Finite Di erence Methods for 3D Viscous Incompressible Flows in the Vorticity-Vector Potential Formulation on Non-staggered Grids

Simple, e cient and accurate nite di erence methods are introduced for 3D unsteady viscous incompressible ows in the vorticity-vector potential formulation on non-staggered grids. Two di erent types of methods are discussed. They di er in the implementation of the normal component of the vorticity boundary condition and consequently the enforcement of the divergence free condition for vorticity. Both second order and fourth order accurate schemes are developed. A detailed accuracy test is performed, revealing the structure of the error and the e ect of how the convective terms are discretized near the boundary. The in uence of the divergence free condition for vorticity to the overall accuracy is studied. Results on the cubic driven cavity ow at Reynolds number 500 and 3200 are shown and compared with that of the MAC scheme. 1 [email protected] 2 [email protected]