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Velocity gradient that looks like checkerboard

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Old   September 26, 2015, 12:57
Default Velocity gradient that looks like checkerboard
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J.-H. Wang
Join Date: Oct 2010
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I am solving an acoustic problem arises from turbulence. For that I am using pimpleFoam + Spalart-Allmaras DES (OpenFOAM 2.4.0 on RHEL) as suggested by some people when grid resolution is not high enough. I am particularly concerned with the velocity gradient as it will act as a quadrupole source term when acoustic analogy is used.

For the current setup, I have two problems:

1. I couldn't seem to get rid of the "checkerboard" velocity gradient despite the relatively smooth velocity field. Quotation because I don't think they are as bad as the real checkerboard issue. Pictures are attached.

2. There seems to be some artifacts when transitioning from coarser grid to denser grid near the region of interest.

Currently I suspected its the convergence issue, but it could also be the gradient scheme I chose to compute the gradient (cell limited gauss linear 0.8)? I posted my fvSolution/fvScheme and hopefully someone with some experience could point out some obvious errors. Any help is appreciated. Thanks.


fvScheme:
Code:
/*--------------------------------*- C++ -*----------------------------------*\
| =========                 |                                                 |
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \\    /   O peration     | Version:  2.1.1                                 |
|   \\  /    A nd           | Web:      www.OpenFOAM.org                      |
|    \\/     M anipulation  |                                                 |
\*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       dictionary;
    object      fvSchemes;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

ddtSchemes
{
    default         backward;
}

gradSchemes
{
    default         Gauss linear;

    grad(nuTilda)   cellLimited Gauss linear 0.8;
    grad(U)         cellLimited Gauss linear 0.8;
}

divSchemes
{
    default         Gauss linear;

    div(phi,U)      Gauss LUST unlimitedGrad(U);//Gauss limitedLinear 1
    //div(phi,U)      Gauss linearUpwind unlimitedGrad(U);
    div(phi,k)      Gauss limitedLinear 1;
    div(phi,B)      Gauss limitedLinear 1;
    div(phi,nuTilda) Gauss limitedLinear 1;
    div(B)          Gauss linear;
    div((nuEff*dev(T(grad(U))))) Gauss linear;
    //default         none;
    //div(phi,U)      Gauss linearUpwindV grad(U);
    //div(phi,k)      Gauss upwind;
    //div(phi,omega)  Gauss upwind;
    //div((nuEff*dev(T(grad(U))))) Gauss linear;
}

laplacianSchemes
{
    default         Gauss linear corrected;
}

interpolationSchemes
{
    default         linear;
    interpolate(U)  linear;
}

snGradSchemes
{
    default         corrected;
}

fluxRequired
{
    default         no;
    p;
}

// ************************************************************************* //

fvSolution:
Code:
/*--------------------------------*- C++ -*----------------------------------*\
| =========                 |                                                 |
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \\    /   O peration     | Version:  2.1.1                                 |
|   \\  /    A nd           | Web:      www.OpenFOAM.org                      |
|    \\/     M anipulation  |                                                 |
\*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       dictionary;
    object      fvSolution;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

solvers
{
    p
    {
       solver PCG;
       preconditioner DIC;
       tolerance 1e-6;
       relTol 0.01;
    }

    pFinal
    {
       solver PCG;
       preconditioner DIC;
       tolerance 1e-8;
       relTol 0;
    }

    U
    {
      solver PBiCG;
      preconditioner DILU;
      tolerance 1e-6;
      relTol 0.1;
    }

    B
    {
      solver PBiCG;
      preconditioner DILU;
      tolerance 1e-6;
      relTol 0.1;
    }

    "(U|k|epsilon|omega|nuTilda)Final"
    {
      solver PBiCG;
      preconditioner DILU;
      tolerance 1e-8;
      relTol 0;
    }
}

PIMPLE
{
    nOuterCorrectors 2; // 1 leads to a piso algorithm
    nCorrectors     3;
    nNonOrthogonalCorrectors 2;
    pRefCell        0;
    pRefValue       0;
}

// ************************************************************************* //
Attached Images
File Type: jpg Ug_grid.jpg (150.6 KB, 23 views)
Attached Files
File Type: pdf Ug.pdf (77.7 KB, 7 views)
File Type: pdf U.pdf (58.4 KB, 7 views)
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