[bmercer]

Hi all,

I am trying to run a problem where thermal conductivity is a non-smooth function of temperature, where the non-smoothness results from dealing with a phase change material. I am having trouble getting the temperature equation of the solver to converge under certain conditions and would be curious if anyone has any thoughts as to what may be going wrong.

In my model, the conductivity is a linear function of temperature. For regions yet to be melted, the conductivity is k1(T) = a*T + b. Once a region has been melted, the conductivity becomes k2 = kfactor*k1(T), even if it re-solidifies. kfactor is between 10 and 100 for problems I want to run. This creates regions in the mesh where cells located next to each other can have similar temperatures but have a jump in conductivity between 10x and 100x. When I set kfactor to 1, my case runs smoothly with no convergence issues. If I modify my code to ignore the melted/unmelted distinction and let conductivity k = k2(T), I get the same (good) behavior as when I use kfactor = 1. This leads me to believe that I don’t have a bug in the implementation of the conductivity function and that the non-smooth jump in conductivity between cells may be the culprit.

Below I include my solver setting files, as well as the last few lines of the OpenFoam equation residual output which includes the initial temperature equation blow-up and subsequent simulation crash. I’d be grateful if anyone has any ideas on how to resolve the issue of the temperature equation blowing up for kfactor > 10. I’m hopeful that tweaking some solver settings could iron out the convergence issues – I’ve made some blind attempts so far, but no luck. Any thoughts are appreciated! Thank you!

fvSchemes:

/*--------------------------------*- C++ -*----------------------------------*\
| =========                 |                                                 |
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \\    /   O peration     | Version:  3.0.0                                 |
|   \\  /    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         Gauss linear;
}

divSchemes
{
    default         Gauss upwind;
    div(phi,U)      Gauss upwind;
    div((phi*interpolate(cp)),T) Gauss upwind;
}

laplacianSchemes
{
    default                   none; //Gauss linear corrected; 
    laplacian((lambda|rho),T) Gauss linear uncorrected; //corrected 
    laplacian(nu,U)           Gauss linear uncorrected; // corrected
    laplacian((1|A(U)),p_rgh)     Gauss linear uncorrected; // corrected
}

interpolationSchemes
{
    default         linear;
}

snGradSchemes
{
    default         uncorrected; //corrected;
}

fluxRequired
{
  default no;
  p_rgh;
}


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

fvSolution:

/*--------------------------------*- C++ -*----------------------------------*\
| =========                 |                                                 |
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \\    /   O peration     | Version:  3.0.0                                 |
|   \\  /    A nd           | Web:      www.OpenFOAM.org                      |
|    \\/     M anipulation  |                                                 |
\*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       dictionary;
    location    "system";
    object      fvSolution;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

solvers
{

    p_rgh
    {
        solver          GAMG;
        smoother        GaussSeidel;
        tolerance       1e-8;
        relTol          0.01;
    }

    p_rghFinal
    {
        $p_rgh;
        relTol          0;
    }

    T
    {
        solver          PBiCG;
        preconditioner   DILU;
        tolerance        1e-7;
        relTol            0.1;
    }

    TFinal
    {
        solver          PBiCG;
        preconditioner   DILU;
        tolerance        1e-9;
        relTol              0;
    }

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

    UFinal
    {
        $U;
        relTol          0;
    }
}

PIMPLE
{
    momentumPredictor yes; //yes;
    nOuterCorrectors 1; //1;
    nCorrectors     1;
    nNonOrthogonalCorrectors 0;
    pRefCell 0;
    pRefValue 0;
}


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

OpenFoam solver output:

...
...
...
Courant Number mean: 0.0006917597 max: 0.27723292
deltaT = 9.9667774e-07
PIMPLE: iteration 1
DILUPBiCG:  Solving for Ux, Initial residual = 0.0047223043, Final residual = 2.1859185e-07, No Iterations 2
DILUPBiCG:  Solving for Uy, Initial residual = 0.0048172404, Final residual = 2.3390652e-07, No Iterations 2
DILUPBiCG:  Solving for Uz, Initial residual = 0.0041326105, Final residual = 1.7710191e-09, No Iterations 3
DILUPBiCG:  Solving for T, Initial residual = 0.00060871525, Final residual = 9.7934538e-10, No Iterations 4
GAMG:  Solving for p_rgh, Initial residual = 0.067143822, Final residual = 8.550094e-09, No Iterations 13
time step continuity errors : sum local = 3.4964727e-13, global = 9.497921e-14, cumulative = 4.9549033e-11
ExecutionTime = 284.84 s  ClockTime = 287 s

