Multigrid solutions of elliptic fluid flow problems

An efficient FAS muldgrid solution strategy is presented for the accurate and economic simulation of convection dominated flows. The use of a high-order approximation to the convective transport terms found in the governing equations of motion has been investigated in conjunction with an unsegregated smoothing technique. Results are presented for a sequence of problems of increasing complexity requiring that careful attention be directed toward; the proper treatment of different types of boundary condition. The classical two-dimensional problem of flow in a lid-driven cavity is investigated in depth for flows at Reynolds numbers of 100,400 and 1000. This gives an extremely good indication of the power of a multigrid approach. Next, the solution methodology is applied to flow in a three-dimensional lid-driven cavity at different Reynolds numbers, with cross-reference being made to predictions obtained in the corresponding two-dimensional simulations, and to the flow over a step discontinuity in the case of an abruptly expanding channel. Although, at first sight, these problems appear to require only minor extensions to the existing approach, it is found that they are rather more idiosyncratic. Finally, the governing equations and numerical algorithm are extended to encompass the treatment of thermally driven flows. Ile solution to two such problems is presented and compared with corresponding results obtained by traditional methods.