[a_bassolillo]

Dear all,

I am writing to ask for help in a problem I am facing regarding the inviscid transonic simulation of the flow around a RAE2822.
I am here attaching the files that could be useful to understand what I'm talking about. Since the solution of each time step is explicit, convergence cannot be assessed looking at the residuals, since their values is always equal to zero.

Since I am studying the steady 2D behaviour of an airfoil I would like to stop the simulation when the drag coefficient arrives at steady state, but this condition seems to be impossible to reach, I have tried to set a total pressure inlet bc to improve stability, but while the flowfield obtained (after a quite low number of iterations) seems reasonable with the shock in the correct position (given by NASA literature), the aerodynamic coefficient values calculated by rhoCentralFoam show a significant oscillation. This oscillation does not allow me to consider this solution at convergence. Even increasing a lot the number of iterations, this problem remains unsolved.

As mesh I am using a structured C-grid, produced with the curiosityfluids tool. I tried several combination of the values, ranging from 30.000 to 120.000 elements.

I am now attaching the files describing my configuration.
CONTROLDICT

/*--------------------------------*- C++ -*----------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     | Website:  https://openfoam.org
    \\  /    A nd           | Version:  8
     \\/     M anipulation  |
\*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       dictionary;
    object      controlDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

application     rhoCentralFoam;

startFrom       latestTime;

startTime       0;

stopAt          endTime;

endTime         0.1;

deltaT          3e-6;

writeControl    adjustableRunTime;

writeInterval   0.005;

purgeWrite      0;

writeFormat     ascii;

writePrecision   8;

writeCompression off;

timeFormat      general;

timePrecision   6;

runTimeModifiable true;

functions
{
    #includeFunc MachNo
    #includeFunc residuals
    forces
    {
        type            forceCoeffs;
        libs            ("libforces.so");
        writeControl   timeStep;
        writeControl   timeStep;
        writeInterval  1;


        pName       p;
        UName       U;
        log         true;
        patches
        (
            airfoil
        );

        rhoInf      0.5966;

        CofR        (0 0 0);
        liftDir     (-0.0403 0.9992 0);
        dragDir     (0.9992 0.0403 0);
        pitchAxis   (0 0 1);
        magUInf     233.6216;
        lRef        1;
        Aref        1;
    }
}

FVSCHEMES

/*--------------------------------*- C++ -*----------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     | Website:  https://openfoam.org
    \\  /    A nd           | Version:  8
     \\/     M anipulation  |
\*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       dictionary;
    location    "system";
    object      fvSchemes;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

fluxScheme      Kurganov;

ddtSchemes
{
    default         CrankNicolson 0;
}

gradSchemes
{
    default         cellLimited Gauss linear 1;
    grad(U)         cellLimited Gauss linear 1;
}

divSchemes
{
    default        				 none;
    div(tauMC)      			Gauss linearUpwind;
    div(phi,U)		 	Gauss linearUpwindV grad(U);
    div(phi,omega) 		Gauss linearUpwind default;
    div(phi,k) 			Gauss linearUpwind default;
    div((nuEff*dev(T(grad(U)))))	 Gauss linear;
}

laplacianSchemes
{
    default         Gauss linear limited 1;
}

interpolationSchemes
{
    default         linear;
    reconstruct(rho) vanLeer;
    reconstruct(U)  vanLeerV;
    reconstruct(T)  vanLeer;
}

snGradSchemes
{
    default         limited 1;
}


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

FVSOLUTION

/*--------------------------------*- C++ -*----------------------------------*\
| =========                 |                                                 |
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \\    /   O peration     | Version:  2.2.2                                 |
|   \\  /    A nd           | Web:      www.OpenFOAM.org                      |
|    \\/     M anipulation  |                                                 |
\*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       dictionary;
    location    "system";
    object      fvSolution;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

solvers
{
    "(rho|rhoU|rhoE)"
    {
        solver          diagonal;
    }

    U
    {
        solver          smoothSolver;
        smoother        GaussSeidel;
        nSweeps         2;
        tolerance       1e-09;
        relTol          0.01;
    }

    h
    {
        $U;
        tolerance       1e-10;
        relTol          0;
    }
}


