Public Member Functions | List of all members
PopeIndex Class Reference

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. More...

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Public Member Functions

 TypeName ("PopeIndex")
 Runtime type information. More...
 
 PopeIndex (const word &name, const fvMesh &mesh, const dictionary &dict)
 Construct from components. More...
 
 PopeIndex (const PopeIndex &)=delete
 No copy construct. More...
 
void operator= (const PopeIndex &)=delete
 No copy assignment. More...
 
virtual ~PopeIndex ()=default
 
virtual bool read (const dictionary &dict)
 Read top-level dictionary. More...
 
virtual bool execute ()
 Calculate the result field. More...
 
virtual bool write ()
 Write the result field. More...
 
- Public Member Functions inherited from resolutionIndexModel
 TypeName ("resolutionIndexModel")
 Runtime type information. More...
 
 declareRunTimeSelectionTable (autoPtr, resolutionIndexModel, dictionary,(const word &name, const fvMesh &mesh, const dictionary &dict),(name, mesh, dict))
 
 resolutionIndexModel (const word &name, const fvMesh &mesh, const dictionary &dict)
 Construct from components. More...
 
 resolutionIndexModel (const resolutionIndexModel &)=delete
 No copy construct. More...
 
void operator= (const resolutionIndexModel &)=delete
 No copy assignment. More...
 
virtual ~resolutionIndexModel ()=default
 Destructor. More...
 
const fvMesh & mesh () const noexcept
 Return const reference to the mesh. More...
 
const word & resultName () const noexcept
 Return const reference to the result name. More...
 

Additional Inherited Members

- Static Public Member Functions inherited from resolutionIndexModel
static autoPtr< resolutionIndexModel > New (const word &name, const fvMesh &mesh, const dictionary &dict)
 Return a reference to the selected resolutionIndex model. More...
 
- Protected Member Functions inherited from resolutionIndexModel
template<class GeoFieldType >
GeoFieldType & getOrReadField (const word &fieldName) const
 Return requested field from the object registry or read+register the field to the object registry. More...
 
tmp< volScalarField > V () const
 Return cell volume field. More...
 

Detailed 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.

\[ \Gamma_{Pope}(\mathbf{x}, t) = \frac{k_{res}}{k_{tot}} \]

with

\[ k_{tot} = k_{res} + k_{sgs} + |k_{num}| \]

where

$ \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]

Inclusion of $k_{num}$ is optional, and set as true by default:

\[ k_{num} = C_n \left(\frac{h}{\Delta}\right)^2 k_{sgs} \]

where

$ C_n $ = Empirical constant [-]
$ h $ = Characteristic length scale with $h = V^{1/3} $ [m]
$ V $ = Cell volume [m^3]
$ \Delta $ = Filter length scale [m]

Typical criterion for acceptable-quality resolution:

\[ \Gamma_{Pope}(\mathbf{x}) \geq 0.8 \]

Required fields: 

      U        | Velocity                                   [m/s]
      UMean    | Mean velocity                              [m/s]
      k        | Subgrid-scale turbulent kinetic energy     [m^2/s^2]
      delta    | Filter length                              [m]

References: 

        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
Usage
Minimal example by using system/controlDict.functions: 
resolutionIndex1
{
    // Inherited entries
    ...
    model       PopeIndex;

    // Optional entries
    U           <word>;
    UMean       <word>;
    k           <word>;
    delta       <word>;
    includeKnum <bool>;

    // Conditional entries
    // when includeKnum = true
    Cn          <scalar>;
}

where the entries mean:

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
Note
  • Some studies measured $\Gamma_{Pope} > 1$ with $k_{res}$ comparisons between a LES and a corresponding filtered DNS. Nonphysical results may occur.
Source files

Definition at line 238 of file PopeIndex.H.

Constructor & Destructor Documentation

◆ PopeIndex() [1/2]

PopeIndex ( const word &  name,
const fvMesh &  mesh,
const dictionary &  dict 
)

Construct from components.

Definition at line 55 of file PopeIndex.C.

References dict, and Foam::read().

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◆ PopeIndex() [2/2]

PopeIndex ( const PopeIndex &  )
delete

No copy construct.

◆ ~PopeIndex()

virtual ~PopeIndex ( )
virtualdefault

Member Function Documentation

◆ TypeName()

TypeName ( "PopeIndex"  )

Runtime type information.

◆ operator=()

void operator= ( const PopeIndex &  )
delete

No copy assignment.

◆ read()

bool read ( const dictionary &  dict)
virtual

Read top-level dictionary.

Reimplemented from resolutionIndexModel.

Definition at line 75 of file PopeIndex.C.

References dict, and resolutionIndexModel::read().

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◆ execute()

bool execute ( )
virtual

Calculate the result field.

Implements resolutionIndexModel.

Definition at line 96 of file PopeIndex.C.

References Foam::mag(), Foam::magSqr(), Foam::max(), tmp< T >::ref(), U, and UMean().

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◆ write()

bool write ( )
virtual

Write the result field.

Implements resolutionIndexModel.

Definition at line 127 of file PopeIndex.C.

References Foam::endl(), Foam::Info, Foam::tab, and Ostream::write().

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The documentation for this class was generated from the following files: