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VenkatakrishnanGradientLimiter.H
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23 
24 Class
25  Foam::fv::gradientLimiters::Venkatakrishnan
26 
27 Description
28  Venkatakrishnan gradient limiter
29 
30  to be used with the Foam::fv::cellLimitedGrad limited gradient.
31 
32  Reference:
33  \verbatim
34  Venkatakrishnan, V. (1993).
35  On the accuracy of limiters and convergence to steady state solutions.
36  In 31st Aerospace Sciences Meeting (p. 880).
37  \endverbatim
38 
39  Example:
40  \verbatim
41  gradSchemes
42  {
43  default Gauss linear;
44  limited cellLimited<Venkatakrishnan> Gauss linear 1;
45  }
46  \endverbatim
47 
48  Note: this limiter formally allows the limiter function to slightly exceed 1
49  which is generally not a good idea and can cause unboundedness. To avoid
50  this problem the limiter function is clipped to 1 which is likely to be
51  better behaved but is then not differentiable and so no longer conforms to
52  the basic principles of this kind of limiter function. All these issues are
53  resolved in a consistent and differentiable manner by the
54  Foam::fv::gradientLimiters::cubic limiter which is recommended in
55  preference to the Foam::fv::gradientLimiters::Venkatakrishnan limiter.
56 
57 See also
58  Foam::fv::cellLimitedGrad
59  Foam::fv::gradientLimiters::cubic
60 
61 \*---------------------------------------------------------------------------*/
62 
63 #ifndef VenkatakrishnanGradientLimiter_H
64 #define VenkatakrishnanGradientLimiter_H
65 
66 #include "Istream.H"
67 
68 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
69 
70 namespace Foam
71 {
72 
73 namespace fv
74 {
75 
76 namespace gradientLimiters
77 {
78 
79 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
80 
81 class Venkatakrishnan
82 {
83 
84 public:
85 
86  // Constructors
87 
89  {}
90 
91 
92  // Member Functions
93 
94  inline scalar limiter(const scalar r) const
95  {
96  return (sqr(r) + 2*r)/(sqr(r) + r + 2);
97  }
98 };
99 
100 
101 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
102 
103 } // End namespace gradientLimiters
104 
105 } // End namespace fv
106 
107 } // End namespace Foam
108 
109 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
110 
111 #endif
112 
113 // ************************************************************************* //
dimensionedSymmTensor sqr(const dimensionedVector &dv)
An Istream is an abstract base class for all input systems (streams, files, token lists etc)...
Definition: Istream.H:57
labelList fv(nPoints)
Namespace for OpenFOAM.