Interactive method for computation of viscous flow with recirculation

An interactive method is proposed for the solution of two-dimensional, laminar flow fields with identifiable regions of recirculation, such as the shear-layer-driven cavity flow. The method treats the flow field as composed of two regions, with an appropriate mathematical model adopted for each region. The shear layer is computed by the compressible boundary layer equations, and the slowly recirculating flow by the incompressible Navier-Stokes equations. The flow field is solved iteratively by matching the local solutions in the two regions. For this purpose a new matching method utilizing an overlap between the two computational regions is developed, and shown to be most satisfactory. Matching of the two velocity components, as well as the change in velocity with respect to depth is amply accomplished using the present approach, and the stagnation points corresponding to separation and reattachment of the dividing streamline are computed as part of the interactive solution. The interactive method is applied to the test problem of a shear layer driven cavity. The computational results are used to show the validity and applicability of the present approach.