limiter.h

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//
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
// Copyright (C) 2023 - 2024 by the ryujin authors
//
 
#pragma once
 
#include <compile_time_options.h>
 
#include "hyperbolic_system.h"
 
#include <multicomponent_vector.h>
#include <simd.h>
 
namespace ryujin
{
  namespace ScalarConservation
  {
    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");
 
        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(relaxation_factor);
 
    private:
      unsigned int 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 = 2;
 
      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 unsigned int *js,
                      const state_type &U_j,
                      const flux_contribution_type &flux_j,
                      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;
      flux_contribution_type flux_i;
 
      Bounds bounds_;
 
      Number u_relaxation_numerator;
      Number u_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 u_i = view.state(U_i);
      return {/*u_min*/ u_i, /*u_max*/ u_i};
    }
 
 
    template <int dim, typename Number>
    DEAL_II_ALWAYS_INLINE inline auto Limiter<dim, Number>::combine_bounds(
        const Bounds &bounds_left, const Bounds &bounds_right) const -> Bounds
    {
      const auto &[u_min_l, u_max_l] = bounds_left;
      const auto &[u_min_r, u_max_r] = bounds_right;
 
      return {std::min(u_min_l, u_min_r), std::max(u_max_l, u_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 &[u_min, u_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();
 
      u_min = std::min((Number(1.) - r) * u_min, (Number(1.) + r) * u_min);
      u_max = std::max((Number(1.) + r) * u_max, (Number(1.) - r) * u_max);
 
      return relaxed_bounds;
    }
 
 
    template <int dim, typename Number>
    DEAL_II_ALWAYS_INLINE inline void
    Limiter<dim, Number>::reset(const unsigned int /*i*/,
                                const state_type &new_U_i,
                                const flux_contribution_type &new_flux_i)
    {
      U_i = new_U_i;
      flux_i = new_flux_i;
 
      /* Bounds: */
 
      auto &[u_min, u_max] = bounds_;
 
      u_min = Number(std::numeric_limits<ScalarNumber>::max());
      u_max = Number(std::numeric_limits<ScalarNumber>::lowest());
 
      /* Relaxation: */
 
      u_relaxation_numerator = Number(0.);
      u_relaxation_denominator = Number(0.);
    }
 
 
    template <int dim, typename Number>
    DEAL_II_ALWAYS_INLINE inline void Limiter<dim, Number>::accumulate(
        const unsigned int * /*js*/,
        const state_type &U_j,
        const flux_contribution_type &flux_j,
        const dealii::Tensor<1, dim, Number> &scaled_c_ij,
        const state_type &affine_shift)
    {
      const auto view = hyperbolic_system.view<dim, Number>();
 
      /* Bounds: */
      auto &[u_min, u_max] = bounds_;
 
      const auto u_i = view.state(U_i);
      const auto u_j = view.state(U_j);
 
      const auto U_ij_bar =
          ScalarNumber(0.5) * (U_i + U_j) -
          ScalarNumber(0.5) * contract(add(flux_j, -flux_i), scaled_c_ij) +
          affine_shift;
 
      const auto u_ij_bar = view.state(U_ij_bar);
 
      /* Bounds: */
 
      u_min = std::min(u_min, u_ij_bar);
      u_max = std::max(u_max, u_ij_bar);
 
      /* Relaxation: */
 
      /* Use a uniform weight. */
      const auto beta_ij = Number(1.);
      u_relaxation_numerator += beta_ij * (u_i + u_j);
      u_relaxation_denominator += std::abs(beta_ij);
    }
 
 
    template <int dim, typename Number>
    DEAL_II_ALWAYS_INLINE inline auto
    Limiter<dim, Number>::bounds(const Number hd_i) const -> Bounds
    {
      const auto &[u_min, u_max] = bounds_;
 
      auto relaxed_bounds = fully_relax_bounds(bounds_, hd_i);
      auto &[u_min_relaxed, u_max_relaxed] = relaxed_bounds;
 
      /* Apply a stricter window: */
 
      constexpr ScalarNumber eps = std::numeric_limits<ScalarNumber>::epsilon();
 
      const Number u_relaxation =
          ScalarNumber(2. * parameters.relaxation_factor()) *
          std::abs(u_relaxation_numerator) /
          (std::abs(u_relaxation_denominator) + Number(eps));
 
      u_min_relaxed = std::max(u_min_relaxed, u_min - u_relaxation);
      u_max_relaxed = std::min(u_max_relaxed, u_max + u_relaxation);
 
      return relaxed_bounds;
    }
  } // namespace ScalarConservation
} // namespace ryujin