cubicGradientLimiter.H

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    Copyright (C) 2018 OpenFOAM Foundation
    Copyright (C) 2021 OpenCFD Ltd.
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License
    This file is part of OpenFOAM.
 
    OpenFOAM is free software: you can redistribute it and/or modify it
    under the terms of the GNU General Public License as published by
    the Free Software Foundation, either version 3 of the License, or
    (at your option) any later version.
 
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    FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
    for more details.
 
    You should have received a copy of the GNU General Public License
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Class
    Foam::fv::gradientLimiters::cubic
 
Description
    Cubic gradient limiter
 
    to be used with the Foam::fv::cellLimitedGrad limited gradient.  This
    limiter function is similar to Foam::fv::gradientLimiters::Venkatakrishnan
    but is a fit to obey the value and gradient constraints and avoids the
    problem of the limiter exceeding 1 present in the Venkatakrishnan function.
 
    The transition point at which the limiter function reaches 1 is an input
    parameter and should be set to a value between 1 and 2 although values
    larger than 2 are physical but likely to significantly reduce the accuracy
    of the scheme.
 
    Reference:
    \verbatim
        Michalak, K., & Ollivier-Gooch, C. (2008).
        Limiters for unstructured higher-order accurate solutions
        of the Euler equations.
        In 46th AIAA Aerospace Sciences Meeting and Exhibition.
        DOI:10.2514/6.2008-776
    \endverbatim
 
Usage
    Example:
    \verbatim
    gradSchemes
    {
        default Gauss linear;
        limited cellLimited<cubic> 1.5 Gauss linear 1;
    }
    \endverbatim
 
See also
  - Foam::fv::cellLimitedGrad
  - Foam::fv::gradientLimiters::Venkatakrishnan
 
\*---------------------------------------------------------------------------*/
 
#ifndef cubicGradientLimiter_H
#define cubicGradientLimiter_H
 
#include "Istream.H"
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
namespace Foam
{
 
namespace fv
{
 
namespace gradientLimiters
{
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
class cubic
{
    // Private Data
 
        //- Limiter transition point at which the limiter function -> 1
        //  Must be > 1
        const scalar rt_;
 
        //- Coefficient of the r^3 term (evaluated from rt)
        const scalar a_;
 
        // - Coefficient of the r^2 term  (evaluated from rt)
        const scalar b_;
 
 
public:
 
    // Constructors
 
        cubic(Istream& schemeData)
        :
            rt_(readScalar(schemeData)),
            a_((rt_ - 2)/pow3(rt_)),
            b_(-(3*a_*sqr(rt_) + 1)/(2*rt_))
        {
            if (rt_ < 1)
            {
                FatalIOErrorInFunction(schemeData)
                    << "coefficient = " << rt_
                    << " should be > 1"
                    << exit(FatalIOError);
            }
        }
 
 
    // Member Functions
 
        inline scalar limiter(const scalar r) const
        {
            if (r < rt_)
            {
                return ((a_*r + b_)*r + 1)*r;
            }
 
            return 1;
        }
};
 
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
} // End namespace gradientLimiters
 
} // End namespace fv
 
} // End namespace Foam
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
#endif
 
// ************************************************************************* //