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

Folder 0/

U

/*--------------------------------*- C++ -*----------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     | Website:  https://openfoam.org
    \\  /    A nd           | Version:  8
     \\/     M anipulation  |
\*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       volVectorField;
    object      U;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

Uinlet          (233.4317 9.4164  0);

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

internalField   uniform $Uinlet;

boundaryField
{
    farfield
    {
        type            freestreamVelocity;
        freestreamValue uniform $Uinlet;
        value           uniform $Uinlet;
    }
    airfoil
    {
        type            slip;
    }

    frontAndBack
    {
        type            empty;
    }
    #includeEtc "caseDicts/setConstraintTypes"
}

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

0/p

/*--------------------------------*- C++ -*----------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     | Website:  https://openfoam.org
    \\  /    A nd           | Version:  8
     \\/     M anipulation  |
\*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       volScalarField;
    object      p;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

pOut            43765;

dimensions      [1 -1 -2 0 0 0 0];

internalField   uniform $pOut;

boundaryField
{
    farfield
    {
        type            fixedValue;
	value		uniform  43765;
    }

    airfoil
    {
        type            zeroGradient;
    }
    
    frontAndBack
    {
    	type 		empty;
    }

    #includeEtc "caseDicts/setConstraintTypes"
}

// ************************************************************************* //[

0/T

/*--------------------------------*- C++ -*----------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     | Website:  https://openfoam.org
    \\  /    A nd           | Version:  8
     \\/     M anipulation  |
\*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       volScalarField;
    object      T;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

Tinlet          255.6;

dimensions      [0 0 0 1 0 0 0];

internalField   uniform $Tinlet;

boundaryField
{
    farfield
    {
        type            inletOutlet;
        inletValue      uniform $Tinlet;
        value           $inletValue;
    }
    
    airfoil
    {
        type            zeroGradient;
    }
    
    frontAndBack
    {
    	type		empty;
    }

    #includeEtc "caseDicts/setConstraintTypes"
}

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

0/Ma

/*--------------------------------*- C++ -*----------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     | Website:  https://openfoam.org
    \\  /    A nd           | Version:  8
     \\/     M anipulation  |
\*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       volScalarField;
    location    "0";
    object      Ma;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

dimensions      [0 0 0 0 0 0 0];

internalField   uniform 0.72783363;

