[parthiv1991]

Deal All,

I have been trying to simulate the Schäfer and Turek circular cylinder case in OpenFOAM using two custom solvers using higher order Runge-Kutta time integration schemes: 1. DIRK 2. ROSW methods.

So, I have simulated the Steady-state 2D cylinder case (stated as test case 2D-1 in Schäfer and Turek's paper). Inlet U = 0.3 m/s, and Re = 20 (Laminar flow)

I have used two different meshes (as seen below).
The problem is that while computing the force Coefficients, the drag value obtained is within the bounds mentioned in the paper, but the lift coeff value is below the bounds. Essentially, I am getting correct drag coeff. values but incorrect lift coeff. values.
I cannot determine from where the error might generate (due to the mesh, or Aref & Lref values, or the various schemes).

The coarse mesh: No. of cells = 4800, No. of points = 9980
anf the checkMesh for this is as below:

    Overall domain bounding box (0 0 -0.0005) (2.2 0.41 0.0005)
    Mesh has 2 geometric (non-empty/wedge) directions (1 1 0)
    Mesh has 2 solution (non-empty) directions (1 1 0)
    All edges aligned with or perpendicular to non-empty directions.
    Boundary openness (-5.28852e-20 1.11437e-19 -3.76119e-16) OK.
    Max cell openness = 2.11208e-16 OK.
    Max aspect ratio = 4.5 OK.
    Minimum face area = 3.86507e-06. Maximum face area = 0.000495.  Face area magnitudes OK.
    Min volume = 2.50828e-08. Max volume = 4.95e-07.  Total volume = 0.000894154.  Cell volumes OK.
    Mesh non-orthogonality Max: 32.295 average: 6.50871
    Non-orthogonality check OK.
    Face pyramids OK.
    Max skewness = 0.576444 OK.
    Coupled point location match (average 0) OK.

Fine mesh: No. of cells = 22620, No. of points = 46056
and the checkMesh for this shows:

    Overall domain bounding box (0 0 -0.0005) (2.2 0.41 0.0005)
    Mesh has 2 geometric (non-empty/wedge) directions (1 1 0)
    Mesh has 2 solution (non-empty) directions (1 1 0)
    All edges aligned with or perpendicular to non-empty directions.
    Boundary openness (-6.66972e-20 5.66631e-20 5.41013e-15) OK.
    Max cell openness = 2.33164e-16 OK.
    Max aspect ratio = 4.98629 OK.
    Minimum face area = 1.3752e-06. Maximum face area = 9.13442e-05.  Face area magnitudes OK.
    Min volume = 2.16552e-09. Max volume = 9.13442e-08.  Total volume = 0.000894147.  Cell volumes OK.
    Mesh non-orthogonality Max: 33.1296 average: 5.87691
    Non-orthogonality check OK.
    Face pyramids OK.
    Max skewness = 0.853518 OK.
    Coupled point location match (average 0) OK.

Mesh OK.

The fvSolution file looks like this:

/*--------------------------------*- C++ -*----------------------------------*\
| =========                 |                                                 |
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \\    /   O peration     | Version:  4.1                                   |
|   \\  /    A nd           | Web:      www.OpenFOAM.org                      |
|    \\/     M anipulation  |                                                 |
\*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       dictionary;
    location    "system";
    object      fvSolution;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

solvers
{
    p
    {
        solver          PCG;
        preconditioner  DIC;
        tolerance       1e-06;
        relTol          0.05;
    }

    pFinal
    {
        $p;
        relTol          0;
    }
    kihelp
     {
      solver          GAMG;
      smoother        DILU;
      tolerance       1e-06;
     }  


     slope
     {
      solver          PBiCGStab;
      smoother        DILU;
      tolerance       1e-06;
     }


    U
    {
        solver          smoothSolver;
        smoother        symGaussSeidel;
        tolerance       1e-06;
        relTol          0;
    }
}

PISO
{
    nCorrectors     3;
    nNonOrthogonalCorrectors 0;
    pRefCell        0;
    pRefValue       0;
}

And the fvSchemes file:

/*--------------------------------*- C++ -*----------------------------------*\
| =========                 |                                                 |
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \\    /   O peration     | Version:  4.1                                   |
|   \\  /    A nd           | Web:      www.OpenFOAM.org                      |
|    \\/     M anipulation  |                                                 |
\*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       dictionary;
    location    "system";
    object      fvSchemes;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

ddtSchemes
{
    default         Euler;
}

gradSchemes
{
    default         leastSquares;
    grad(p)         leastSquares;
}

divSchemes
{
    default         Gauss linear;
    div(phi,U)      Gauss linearUpwind cellLimited Gauss linear 1;
    div(U)          Gauss linear;
}

laplacianSchemes
{
    default         Gauss linear uncorrected;
}

interpolationSchemes
{
    default         linear;
}

snGradSchemes
{
    default         uncorrected;
}

My forceCoeffs code snippet in controlDict look like this:

  forces
    {
       type    forces;
       functionObjectLibs ("libforces.so");

       patches ( cylinder );
       pName p;
       UName U;

       log   true;
       CofR (0.2 0.2 0);
       rho   rhoInf;
       rhoInf 1;

       outputControl timeStep;
       outputInterval 10;

