Rigorous numerical treatment of the no-slip condition in a vorticity formulation

It is shown that a rigorous mathematical treatment of the boundary conditions for rigid no-slip surfaces requires, in general, that two passes be made in solving Poisson's equation. A Fourier solution procedure was the key to this realization. It is also shown that a corresponding method exists for finite and, for the same local approximation, the usual one step method gives the same result for the geometry considered here. The more fundamental two step method gives a new insight into the physical significance of boundary vorticity.