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...

#include <PopeIndex.H>

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

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.
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.
tmp< volScalarField >	V () const
	Return cell volume field.

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

	=	Empirical constant [-]
	=	Characteristic length scale with $h = V^{1/3}$ [m]
	=	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:

resolutionIndexFO
{
    // 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 54 of file PopeIndex.C.

References dict, resolutionIndexModel::mesh(), Foam::name(), read(), and resolutionIndexModel::resolutionIndexModel().

Referenced by operator=(), and PopeIndex().

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◆ PopeIndex() [2/2]

PopeIndex ( const PopeIndex & )

delete

No copy construct.

References PopeIndex().

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◆ ~PopeIndex()

virtual ~PopeIndex ( )

virtualdefault

References dict.

Member Function Documentation

◆ TypeName()

TypeName ( "PopeIndex" )

Runtime type information.

References dict, resolutionIndexModel::mesh(), and Foam::name().

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◆ operator=()

void operator= ( const PopeIndex & )

delete

No copy assignment.

References PopeIndex().

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◆ read()

bool read ( const dictionary & dict )

virtual

Read the function-object dictionary.

Reimplemented from resolutionIndexModel.

Definition at line 75 of file PopeIndex.C.

References dict, and resolutionIndexModel::read().

Referenced by PopeIndex().

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◆ execute()

bool execute ( )

virtual

Execute the function-object operations.

Implements resolutionIndexModel.

Definition at line 96 of file PopeIndex.C.

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

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◆ write()

bool write ( )

virtual

Write the function-object results.

Implements resolutionIndexModel.

Definition at line 127 of file PopeIndex.C.

References Foam::endl(), resolutionIndexModel::getOrReadField(), Foam::Info, resolutionIndexModel::resultName(), and Foam::tab.

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

src/functionObjects/field/resolutionIndex/resolutionIndexModels/PopeIndex/PopeIndex.H
src/functionObjects/field/resolutionIndex/resolutionIndexModels/PopeIndex/PopeIndex.C

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ PopeIndex() [1/2]

◆ PopeIndex() [2/2]

◆ ~PopeIndex()

Member Function Documentation

◆ TypeName()

◆ operator=()

◆ read()

◆ execute()

◆ write()