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

A finite difference method for solving the incompressible viscous flow in v elocity-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 explici t three-level backward scheme is used to update the vorticity transport equ ation for the vorticity at the next time level. To solve the Poisson equati ons for velocity, a restarted version of the Generalized Minimal Residual m ethod (GMRES) implemented with incomplete lower-upper (ILU) decompositions preconditioner has been adopted. Two- and three-dimensional driven cavity f lows with impulsively started and oscillating lids are used to test the met hod. Detailed results and comparisons with the numerical literature data sh ow that the proposed method is accurate and efficient. Copyright (C) 2001 J ohn Wiley & Sons, Ltd.