3-DIMENSIONAL INCOMPRESSIBLE NAVIER-STOKES EQUATIONS ON NONORTHOGONALSTAGGERED GRIDS USING THE VELOCITY-VORTICITY FORMULATION

This paper is concerned with the numerical resolution of the incompres sible Navier-Stokes equations in the velocity-vorticity form on non-or thogonal structured grids. The discretization is performed in such a w ay, that the discrete operators mimic the properties of the continuous ones. This allows the discrete equivalence between the primitive and velocity-vorticity formulations to be proved. This last formulation ca n thus be seen as a particular technique for solving the primitive equ ations. The difficulty associated with non-simply connected computatio nal domains and with the implementation of the boundary conditions are discussed. One of the main drawback of the velocity-vorticity formula tion, relative to the additional computational work required for solvi ng the additional unknowns, is alleviated. Two- and three-dimensional numerical test cases validate the proposed method. (C) 1998 John Wiley & Sons, Ltd.