NULL-SPACE-FREE METHODS FOR THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS ON NON-STAGGERED CURVILINEAR GRIDS

The discrete Poisson equation used to enforce incompressibility in the projection method of Chorin has a null space. The null space often manifests itself in producing solutions with checkerboard pressure fields. The staggering of variables by Harlow and Welch effectively eliminates the null space; however, when it is used in the context of curvilinear coordinates its consistent implementation is complicated because it requires the use of contravariant velocity components and variable coordinate base vectors. In this paper we present and analyze a null-space-free approximate projection method, which is based on cartesian vector components and non-staggered grids. The approximate projection method has been implemented in the computer code HEMO. Several examples of two- and three-dimensional flows using HEMO are presented.