    } 

    forceCoefficients
    {
       type    forceCoeffs;
       functionObjectLibs ("libforces.so");
       log yes;

       outputControl timeStep;
       outputInterval 10;

       patches ( cylinder );
       pName p;
       UName U;
       rho   rhoInf;
       rhoInf 1;
    //   origin (0 0 0);

     //  porosity   no;

       liftDir (0 -1 0);
       dragDir (1 0 0);
       CofR    (0.2 0.2 0);  // Centre of cylinder
       pitchAxis (0 0 1);

       magUInf 0.2;  // 2*U/3 , where U = 0.3 m/s (inflow velocity)
       rhoInf 1;
       lRef 0.1;  // Dia of cylinder 0.1m
       Aref 0.0001; // (Dia = 0.1) * (z-axis cylinder length = 0.001m)

And I have attached the Lift and Drag Coeff plots below for the two meshes.
Acc. to Schäfer and Turek, the bound for Drag coeff : [5.57, 5.59] and Lift: [0.0104, 0.0110]

Could anyone suggest where the error might come from??
Also I have notices that a finer mesh gives me a lower value of Lift Coeff (which is far lower than the bound, than for a coarse mesh which gives a Lift coeff value a bit closer to the bound).

Any help would be appreciated.

Thank You

[piu58]

I would avoid the sudden changes in mesh density. It is far better to change the mesh gradually. blockMesh gives a good support for that.

[Santiago]

Originally Posted by parthiv1991

Deal All,

I have been trying to simulate the Schäfer and Turek circular cylinder case in OpenFOAM using two custom solvers using higher order Runge-Kutta time integration schemes: 1. DIRK 2. ROSW methods.

So, I have simulated the Steady-state 2D cylinder case (stated as test case 2D-1 in Schäfer and Turek's paper). Inlet U = 0.3 m/s, and Re = 20 (Laminar flow)

I have used two different meshes (as seen below).
The problem is that while computing the force Coefficients, the drag value obtained is within the bounds mentioned in the paper, but the lift coeff value is below the bounds. Essentially, I am getting correct drag coeff. values but incorrect lift coeff. values.
I cannot determine from where the error might generate (due to the mesh, or Aref & Lref values, or the various schemes).

The coarse mesh: No. of cells = 4800, No. of points = 9980
anf the checkMesh for this is as below:

    Overall domain bounding box (0 0 -0.0005) (2.2 0.41 0.0005)
    Mesh has 2 geometric (non-empty/wedge) directions (1 1 0)
    Mesh has 2 solution (non-empty) directions (1 1 0)
    All edges aligned with or perpendicular to non-empty directions.
    Boundary openness (-5.28852e-20 1.11437e-19 -3.76119e-16) OK.
    Max cell openness = 2.11208e-16 OK.
    Max aspect ratio = 4.5 OK.
    Minimum face area = 3.86507e-06. Maximum face area = 0.000495.  Face area magnitudes OK.
    Min volume = 2.50828e-08. Max volume = 4.95e-07.  Total volume = 0.000894154.  Cell volumes OK.
    Mesh non-orthogonality Max: 32.295 average: 6.50871
    Non-orthogonality check OK.
    Face pyramids OK.
    Max skewness = 0.576444 OK.
    Coupled point location match (average 0) OK.

Fine mesh: No. of cells = 22620, No. of points = 46056
and the checkMesh for this shows:

    Overall domain bounding box (0 0 -0.0005) (2.2 0.41 0.0005)
    Mesh has 2 geometric (non-empty/wedge) directions (1 1 0)
    Mesh has 2 solution (non-empty) directions (1 1 0)
    All edges aligned with or perpendicular to non-empty directions.
    Boundary openness (-6.66972e-20 5.66631e-20 5.41013e-15) OK.
    Max cell openness = 2.33164e-16 OK.
    Max aspect ratio = 4.98629 OK.
    Minimum face area = 1.3752e-06. Maximum face area = 9.13442e-05.  Face area magnitudes OK.
    Min volume = 2.16552e-09. Max volume = 9.13442e-08.  Total volume = 0.000894147.  Cell volumes OK.
    Mesh non-orthogonality Max: 33.1296 average: 5.87691
    Non-orthogonality check OK.
    Face pyramids OK.
    Max skewness = 0.853518 OK.
    Coupled point location match (average 0) OK.

Mesh OK.

