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- W2164437237 abstract "SUMMARY A residual method of finite differencing the governing differential equation for the elliptic transport problem is presented. The new finite differencing technique is applied to (1) the one-dimensional transport problem and ' (2) the cavity flow problem for numerical illustrations. The results indicate the validity of the residual method of finite differencing. The usual method of term-by-term finite differencing, and considerations such as central differencing, hybrid differencing and upwind differencing are not needed in the present residual method. have been developed and investigated for such problems. The finite difference equation obtained by the residual approach has been compared with those obtained by CDS, UDS and HDS for the one-dimensional problem. As a numerical illustration for the two-dimensional elliptic problem, the classical problem of flow in a square cavity has been chosen. The results are compared with those of Burggraf4 who has given extensive finite difference results for low and moderate Reynolds numbers. In this context it may be worth- while to mention that in an earlier work the authors5 applied the residual approach to solve the parabolic transport problem and found encouraging results. It should be mentioned that the residual method proposed independently by the authors appears similar to the finite analytic method by Chen and Chen.6 However, there are conceptual and procedural differences between the two methods which make the residual method more versatile. Specifically, the present method provides algebraic expressions which correspond to the differential expressions in the governing equations both in sign and magnitude. Thus, the residual method allows the physical interpretation and logical extension of the finite difference expression for simple cases to complicated cases without recourse to the residual method of formulation in 0271-2091/85/010071-10$01.00" @default.
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- W2164437237 date "1985-01-01" @default.
- W2164437237 modified "2023-09-27" @default.
- W2164437237 title "A residual method of finite differencing for the elliptic transport problem and its application to cavity flow" @default.
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- W2164437237 doi "https://doi.org/10.1002/fld.1650050106" @default.
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