uniform weight. */
      const auto beta_ij = Number(1.);
 
      relaxation_denominator += std::abs(beta_ij);
 
      const auto h_i = view.water_depth(U_i);
      const auto h_j = view.water_depth(U_j);
      h_relaxation_numerator += beta_ij * (h_i + h_j);
 
      const auto vel_i =
          view.momentum(U_i) * view.inverse_water_depth_mollified(U_i);
      const auto vel_j =
          view.momentum(U_j) * view.inverse_water_depth_mollified(U_j);
      v2_relaxation_numerator +=
          beta_ij * (-vel_i.norm_square() + vel_j.norm_square());
    }
 
 
    template <int dim, typename Number>
    DEAL_II_ALWAYS_INLINE inline auto
    Limiter<dim, Number>::bounds(const Number hd_i) const -> Bounds
    {
      const auto &[h_min, h_max, v2_max] = bounds_;
 
      auto relaxed_bounds = fully_relax_bounds(bounds_, hd_i);
      auto &[h_min_relaxed, h_max_relaxed, v2_max_relaxed] = relaxed_bounds;
 
      /* Apply a stricter window: */
 
      constexpr ScalarNumber eps = std::numeric_limits<ScalarNumber>::epsilon();
 
      const Number h_relaxed =
          ScalarNumber(2. * parameters.relaxation_factor()) *
          std::abs(h_relaxation_numerator) /
          (relaxation_denominator + Number(eps));
 
      const Number v2_relaxed =
          ScalarNumber(2. * parameters.relaxation_factor()) *
          std::abs(v2_relaxation_numerator) /
          (relaxation_denominator + Number(eps));
 
      h_min_relaxed = std::max(h_min_relaxed, h_min - h_relaxed);
      h_max_relaxed = std::min(h_max_relaxed, h_max + h_relaxed);
      v2_max_relaxed = std::min(v2_max_relaxed, v2_max + v2_relaxed);
 
      return relaxed_bounds;
    }
  } // namespace ShallowWater
} // namespace ryujin