A review of vorticity conditions in the numerical solution of the zeta-psiequations

In this review the conditions to be imposed on the vorticity in the calcula tion of two-dimensional incompressible viscous flows are discussed. Existin g boundary vorticity formulas, commonly regarded as a surrogate Dirichlet b oundary condition for the vorticity, are more properly interpreted as the d iscrete counterpart of the Neumann boundary condition for the stream functi on. This viewpoint helps to elucidate the algebraic equivalence of coupled numerical methods with uncoupled methods based on conditions of integral ty pe for the vorticity. A unified understanding of several available treatmen ts for determining correct vorticity boundary values is achieved by includi ng in the present analysis spatial discretizations by finite differences an d finite elements, coupled and uncoupled formulations of the problem as wel l as steady and unsteady equations. Results of some test calculations are p resented to illustrate the numerical consequences of the analysis. (C) 1999 Elsevier Science Ltd. All rights reserved.