van_albada_limiter.hh

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#pragma once
 
#include <DiFfRG/discretization/FV/limiter/abstract_limiter.hh>
 
#include <algorithm>
#include <cmath>
 
namespace DiFfRG
{
  namespace def
  {
    class VanAlbadaLimiter
    {
    public:
      template <typename NumberType> static NumberType slope_limit(const NumberType &a, const NumberType &b)
      {
        // Strict TVD: vanish on sign disagreement, including either argument zero.
        const auto ab = a * b;
        if (ab <= NumberType(0)) return NumberType(0);
 
        // ε_floor: defensive against the truly-zero-slope smooth-extremum case
        // where a² + b² could be machine zero. Set far below any physical
        // (du/h)² scale; ~1e-300 is safely below double's denormal range.
        const NumberType eps_floor = NumberType(1e-300);
 
        const auto a2 = a * a;
        const auto b2 = b * b;
        return (a * b2 + b * a2) / (a2 + b2 + eps_floor);
      }
    };
    static_assert(HasSlopeLimiter<VanAlbadaLimiter>);
 
  } // namespace def
} // namespace DiFfRG