Numerical solutions for recirculating flow in a cavity

Numerical solutions have been obtained for the steady-two-dimensional flow of a viscous incompressible fluid in rectangular cavities by solving various Implicit finite- difference approximations of the Navier-Stokes equations, The sets of implicit difference equations were solved using a recently introduced iterative numerical procedure called the strongly implicit procedure (SIP). The strongly implicit procedure was found to be an effective and economical numerical procedure for obtaining iterative numerical solutions for sets of linear and/or nonlinear finite-difference equations. Various qualitative and quantitative comparisons have been made to determine the effects of the Reynolds number, the grid size, and the difference approximation on the numerical solutions and computational procedures. The results show that one difference scheme was particularly accurate for Reynolds numbers and grid sizes which satisfy the stability restriction. Streamline patterns and equivorticity plots for a range of Reynolds numbers are shown for various difference approximations and grid sizes. Changes in the principal features of the flow field have been discussed and correlated with changes in the Reynolds number of the flow.Mechanical Engineering, Department o