A PROCEDURE FOR CALCULATING VORTICITY BOUNDARY-CONDITIONS IN THE STREAM-FUNCTION VORTICITY METHOD

The stream-function-vorticity (Ψ, ω) formulation is a standard approach for numerical treatment of 2D viscous flows. In this procedure the problem reduces to solution of a coupled pair of partial differential equations - the vorticity transport equation and stream-function equation. These equations can be discretized and iteratively decoupled, and then solved for iterates approximating Ψ and ω. A well-known difficulty in this algorithm is the problem of specifying vorticity boundary data as essential data for the vorticity transport equation. This paper presents an alternative approach based on superconvergent flux ideas that applies to both straight and curved boundaries and can be used for either finite-element or finite-difference computations.