The fvSolution file looks like this:

/*--------------------------------*- C++ -*----------------------------------*\
| =========                 |                                                 |
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \\    /   O peration     | Version:  4.1                                   |
|   \\  /    A nd           | Web:      www.OpenFOAM.org                      |
|    \\/     M anipulation  |                                                 |
\*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       dictionary;
    location    "system";
    object      fvSolution;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

solvers
{
    p
    {
        solver          PCG;
        preconditioner  DIC;
        tolerance       1e-06;
        relTol          0.05;
    }

    pFinal
    {
        $p;
        relTol          0;
    }
    kihelp
     {
      solver          GAMG;
      smoother        DILU;
      tolerance       1e-06;
     }  


     slope
     {
      solver          PBiCGStab;
      smoother        DILU;
      tolerance       1e-06;
     }


    U
    {
        solver          smoothSolver;
        smoother        symGaussSeidel;
        tolerance       1e-06;
        relTol          0;
    }
}

PISO
{
    nCorrectors     3;
    nNonOrthogonalCorrectors 0;
    pRefCell        0;
    pRefValue       0;
}

And the fvSchemes file:

/*--------------------------------*- C++ -*----------------------------------*\
| =========                 |                                                 |
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \\    /   O peration     | Version:  4.1                                   |
|   \\  /    A nd           | Web:      www.OpenFOAM.org                      |
|    \\/     M anipulation  |                                                 |
\*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       dictionary;
    location    "system";
    object      fvSchemes;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

ddtSchemes
{
    default         Euler;
}

gradSchemes
{
    default         leastSquares;
    grad(p)         leastSquares;
}

divSchemes
{
    default         Gauss linear;
    div(phi,U)      Gauss linearUpwind cellLimited Gauss linear 1;
    div(U)          Gauss linear;
}

laplacianSchemes
{
    default         Gauss linear uncorrected;
}

interpolationSchemes
{
    default         linear;
}

snGradSchemes
{
    default         uncorrected;
}

My forceCoeffs code snippet in controlDict look like this:

  forces
    {
       type    forces;
       functionObjectLibs ("libforces.so");

       patches ( cylinder );
       pName p;
       UName U;

       log   true;
       CofR (0.2 0.2 0);
       rho   rhoInf;
       rhoInf 1;

       outputControl timeStep;
       outputInterval 10;

    } 

    forceCoefficients
    {
       type    forceCoeffs;
       functionObjectLibs ("libforces.so");
       log yes;

       outputControl timeStep;
       outputInterval 10;

       patches ( cylinder );
       pName p;
       UName U;
       rho   rhoInf;
       rhoInf 1;
    //   origin (0 0 0);

     //  porosity   no;

       liftDir (0 -1 0);
       dragDir (1 0 0);
       CofR    (0.2 0.2 0);  // Centre of cylinder
       pitchAxis (0 0 1);

       magUInf 0.2;  // 2*U/3 , where U = 0.3 m/s (inflow velocity)
       rhoInf 1;
       lRef 0.1;  // Dia of cylinder 0.1m
       Aref 0.0001; // (Dia = 0.1) * (z-axis cylinder length = 0.001m)

And I have attached the Lift and Drag Coeff plots below for the two meshes.
Acc. to Schäfer and Turek, the bound for Drag coeff : [5.57, 5.59] and Lift: [0.0104, 0.0110]

Could anyone suggest where the error might come from??
Also I have notices that a finer mesh gives me a lower value of Lift Coeff (which is far lower than the bound, than for a coarse mesh which gives a Lift coeff value a bit closer to the bound).

Any help would be appreciated.

Thank You

I have tested a similar case, that of Muzaferija et al. (1995) with Re=100, using a variant of PISO. I got decent results, within bounds, and a relative error on Cd & Cf of 3% on the Richardsons' extrapolated values when confronted with reference ones. One question: you said you use RK ad time scheme, but I see Euler as your ddt, could it be the problem?

Why you use such a scheme for div(phi,U)? Gauss linear is enough.

What is your maxCo?

Finally, is there any reference on your particular code? Is difficult to know if the algorithm is not clear.

[parthiv1991]

Hello Santiago,

Thank you for your reply.

My max Courant number is 0.181081

Yes I am using a custom RK scheme for time integration which I have put in the code, which is a modified version of icoFoam solver. So my entire time integration is done inside the solver itself. Then should I set the ddt scheme as "none" and run? I will try this once and let you know.

But I think that it would give me an error because for example, the initial guess for the velocity slope "k" I have chosen as ddt(U). Then I guess I should not use this ddt(U) if I have to turn off the ddt schemes in fvSchemes.

But I don't think that the ddtScheme is causing the problem. But I will try your suggestion.

Thank you

[pi06jl6]

Greetings,

I tried Turek's case on OpenFOAM a few years ago. It works fine for FSI1 but not FSI2 and FSI3. I would appreciate for a solution, it doesn't work on for at least OF2.3.X

The problem is the following: Mesh motion solver and the boundary condition, you need to create your own point field distribution and move the whole field of points on the walls that define your 3D case, since you run the case in 2D frozen mode.

This is solved however for extended Foam, using their tetFem mesh motion solver. But I have not adapted my FSI solver to that distribution.

If you need to validate with using 3D mesh, I do recommend to use the 3D pipe problem, used by many, for example, Degroote/IQN-ILS.

I wish you best luck with the problem

/J

PS. I am still curious if there is a solution to this problem. However, it is of minor importance for my work since I have validated my solver on other cases.