A compact monotonic discretization scheme for solving second-order vorticity-velocity equations

This paper presents a numerical method for solving the steady-state Navier- Stokes equations for incompressible fluid Rows using velocities and vortici ty as working variables. The method involves solving a second-order differe ntial equation fur the velocity and a convection-diffusion equation for the vorticity in Cartesian grids. The key to the success of the numerical simu lation of this class of flow equations depends largely on proper simulation of vorticity transport equation subject to proper boundary vorticity. In t his paper. we present a monotonic advection-diffusion multi-dimensional sch eme and a theoretically rigorous implementation of vorticity boundary condi tions. While the derivation of the proposed integral vorticity boundary con dition is more elaborate and is mure difficult to solve than conventional l ocal approaches, the present approach offers significant advantages. In thi s study, both lid-driven and backward-facing step problems have been select ed for comparison and validation purposes. (C) 2000 Elsevier Science S.A. A ll rights reserved.