boundaryField
{
    frontAndBack
    {
        type            empty;
    }
    farfield
    {
        type            calculated;
        value           uniform 0.72783363;
    }
    airfoil
    {
        type            calculated;
        value           nonuniform List<scalar> 
279
(
0.72740526
0.72752391
0.72761278
0.72766195
0.72771781
0.72775799
0.72778947
0.72781218
0.72782649
0.72783318
0.727832
0.72782342
0.72780736
0.7277846
0.72775494
0.72771814
0.72767549
0.72762621
0.72757024
0.72750946
0.72744064
0.72736365
0.72728327
0.72719184
0.72708834
0.72698236
0.72686371
0.72672977
0.72659307
0.7264429
0.72627441
0.7261006
0.72591512
0.72571171
0.72549896
0.72527643
0.72503863
0.72478542
0.72452486
0.72426033
0.72398111
0.72368902
0.72341188
0.7231371
0.72283693
0.72255611
0.7222897
0.72199419
0.72171452
0.72145535
0.72117104
0.72089257
0.72063089
0.7203475
0.72006694
0.71980525
0.71952567
0.71924316
0.71897711
0.71869341
0.71840618
0.71813767
0.71784821
0.71755899
0.71729721
0.71701509
0.71673143
0.71646763
0.71617573
0.71589664
0.71564041
0.71535298
0.71508676
0.71482636
0.71454156
0.714296
0.71403375
0.71376988
0.71352645
0.71325387
0.71300002
0.71272193
0.71245187
0.71219092
0.7119048
0.71162631
0.71131884
0.71103845
0.71072331
0.71041534
0.71007744
0.70974872
0.70940547
0.70904403
0.70864046
0.70820874
0.70774286
0.7072251
0.70662257
0.705761
0.23565479
0.4942156
0.59826104
0.64457367
0.66900423
0.68348314
0.69293235
0.69935912
0.70393791
0.7074516
0.71018572
0.71241376
0.71427102
0.71582701
0.71716696
0.71831201
0.71932129
0.72019588
0.72098398
0.72167496
0.72230022
0.72285529
0.72335789
0.72381848
0.72422938
0.72461596
0.72496114
0.72528173
0.72557749
0.7258414
0.72608386
0.72630135
0.7265018
0.72668429
0.7268477
0.7270059
0.72716456
0.72723694
0.72742998
0.17965274
0.44770176
0.55902032
0.61050174
0.63884281
0.65675539
0.66914382
0.67801468
0.68470207
0.69000323
0.69425982
0.69775999
0.70066501
0.70312516
0.70522971
0.70705389
0.70864756
0.71005481
0.71130708
0.71242375
0.71345661
0.71439189
0.71525418
0.7160654
0.71680183
0.71749099
0.71812299
0.71872075
0.71928069
0.71980124
0.7203073
0.72077423
0.72122663
0.72165914
0.72206146
0.72247329
0.72290992
0.72312281
0.72375472
0.72365608
0.72410646
0.72447562
0.72473033
0.72508004
0.72536245
0.7256733
0.72597073
0.72623476
0.72652519
0.72678023
0.72700686
0.72722766
0.72740724
0.72755624
0.72767969
0.72776523
0.72781595
0.72783362
0.72781788
0.72777134
0.7276973
0.72759238
0.72746584
0.72732627
0.72715831
0.72697731
0.72680135
0.7266035
0.72639446
0.72620772
0.72601521
0.72580284
0.72562499
0.72546319
0.725272
0.72511216
0.72497933
0.72481751
0.72468072
0.72457855
0.72445537
0.72434442
0.72426746
0.7241828
0.72409759
0.72404448
0.72399821
0.72393978
0.72391195
0.72390091
0.72387218
0.72387216
0.7238973
0.72390438
0.72393337
0.72398945
0.72403139
0.72408946
0.72417457
0.72424969
0.7243369
0.7244502
0.72455827
0.72467333
0.72480785
0.72494188
0.7250769
0.72521856
0.7253607
0.72550376
0.72564868
0.72579381
0.72594189
0.72609275
0.72624339
0.72639486
0.72654755
0.72669867
0.7268476
0.72699514
0.72713385
0.72726886
0.72739564
0.72751237
0.72761772
0.72770341
0.72777294
0.72781638
0.72783362
0.72781857
0.72776454
0.72766862
0.72751844
0.72729805
0.72701829
0.7266616
0.72623408
0.72574904
0.72520315
0.72461104
)
;
    }
}


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

Please feel free to ask for more information if you need them, as I am quite desperate

[janibo]

Hi,

maybe try to limit your max. courant number in conrolDict and
set maxCo to 0.1.

[a_bassolillo]

It is working quite fine, there still are a little bit of oscillations but I think I can accept those, thank you very much. May I ask why you suggested this solution? As far as I now, for explicit calculations the courant number should stay below one.

Thanks a lot again

[janibo]

Hi aniello,

I'm glad it worked.
Generally speaking you are right.
But rhoCentralFoam seems to be an exception.
rhoCentralFoam or better speaking the central schemes used
have their stability limit at 0.5 or rather 0.2 and below,
as it is stated in the paper "Implementation of semi-discrete, non-staggered central schemes
in a colocated, polyhedral, finite volume framework, for highspeed viscous flows" by Greenshields et al.

In order to get rid of the remaining oscillation, you could further decrease the courant number, if you can spare the time.

[a_bassolillo]

Thank you very much for the explanation. I was going crazy trying to fix this.

Have a nice day and see you again on this forum!