[sylvester]

For an optimization study I am working with an Ahmed body using adjointShapeOptimizationFoam.

As you can see from the picture 'ahmed_alpha.jpg' the solver works really well near the body, trying to extend the body with an aerodynamic fairing. However near the inlet I am experiencing a strange checkerboarding problem in my adjoint equations, see pictures 'ahmed_pa.jpg' and 'ahmend_Ua.jpg'. All pictures are taken after (only) 100 iterations.After a further several hundred iterations the adjoint flow field fully diverges. The primal flow field is smooth, as expected, see pictures 'ahmed_p.jpg' and 'ahmed_U.jpg'.

The adjoint boundary conditions are taken from the adjointShapeOptimizationFoam tutorial (see below), as are the values for lambda and alphaMax. The fvSolution and fvSchemes settings (see below) are based on the tutorials with lower adjoint relaxations and uncorrected in stead of corrected schemes. Lower values of relTol and relaxation where also tested, but without improvements. CheckMesh reports 'Mesh OK', with no warnings.

Does anyone have suggestions on how best to solve this?

Thanks!

regards,
Sylvester

solvers
{
    "(p|pa)"
    {
        solver          GAMG;
        tolerance       1e-08;
        relTol          0.01;
        smoother        GaussSeidel;
        nPreSweeps      0;
        nPostSweeps     2;
        cacheAgglomeration true;
        nCellsInCoarsestLevel 10;
        agglomerator    faceAreaPair;
        mergeLevels     1;
    }
    "(U|Ua|k|omega)"
    {
        solver          smoothSolver;
        smoother        GaussSeidel;
        nSweeps         2;
        tolerance       1e-08;
        relTol          0.1;
    }
}

SIMPLE
{
    nNonOrthogonalCorrectors 0;
}
relaxationFactors
{
    fields
    {
        p               0.3;
        pa              0.1;
        alpha           0.1;
    }
    equations
    {
        U               0.7;
        Ua              0.1;  
        "(k|omega)"     0.7;
    }

ddtSchemes
{
    default         steadyState;
}

gradSchemes
{
    default         Gauss linear;
}

divSchemes
{
    default         Gauss upwind;
    div((nuEff*dev(T(grad(U))))) Gauss linear;
    div((nuEff*dev(T(grad(Ua))))) Gauss linear;
}

laplacianSchemes
{
    default         Gauss linear uncorrected;
}

interpolationSchemes
{
    default         linear;
}

snGradSchemes
{
    default         uncorrected;
}

fluxRequired
{
    default         no;
    p;
    pa;
}

FoamFile
{
    version     2.0;
    format      ascii;
    class       volScalarField;
    object      p;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

dimensions      [ 0 2 -2 0 0 0 0 ];

internalField   uniform 0;

boundaryField
{
    ".*"
    {
        type            zeroGradient;
    }
    outlet
    {
        type            adjointOutletPressure;
        value           uniform 0;
    }
    symmetry
    {
        type            symmetryPlane;
    }
}

FoamFile
{
    version     2.0;
    format      ascii;
    class       volVectorField;
    object      Ua;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

dimensions      [ 0 1 -1 0 0 0 0 ];

internalField   uniform ( -1 0 0 );

boundaryField
{
    ".*"
    {
        type            fixedValue;
        value           uniform ( 0 0 0 );
    }
    inlet
    {
        type            fixedValue;
        value           uniform ( -1 0 0 );
    }
    outlet
    {
        type            adjointOutletVelocity;
        value           uniform ( 0 0 0 );
    }
    farfield
    {
        type            slip;
    }
    symmetry
    {
        type            symmetryPlane;
    }
}

[sylvester]

Hi!

Using a pseudo staggered approach for the adjoint equations helps, see the images below.

I've modified adjointShapeOptimizationFoam a bit so it uses the pseudo staggered grid approach also used in, for example, buoyantBoussinesqSimpleFoam.

As you can see in the images, this approach removes the checkerboarding near the floor, but it does not completely remove it over the full surface of the inlet. The adjoint equations only diverge at the inlet, the rest of the domain are OK. The second image also shows that the calculation of 'alpha' is unaffected by the pseudo staggering.

Any directions on how to proceed would be much appreciated!

Regards,
Sylvester

[immortality]

hi.how did you solved the problem?can this solver be used for compressible flows?could you introduce me some useful papers or texts about using the method?i want to know how points are changed according to this solver.can it be used with optimization algorithms like ant colony or other ones?thank you.

[sylvester]

Hi,

I haven't been able to work on this, so not much progress has been made. The adjoint solver in OpenFOAM is for incompressible flows only. For compressible flows the adjoint equations also exist, so you should be able to make a compressible version. A Google search will probably provide you with references on this.

regards,
Sylvester

[immortality]

thanks.if send me a suitable to start pdf ill be very thankful to you!
Force.of.love@gmail.com

[C. Okubo]

Hi!

I know its been a while since this post started. Any news? I am facing the same problem. Even though I was able to have some better results by using a limited grad(Ua) and relaxation factors higher for pa than Ua, I would say that something inside the solver needs attention. If you check adjoint velocities at the inlet, they point to an akward direction, this make confuse sensitivities and inlet of the domains happens to have some checkerboard. See this other post:

adjointShapeOptimizationFoam - inlet velocity weird behavior

I still was not able to fix this (if this is something that needs to be fixed).

Regards,

Okubo