PopeIndex.H

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Class
    Foam::resolutionIndexModels::PopeIndex
 
Description
    Computes a single-mesh resolution index according to Pope's index,
    which is used as a LES/DES quality/post-verification metric that does
    not require any experimental or DNS data.
 
    \f[
        \Gamma_{Pope}(\mathbf{x}, t) = \frac{k_{res}}{k_{tot}}
    \f]
 
    with
 
    \f[
        k_{tot} = k_{res} + k_{sgs} + |k_{num}|
    \f]
 
    where
    \vartable
        \Gamma_{Pope}(\mathbf{x}, t) | Pope's index                 [-]
        k_{tot} | Total turbulent kinetic energy                    [m^2/s^2]
        k_{res} | Resolved turbulent kinetic energy                 [m^2/s^2]
        k_{sgs} | Subgrid-scale turbulent kinetic energy            [m^2/s^2]
        k_{num} | Numerical turbulent kinetic energy                [m^2/s^2]
    \endvartable
 
    Inclusion of \f$k_{num}\f$ is optional, and set as \c true by default:
 
    \f[
        k_{num} = C_n \left(\frac{h}{\Delta}\right)^2 k_{sgs}
    \f]
 
    where
    \vartable
        C_n     | Empirical constant                                  [-]
        h       | Characteristic length scale with \f$h = V^{1/3} \f$ [m]
        V       | Cell volume                                         [m^3]
        \Delta  | Filter length scale                                 [m]
    \endvartable
 
    Typical criterion for acceptable-quality resolution:
 
    \f[
        \Gamma_{Pope}(\mathbf{x}) \geq 0.8
    \f]
 
    Required fields:
    \verbatim
      U        | Velocity                                   [m/s]
      UMean    | Mean velocity                              [m/s]
      k        | Subgrid-scale turbulent kinetic energy     [m^2/s^2]
      delta    | Filter length                              [m]
    \endverbatim
 
    References:
    \verbatim
        Governing equation (tag:P):
            Pope, S. B. (2000).
            Turbulent flows.
            Cambridge, UK: Cambridge Univ. Press
            DOI:10.1017/CBO9780511840531
 
        Governing equations for the denominator kNum term (tag:CKJ):
            Celik, I., Klein, M., & Janicka, J. (2009).
            Assessment measures for engineering LES applications.
            Journal of fluids engineering, 131(3).
            DOI:10.1115/1.3059703
    \endverbatim
 
Usage
    Minimal example by using \c system/controlDict.functions:
    \verbatim
    resolutionIndexFO
    {
        // Inherited entries
        ...
        model       PopeIndex;
 
        // Optional entries
        U           <word>;
        UMean       <word>;
        k           <word>;
        delta       <word>;
        includeKnum <bool>;
 
        // Conditional entries
        // when includeKnum = true
        Cn          <scalar>;
    }
    \endverbatim
 
    where the entries mean:
    \table
      Property    | Description                       | Type | Reqd | Deflt
      model       | Model name: PopeIndex             | word | yes  | -
      U           | Name of velocity field            | word | no   | U
      UMean       | Name of mean velocity field       | word | no   | UMean
      k           | Name of subgrid-scale turbulent kinetic energy field <!--
                  -->                                 | word   | no | k
      delta       | Name of filter field              | word   | no | delta
      includeKnum | Flag to include numerical k field | bool   | no | true
      Cn          | Empirical constant                | choice | no | 1.0
    \endtable
 
Note
  - Some studies measured \f$\Gamma_{Pope} > 1\f$ with \f$k_{res}\f$ comparisons
    between a LES and a corresponding filtered DNS. Nonphysical results may
    occur.
 
SourceFiles
    PopeIndex.C
 
\*---------------------------------------------------------------------------*/
 
#ifndef Foam_resolutionIndexModels_PopeIndex_H
#define Foam_resolutionIndexModels_PopeIndex_H
 
#include "resolutionIndexModel.H"
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
namespace Foam
{
namespace resolutionIndexModels
{
 
/*---------------------------------------------------------------------------*\
                          Class PopeIndex Declaration
\*---------------------------------------------------------------------------*/
 
class PopeIndex
:
    public resolutionIndexModel
{
    // Private Data
 
        //- Flag to include numerical turbulent kinetic energy field
        bool includeKnum_;
 
        //- Empirical constant in numerical turbulent kinetic energy estimation
        scalar Cn_;
 
        //- Name of velocity field
        word UName_;
 
        //- Name of mean velocity field
        word UMeanName_;
 
        //- Name of subgrid-scale turbulent kinetic energy field
        word kName_;
 
        //- Name of filter field
        word deltaName_;
 
 
    // Private Member Functions
 
        //- Return numerical turbulent kinetic energy field
        tmp<volScalarField> kNum() const;
 
 
public:
 
    //- Runtime type information
    TypeName("PopeIndex");
 
 
    // Constructors
 
        //- Construct from components
        PopeIndex
        (
            const word& name,
            const fvMesh& mesh,
            const dictionary& dict
        );
 
        //- No copy construct
        PopeIndex(const PopeIndex&) = delete;
 
        //- No copy assignment
        void operator=(const PopeIndex&) = delete;
 
 
    // Destructor
    virtual ~PopeIndex() = default;
 
 
    // Member Functions
 
        //- Read the function-object dictionary
        virtual bool read(const dictionary& dict);
 
        //- Execute the function-object operations
        virtual bool execute();
 
        //- Write the function-object results
        virtual bool write();
};
 
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
} // End namespace resolutionIndexModels
} // End namespace Foam
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
#endif
 
// ************************************************************************* //