[jd87]

Hello everyone,

I am trying to solve the Darcy equations using the classical stream function formulation. Although it is a CLASSICAL CASE, I did not find any related thread regarding this topic, so decided to start a new thread. My question is simple, I solve for the stream function (named, p) using the LaplacianFoam and then find the velocities using the expressions (2D case):

volVectorField gradP = fvc::grad(p);
ux = -gradP.component(vector::Y);
uy = gradP.component(vector::X);

Then I define a velocity vector (U) as

const vector ii(1, 0, 0);
const vector jj(0, 1, 0);
U = ii*ux + jj*uy;

and save it at given time intervals. Boundary conditions for U (or ux and uy) are NOT read from any file, therefore when I save them, I get the obvious 'calculated' boundary values. Thereafter I use this U to calculate other equations (which is not the focus of the thread).

My right-left walls are cyclic and frontBack patches are empty. At the top and bottom walls (walls running parallel to x), p is set as uniform 0 since there is no penetration velocity (uy should be zero). From the expression above, uy at the top and bottom walls are just derivatives of p along x and must be zero (since p is constant at top and bottom walls). However, when I view the velocity file (U file), the calculated boundary values for uy at the top and bottom wall is not exactly 0. It has value one to two order magnitude lower than ux though (my ux is usually ~1e-03 and uy~1e-04 or lower, so nowhere close to eps of the system).

Can anybody shed light on why this is occurring and how to circumvent the issue? It would be very helpful if anyone can point out why this simple fulfilment of the boundary condition is not working.

PS: Later, I also tried to set uy as a separate file in 0-folder where the top and bottom conditions are set to uniform 0 and uy is read in each iteration using the

uy.correctBoundaryConditions();

command (Note: uy is not stored in future times, only U, the vectorField is stored). But the results remain the same, uy is not equal to zero at the top and bottom walls!!!