Block-implicit multigrid calculation of three-dimensional recirculating flows

An efficient finite difference calculation procedure for three-dimensional recirculating flows is presented. The algorithm is based on a coupled solution of the three-dimensional momentum and continuity equations in primitive variables by the multigrid technique. A symmetrical coupled Gauss-Siedel technique is used for iterations and is observed to provide good rates of smoothing. Calculations were made of the fluid motion in a three-dimensional cubic cavity with a moving top wall. The efficiency of the method is demonstrated by performing calculations at different Reynolds numbers with finite difference grids as large as 66 x 66 x 66 nodes. The CPU times and storage requirements for these calculations are observed to be very modest. The algorithm has the potential to be the basis for an efficient general purpose calculation procedure for practical fluid flows.