limiter.template.h

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//
// SPDX-License-Identifier: MIT
// Copyright (C) 2020 - 2023 by the ryujin authors
//
 
#pragma once
 
#include "limiter.h"
 
namespace ryujin
{
  namespace ScalarConservation
  {
    template <int dim, typename Number>
    std::tuple<Number, bool>
    Limiter<dim, Number>::limit(const Bounds &bounds,
                                const state_type &U,
                                const state_type &P,
                                const Number t_min /* = Number(0.) */,
                                const Number t_max /* = Number(1.) */)
    {
      bool success = true;
      Number t_r = t_max;
 
      constexpr ScalarNumber eps = std::numeric_limits<ScalarNumber>::epsilon();
      const ScalarNumber relax = ScalarNumber(1. + 10000. * eps);
 
      const auto &u_U = hyperbolic_system.state(U);
      const auto &u_P = hyperbolic_system.state(P);
 
      const auto &u_min = std::get<0>(bounds);
      const auto &u_max = std::get<1>(bounds);
 
      /*
       * Verify that u_U is within bounds. This property might be
       * violated for relative CFL numbers larger than 1.
       */
      const auto test_min = std::max(Number(0.), u_U - relax * u_max);
      const auto test_max = std::max(Number(0.), u_min - relax * u_U);
      if (!(test_min == Number(0.) && test_max == Number(0.))) {
#ifdef DEBUG_OUTPUT
        std::cout << std::fixed << std::setprecision(16);
        std::cout << "Bounds violation: low-order state (critical)!"
                  << "\n\t\tu min:         " << u_min
                  << "\n\t\tu min (delta): " << negative_part(u_U - u_min)
                  << "\n\t\tu:             " << u_U
                  << "\n\t\tu max (delta): " << positive_part(u_U - u_max)
                  << "\n\t\tu max:         " << u_max << "\n"
                  << std::endl;
#endif
        success = false;
      }
 
      const Number denominator =
          ScalarNumber(1.) / (std::abs(u_P) + eps * u_max);
 
      t_r = dealii::compare_and_apply_mask<dealii::SIMDComparison::less_than>(
          u_max,
          u_U + t_r * u_P,
          /*
           * u_P is positive.
           *
           * Note: Do not take an absolute value here. If we are out of
           * bounds we have to ensure that t_r is set to t_min.
           */
          (u_max - u_U) * denominator,
          t_r);
 
      t_r = dealii::compare_and_apply_mask<dealii::SIMDComparison::less_than>(
          u_U + t_r * u_P,
          u_min,
          /*
           * u_P is negative.
           *
           * Note: Do not take an absolute value here. If we are out of
           * bounds we have to ensure that t_r is set to t_min.
           */
          (u_U - u_min) * denominator,
          t_r);
 
      /*
       * Ensure that t_min <= t <= t_max. This might not be the case if
       * u_U is outside the interval [u_min, u_max]. Furthermore,
       * the quotient we take above is prone to numerical cancellation in
       * particular in the second pass of the limiter when u_P might be
       * small.
       */
      t_r = std::min(t_r, t_max);
      t_r = std::max(t_r, t_min);
 
#ifdef CHECK_BOUNDS
      /*
       * Verify that the new state is within bounds:
       */
      const auto u_new = hyperbolic_system.state(U + t_r * P);
      const auto test_new_min = std::max(Number(0.), u_new - relax * u_max);
      const auto test_new_max = std::max(Number(0.), u_min - relax * u_new);
      if (!(test_new_min == Number(0.) && test_new_max == Number(0.))) {
#ifdef DEBUG_OUTPUT
        std::cout << std::fixed << std::setprecision(16);
        std::cout << "Bounds violation: high-order state!"
                  << "\n\t\tu min:         " << u_min
                  << "\n\t\tu min (delta): " << negative_part(u_new - u_min)
                  << "\n\t\tu:             " << u_new
                  << "\n\t\tu max (delta): " << positive_part(u_new - u_max)
                  << "\n\t\tu max:         " << u_max << "\n"
                  << std::endl;
#endif
        success = false;
      }
#endif
 
      return {t_r, success};
    }
 
  } // namespace ScalarConservation
} // namespace ryujin