Abstract
The method of “upwind differencing” to approximate the convection terms in numerical studies of fluid motion was introduced to overcome stability restrictions believed to be imposed by the use of central differencing. Here, both methods are applied to a two dimensional model of the recirculating flow in a cavity with a sliding top. It is shown that the false diffusion associated with first order upwind difference approximations can cause the numerical solution to severely misrepresent the physical transport processes. The instability exhibited by solutions based upon second order approximations is elucidated by examining the conservation laws implied by the governing equations. Finally, by calculating three dimensional solutions, it is shown that the assumption of two dimensionality is of questionable validity at high values of the Reynolds number.
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