A boundary element solution of the stream function vorticity formulation of the Navier-Stokes equations.

The Boundary Element Method is applied to solve the stream function vorticity formulation of the steady state Navier Stokes equations. The procedure developed relies on the use of fundamental solutions that take into account the coupling between the differential equations through the vorticity term in the stream function equation. The nonlinear terms are considered as inhomogeneities in the development of the boundary integral equations and treated by means of direct iteration. The method allows the handling of no slip boundary conditions in a direct manner, avoiding iteration to find the vorticity values on no slip boundaries. The discretization of the resulting boundary integral equations is performed by placing the singular points outside the solution domain, as it is done in the Regular Boundary Element Method.