A calculation procedure for three-dimensional steady recirculating flows using multigrid methods

Abstract 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-Seidel technique is used for iterations and is observed to provide good rates of smoothing. Calculations have been 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 × 66 × 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.

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