stabilityBlendingFactor

Description

The stabilityBlendingFactor function object computes the stabilityBlendingFactor to be used by the local blended convection scheme. The output is a surface field weight between 0-1.

The weight of a blended scheme, i.e. w, is given by a function of the blending factor, f:

$$w = f_{scheme_1} + (1 - f_{scheme_2})$$

The factor is calculated based on six criteria:

1. mesh non-orthogonality field
2. magnitude of cell centres gradient
3. convergence rate of residuals
4. faceWeight
5. skewness
6. Courant number

The user can enable them individually.

For option 1, the following relation is used, where $\phi_1$ is the non-orthogonality:

$$fNon = min ( max ( 0.0, (\phi_1 - max(\phi_1)) /(min(\phi_1) - max(\phi_1)) ), 1.0 )$$

For option 2, the following relation is used, where $\phi_2$ is the magnitude of cell centres gradient (Note that $\phi_2 = 3$ for orthogonal meshes):

$$fMagGradCc = min ( max ( 0.0, (\phi_2 - max(\phi_2)) / (min(\phi_2) - max(\phi_2)) ), 1.0 )$$

For option 3, a PID control is used in order to control residual unbounded fluctuations for individual cells.

$$factor = P*residual + I*residualIntegral + D*residualDifferential$$

where P, I and D are user inputs.

The following relation is used:

$$fRes = (factor - meanRes)/(maxRes*meanRes);$$

where

$meanRes$ : Average(residual)

$maxRes$ : User input

Note that $f_{Res}$ will blend more towards one as the cell residual is larger then the domain mean residuals.

For option 4, the following relation is used, where $\phi_4$ is the face weight (Note that $\phi_4 = 0.5$ for orthogonal meshes):

$$ffaceWeight = min ( max ( 0.0, (min(\phi_4) - \phi_4) / (min(\phi_4) - max(\phi_4)) ), 1.0 )$$

For option 5, the following relation is used, where $\phi_5$ is the cell skewness:

$$fskewness = min ( max ( 0.0, (\phi_5 - max(\phi_5)) / (min(\phi_5) - max(\phi_5)) ), 1.0 )$$

For option 6, the following relation is used:

$$fCoWeight = min(max((Co - Co1)/(Co2 - Co1), 0), 1)$$

where

Co1 : Courant number below which scheme2 is used

Co2 : Courant number above which scheme1 is used

The final factor is determined by:

$$f = max(fNon, fMagGradCc, fRes, ffaceWeight, fskewness, fCoWeight)$$

An indicator (volume) field, named blendedIndicator is generated if the log flag is on:

1 : represent scheme1 as active,

0 : represent scheme2 as active.

Additional reporting is written to the standard output, providing statistics as to the number of cells used by each scheme.

Operands

Operand	Type	Location
input	-	-
output file	dat	$FOAM_CASE/postProcessing/<FO>/<time>/<file>
output field	volScalarField	$FOAM_CASE/<time>/<outField>

Usage

Example of the stabilityBlendingFactor function object by using functions sub-dictionary in system/controlDict file:

stabilityBlendingFactor1
{
    // Mandatory entries (unmodifiable)
    type                 stabilityBlendingFactor;
    libs                 (fieldFunctionObjects);

    // Mandatory entries (unmodifiable)
    field               <field>;    // U;
    result              <outField>; // UBlendingFactor;

    // Optional entries (runtime modifiable)
    tolerance           0.001;

    // Any of the options can be chosen in combinations

    // Option-1
    switchNonOrtho      true;
    nonOrthogonality    nonOrthoAngle;
    maxNonOrthogonality 20;
    minNonOrthogonality 60;

    // Option-2
    switchGradCc        true;
    maxGradCc           3;
    minGradCc           4;

    // Option-3
    switchResiduals     true;
    maxResidual         10;
    residual            initialResidual:p;
    P                   1.5;
    I                   0;
    D                   0.5;

    // Option-4
    switchFaceWeight    true;
    maxFaceWeight       0.3;
    minFaceWeight       0.2;

    // Option-5
    switchSkewness      true;
    maxSkewness         2;
    minSkewness         3;

    // Option-6
    switchCo            true;
    U                   U;
    Co1                 1;
    Co2                 10;

    // Optional (inherited) entries
    writePrecision      8;
    writeToFile         true;
    useUserTime         true;
    region              region0;
    enabled             true;
    log                 true;
    timeStart           0;
    timeEnd             1000;
    executeControl      timeStep;
    executeInterval     1;
    writeControl        timeStep;
    writeInterval       1;
}

where the entries mean:

Property	Description	Type	Required	Default
type	Type name: stabilityBlendingFactor	word	yes	-
libs	Library name: fieldFunctionObjects	word	yes	-
field	Name of the operand field	word	yes	-
result	Name of surface field used in the localBlended scheme	word	yes	-
switchNonOrtho	Select non-orthogonal method	bool	no	false
nonOrthogonality	Name of the non-orthogonal field	word	no	nonOrthoAngle
maxNonOrthogonality	Maximum non-orthogonal for scheme2	scalar	no	20
minNonOrthogonality	Minimum non-orthogonal for scheme1	scalar	no	60
switchGradCc	Select cell centre gradient method	bool	no	false
maxGradCc	Maximum gradient for scheme2	scalar	no	2
minGradCc	Minimum gradient for scheme1	scalar	no	4
switchResiduals	Select residual evolution method	bool	no	false
residual	Name of the residual field	word	no	initialResidual:p
maxResidual	Maximum residual-mean ratio for scheme1	scalar	no	10
P	Proportional factor for PID	scalar	no	3
I	Integral factor for PID	scalar	no	0
D	Differential factor for PID	scalar	no	0.25
switchFaceWeight	Select face weight method	bool	no	false
faceWeight	Name of the faceWeight field	word	no	faceWeight
maxFaceWeight	Maximum face weight for scheme1	scalar	no	0.2
minFaceWeight	Minimum face weight for scheme2	scalar	no	0.3
switchSkewness	Select skewness method	bool	no	false
skewness	Name of the skewness field	word	no	skewness
maxSkewness	Maximum skewness for scheme2	scalar	no	2
minSkewness	Minimum skewness for scheme1	scalar	no	3
switchCo	Select Co blended method	bool	no	false
U	Name of the flux field for Co blended	word	no	U
Co1	Courant number below which scheme2 is used	scalar	no	1
Co2	Courant number above which scheme1 is used	scalar	no	10
tolerance	Tolerance for number of blended cells	scalar	no	0.001

The result entry is the field which is read by the localBlended scheme specified in fvSchemes. This name is determined by the localBlended class.

The inherited entries are elaborated in:

• functionObject
• fieldExpression
• writeFile

Usage by the postProcess utility is not available.

Further information

Tutorial:

• motorBike

Source code:

• stabilityBlendingFactor

API:

• Foam::functionObjects::stabilityBlendingFactor

History: Introduced in version v1806