[Patryk Stawicki]

Hello everyone. I'm working on a solver that solves vorticiy-stream function equation. One of the things I wanted to apply, to one of my case, was 0 velocity at the boundary. To achieve that, I wasn't simply applying 0 velocity at the boundary, since I'm not using primitive variables. My idea was to, make such boundary condition that will create vortex itself, that in result of "mixing" will create a 0-velocity slice near the wall.

So this is a code of my Thoms formula, atleast this is what i think its called.

const fvPatch& boundaryPatch = patch(); // this patch
            // make a reference to the mesh so that I can access variables
            const fvMesh& mesh = patch().boundaryMesh().mesh();
            const volScalarField& psi = db().lookupObject<volScalarField>("psi");
            const volScalarField& OM = db().lookupObject<volScalarField>("OM");
            label inletPatchID = mesh.boundaryMesh().findPatchID("bottom");
            label inletPatchID2 = mesh.boundaryMesh().findPatchID("left");
            // Get reference to boundary field value
            const scalarField& psib = psi.boundaryField()[inletPatchID];  
            const scalarField& OMb = OM.boundaryField()[inletPatchID];
            
            // get coordinate for cell centres
            const fvPatchVectorField& centre = mesh.C().boundaryField()[inletPatchID];
            const fvPatchVectorField& centreleft = mesh.C().boundaryField()[inletPatchID2];
            //const fvPatchVectorField& centre = mesh.C().boundaryField()[inletPatchID];
            
            //area of patch
            scalarField areasc = mesh.magSf().boundaryField()[inletPatchID];
            scalarField OMwall = OMb;
            scalar area = sum(areasc);
            
             scalar d;
         
          // THOMAS FORMULA      
			forAll (psib, cellI)
			{
				d = mag(mesh.C()[cellI].component(vector::Y) - centre[cellI].component(vector::Y));
				OMwall [cellI] = -2.0*psib[cellI]/(d*d);
			}
			Info << (OMwall);

         operator==(OMwall);

Generally all i want to achieve is the vorticity at the wall that will be equal to:

=