Equations as boundary condition
 

Hi, I'm wondering if it is possible to specify the boundary condition as a set of equations rather than specific variable.

I've trying to solve the potential flow with an unusual boundary condition dP/dn=f, in which P is the potential, n is the surface normal and f is an explicit variable. I know that in potentialFoam, the boundary condition enters by specifying velocity. By definition of potential flow we have dP/dx=Ux, dP/dy=Uy. Thus, the boundary condition breaks down to Ux*nx+Uy*ny=f, in which nx and ny are the two components of the surface normal vector.

How should I set the this kind of boundary condition?

I think this kind of boundary is very similar to the slip boundary, in which Ux*nx+Uy*ny=0 is ensured for the no-penetration condition. I wonder how openfoam implement such kind of boundary condition, in which the components of the velocity vector form an equation rather than appearing as explicit values.

After a few's days search I found surfaceNormalFixedValue may suit my needs.

I'm testing flow around a cylinder with both slip boundary condition and surfaceNormalFixedValue with refValue=0 on the cylinder wall. I suppose these two conditions are equivalent. However, I'm getting totally different results.
For the slip, I get a stable flow (left figure), while for the surfaceNormalFixedValue I get periodic shedding (right figure).

I'm wondering why is this happening.