Numerical solution of three-dimensional Navier-Stokes equations by a velocity-vorticity method

A finite difference method for solving the incompressible viscous flow in velocity-vorticity form is presented. A staggered mesh is employed to ensure continuity. To enforce the zero divergence of the vorticity, the computed vorticity is replaced at each time step with del /boolean AND u. An explicit three-level backward scheme is used to update the vorticity transport equation for the vorticity at the next time level. To solve the Poisson equations for velocity, a restarted version of the Generalized Minimal Residual method (GMRES) implemented with incomplete lower-upper (ILU) decompositions preconditioner has been adopted. Two- and three-dimensional driven cavity flows with impulsively started and oscillating lids are used to test the method. Detailed results and comparisons with the numerical literature data show that the proposed method is accurate and efficient. Copyright (C) 2001 John Wiley & Sons, Ltd.