## 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

// 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
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:

Usage by the postProcess utility is not available.

## Further information🔗

Tutorial:

Source code:

API:

History:

• Introduced in version v1806