[Ghukka]

Hello fellow Foamers,

I'm currently working on a simulation involving passive transport of particles inside a mesh representing the left atrium. I'm using OpenFOAM version 11 with its new modular architecture. I've successfully compiled a custom module for the foamRun application with the appropriate equations, and it has been tested on a simpler 2D case with satisfactory results.

However, I am facing challenges in setting up a pseudo-parabolic velocity profile at the inlets. The inlets have oval-shaped cross-sections, but they are not perfectly regular. My goal is to create a normalized pseudo-parabolic scalar distribution by solving a Poisson problem of the form -Δ𝑍 = 1, where 𝑍=0 at the boundary. I would then multiply this distribution by a maximum velocity value (obtained experimentally and retrieved from an external file) to approximate a parabolic velocity profile similar to that in a circular tube.

I've tried initializing the velocity field U at the inlet using the codedFixedValue boundary condition. My idea was to create an auxiliary field 𝑍, and another auxiliary field representing the source term (constant at −1). I would then solve the Poisson problem using these fields since fvm::laplacian(Z) requires a volScalarField. The resulting values of Z, when multiplied by Umax, would give the correct initial values for U.

However I don't know how to proceed. I'm not even sure this path is viable since I don't know how to set initial conditions for solving the Poisson problem in the first place. I tried solving the equation anyway, since maybe it could have thrown any meaningful error

boundaryField
{
    ...
    ...
    inlet
    {
        type    codedFixedValue;
        value   uniform (0 0 0);
        name   codedStuff;
        code
        #{
            ....
            ....
            volScalarField Z 
            ( 
                IOobject 
                ( 
                    "Z", 
                    runTime.name(), 
                    mesh, 
                    IOobject::NO_READ, 
                    IOobject::AUTO_WRITE 
                ), 
                mesh, 
                dimensionedScalar("zero", dimensionSet(0, 2, 0, 0, 0, 0, 0), 0.0),             "fixedValue" 
            ); 
			 
            volScalarField sourceTerm 
            ( 
                IOobject 
                ( 
                    "sourceTerm", 
                    runTime.name(), 
                    mesh, 
                    IOobject::NO_READ, 
                    IOobject::AUTO_WRITE 
                ), 
                mesh, 
                dimensionedScalar("sourceTerm", dimensionSet(0, 0, 0, 0, 0, 0, 0), -1)   );
			 
            tmp<fvScalarMatrix> tTempZEqn
            tTempZEqn = 
            (
                fvm::laplacian(Z) + sourceTerm
            );

            fvScalarMatrix& tempZEqn = tTempZEqn.ref();
            tempZEqn.relax();
            tempZEqn.solve();

            ...
            ...

            vectorField& field = *this
            forAll(Cf, i)
            {
                //After computing the normal vector, for each cell of the patch I should multiply Umax by the result of the Poisson problem, and then multiply by the normal vector. Lastly, I assign the result to field[i]
            }
        #}

        ...
        ...
}

Unfortunately, no errors are thrown and it does not seem to have any effect on the field Z looking at it in ParaView.



Alternative Approach:
Another idea I had was to preprocess the mesh using Python before running foamRun. I would solve the Poisson problem numerically for each inlet patch and store the results in external files. Later, I would read these files in the 0/U directory for each inlet, similar to how I retrieve the value of Umax depending on the time. However, I'm unsure how to store these results and retrieve them while looping through the patch cells, as I'm struggling to understand the indexing.


I hope my explanation was clear. I'm looking for advice on how to proceed or any alternative solutions that might be more suitable for this case. If more details are needed, I am happy to provide them.

Thank you for your help!

Best regards.