Time = 0.000703654485

Interpolating laser coordinate
Interpolating laser coordinate
Vx   = 100
Vy   = 0
Vmag = 100

Courant Number mean: 0.00069140376 max: 0.27616178
deltaT = 9.9667774e-07
PIMPLE: iteration 1
DILUPBiCG:  Solving for Ux, Initial residual = 0.0043974518, Final residual = 4.3794962e-07, No Iterations 2
DILUPBiCG:  Solving for Uy, Initial residual = 0.0044430772, Final residual = 3.5340057e-07, No Iterations 2
DILUPBiCG:  Solving for Uz, Initial residual = 0.0047550922, Final residual = 1.9589747e-09, No Iterations 3
DILUPBiCG:  Solving for T, Initial residual = 0.00061698156, Final residual = 93345.397, No Iterations 1001
GAMG:  Solving for p_rgh, Initial residual = 0.99749556, Final residual = 6.74928e-09, No Iterations 21
time step continuity errors : sum local = 5.4155474e-11, global = 6.3819725e-14, cumulative = 4.9612853e-11
ExecutionTime = 291.17 s  ClockTime = 293 s

Time = 0.0007046511628

Interpolating laser coordinate
Interpolating laser coordinate
Vx   = 100
Vy   = 0
Vmag = 100

Courant Number mean: 0.00073293333 max: 2.4614658
deltaT = 4.0444894e-07
PIMPLE: iteration 1
DILUPBiCG:  Solving for Ux, Initial residual = 0.99996533, Final residual = 4.1997867e-08, No Iterations 3
DILUPBiCG:  Solving for Uy, Initial residual = 0.99996593, Final residual = 7.471817e-07, No Iterations 3
DILUPBiCG:  Solving for Uz, Initial residual = 0.84149551, Final residual = 4.3093462e-09, No Iterations 3
DILUPBiCG:  Solving for T, Initial residual = 1, Final residual = 5.326721e-10, No Iterations 11
GAMG:  Solving for p_rgh, Initial residual = 1, Final residual = 8.2242381e-09, No Iterations 41
time step continuity errors : sum local = 3187537.2, global = -3187537.1, cumulative = -3187537.1
ExecutionTime = 291.84 s  ClockTime = 294 s

Time = 0.0007050556117

Interpolating laser coordinate
Interpolating laser coordinate
Vx   = 100
Vy   = 0
Vmag = 100

Courant Number mean: 5.0625884e+08 max: 2.3247589e+12
deltaT = 1.7397457e-19
PIMPLE: iteration 1
DILUPBiCG:  Solving for Ux, Initial residual = 0.002170343, Final residual = 1.3269969e-08, No Iterations 2
DILUPBiCG:  Solving for Uy, Initial residual = 0.004592665, Final residual = 2.2649814e-07, No Iterations 2
DILUPBiCG:  Solving for Uz, Initial residual = 0.011799993, Final residual = 4.0934735e-10, No Iterations 3
DILUPBiCG:  Solving for T, Initial residual = 1, Final residual = 4.219571e-10, No Iterations 4
GAMG:  Solving for p_rgh, Initial residual = 1, Final residual = 6.0997958e-09, No Iterations 28
time step continuity errors : sum local = 2.5050765e+21, global = -2.5050765e+21, cumulative = -2.5050765e+21
ExecutionTime = 292.35 s  ClockTime = 294 s

Time = 0.0007050556117

Interpolating laser coordinate
Interpolating laser coordinate
Vx   = 79.769059
Vy   = 0
Vmag = 79.769059

Courant Number mean: 4.0417955e+23 max: 1.9357799e+27
deltaT = 8.9873118e-47
PIMPLE: iteration 1
DILUPBiCG:  Solving for Ux, Initial residual = 0.00087760067, Final residual = 5.1400685e-08, No Iterations 2
DILUPBiCG:  Solving for Uy, Initial residual = 0.0011133698, Final residual = 9.93714e-09, No Iterations 2
DILUPBiCG:  Solving for Uz, Initial residual = 0.013898725, Final residual = 2.1458128e-08, No Iterations 3
[5] #0  [9] [4] #0  Foam::error::printStack(Foam::Ostream&)[8] #0  Foam::error::printStack(Foam::Ostream&)Foam::error::printStack(Foam::Ostream&)#0  Foam::error::printStack(Foam::Ostream&)--------------------------------------------------------------------------
An MPI process has executed an operation involving a call to the
"fork()" system call to create a child process.  Open MPI is currently
operating in a condition that could result in memory corruption or
other system errors; your MPI job may hang, crash, or produce silent
data corruption.  The use of fork() (or system() or other calls that
create child processes) is strongly discouraged.  
...
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