Numerical solutions of high‐Re recirculating flows in vorticity‐velocity form

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Abstract
A numerical method for computing high‐Re laminar steady flows is presented. The incompressible Navier‐Stokes equations are expressed in terms of vorticity‐velocity variables, discretized in space by finite differences on a staggered grid and advanced in time by a scalar alternating direction implicit (ADI) procedure, which allows a fully vectorized computer code. The accuracy and efficiency of the present formulation are discussed in comparison with the standard ω‐ψ and u, v, P forms. Numerical results are presented for two test cases: the driven cavity at Re up to 5000 and the backward‐facing step at Re up to 800.