[Adam_K]

Hello,

I've been banging my head trying to figure this out and was hoping that someone here could help shed some light on my issue.

My overall goal is the simulate the diffusion across a porous film defined by the interparticle spaces in a spherical compact. I start with a solid matrix, and then subtract a series of spheres, leaving me with a continuous mesh around the sphereical pores. Before subtracting the spheres, the sphere-sphere contact points are "trimmed" in order to avoid the issues associated with meshing the contact points (see this article for more info). Here is an example image, only the sphere-matrix interface is shown for simplicity. The smallest spheres have a radius of 1 cm:



I set-up my case using the files at the end of this post and the solve it using laplacianFoam. After completion I run the command

postProcess -func 'patchIntegrate(name=Bottom,gradTz)' -latestTime |grep 'areaIntegrate(Bottom)'

in order to calculate the integrated flux across the bottom patch (I also do this for the top patch). The flux is then used to calculate the effective diffusivity of the medium.

When I mesh using gmsh and then run the OpenFOAM simulation (files at the end), for a range of mesh critical lengths I get the following results. For smaller mesh lengths, the overall volume of the mesh and the surface area of the top and bottom surfaces start to converge and there isn't much change. However, the integrated flux divided does not converge with the mesh critical length.



Here is my O/T file

/*--------------------------------*- 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;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

dimensions      [0 -3 0 0 1 0 0];

internalField   uniform 0.08;

boundaryField
{
    Top
    {
        type            fixedValue;
        value           uniform 0.16;
    }
    Bottom
    {
        type            fixedValue;
        value           uniform 0;
    }
    Left
    {
        type            zeroGradient;
    }
    Right
    {
        type            zeroGradient;
    }
    Back
    {
        type            zeroGradient;
    }
    Front
    {
        type            zeroGradient;
    }
    Interior
    {
        type            zeroGradient;
    }
}

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

And 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;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

ddtSchemes
{
    default         steadyState;
}

gradSchemes
{
    default         Gauss linear;
    grad(T)         Gauss linear;
}

divSchemes
{
    default         none;
}

laplacianSchemes
{
    default         none;
    laplacian(DT,T) Gauss linear orthogonal;
}

interpolationSchemes
{
    default         linear;
}

snGradSchemes
{
    default         corrected;
}

fluxRequired
{
    default         yes;
    T               ;
}


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

and fvSolution

/*--------------------------------*- 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      fvSolution;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

solvers
{
    T
    {
        preconditioner  FDIC;
		solver          GAMG;
		mergeLevels		1;
		smoother 		GaussSeidel;
		agglomerator	faceAreaPair;
		nCellsInCoarsestLevel	2;
        nPreSweeps 		3;
		nPostSweeps		2;
		nFinestSweeps	2;
        tolerance       1e-10;
        relTol          0;
    }
}

SIMPLE
{
//    nNonOrthogonalCorrectors 2;
	consistent 	yes;	
	 residualControl
    {
        T               1e-9;
    }
}


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

and 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;
    location    "system";
    object      controlDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

application     laplacianFoam;

startFrom       startTime;

startTime       0;

stopAt          endTime;

endTime         10;

deltaT          1;

writeControl    timeStep;

writeInterval   1;

purgeWrite	2;

writeFormat     binary;

writePrecision  32;

writeCompression uncompressed;

timeFormat      general;



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