A multistep technique with implicit difference schemes for calculating two- or three-dimensional cavity flows

Abstract

A numerical algorithm for solving two- or three-dimensional incompressible viscous Navier-Stokes equations is presented. The technique presented here is based on a simple variant of the Chorin method and is related to the MAC method. Auxiliary velocity fields are introduced, which are calculated by the use of a fractional-step procedure for the convective and diffusive part of the solution. For the pressure resolution, a triple sweep is used to obtain the fluid pressure. By these fractional techniques, the three-dimensional equations are separated into only one-dimensional forms. Thus, this saves more computation time and makes algorithm simple. Some numerical computations are made on flows within square and cubic cavities, and some comparisons are made in regard to boundary effects in three-dimensional flows. Further, some discussions are made on primary and secondary eddies generated in a cubic cavity, and comparisons with those in a square cavity are also made. It was found that boundary effects mainly locate near a side wall, but these are not negligibly small in a central region in a cubic cavity.