VenkatakrishnanGradientLimiter.H

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License
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Class
    Foam::fv::gradientLimiters::Venkatakrishnan
 
Description
    Venkatakrishnan gradient limiter
 
    to be used with the Foam::fv::cellLimitedGrad limited gradient.
 
    Reference:
    \verbatim
        Venkatakrishnan, V. (1993).
        On the accuracy of limiters and convergence to steady state solutions.
        In 31st Aerospace Sciences Meeting (p. 880).
    \endverbatim
 
    Example:
    \verbatim
    gradSchemes
    {
        default Gauss linear;
        limited cellLimited<Venkatakrishnan> Gauss linear 1;
    }
    \endverbatim
 
    Note: this limiter formally allows the limiter function to slightly exceed 1
    which is generally not a good idea and can cause unboundedness.  To avoid
    this problem the limiter function is clipped to 1 which is likely to be
    better behaved but is then not differentiable and so no longer conforms to
    the basic principles of this kind of limiter function.  All these issues are
    resolved in a consistent and differentiable manner by the
    Foam::fv::gradientLimiters::cubic limiter which is recommended in
    preference to the Foam::fv::gradientLimiters::Venkatakrishnan limiter.
 
See also
    Foam::fv::cellLimitedGrad
    Foam::fv::gradientLimiters::cubic
 
\*---------------------------------------------------------------------------*/
 
#ifndef VenkatakrishnanGradientLimiter_H
#define VenkatakrishnanGradientLimiter_H
 
#include "Istream.H"
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
namespace Foam
{
 
namespace fv
{
 
namespace gradientLimiters
{
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
class Venkatakrishnan
{
 
public:
 
    // Constructors
 
        Venkatakrishnan(Istream&)
        {}
 
 
    // Member Functions
 
        inline scalar limiter(const scalar r) const
        {
            return (sqr(r) + 2*r)/(sqr(r) + r + 2);
        }
};
 
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
} // End namespace gradientLimiters
 
} // End namespace fv
 
} // End namespace Foam
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
#endif
 
// ************************************************************************* //