Hybrid vortex-ADI solution for flows of low viscosity

A hybrid numerical scheme is presented for use on two-dimensional, incompressible flows of low viscosity. The scheme divides the domain D into two regions, D1, and D2, and the Navier-Stokes equations are solved by different methods in each. in the region D1, which is composed of a narrow strip adjoining the boundary, the grid-free vortex method is used. An alternating direction implicit (ADI) method is used in the interior domain D2 which contains that part of D that lies a short distance away from the boundary. The hybrid method allows vorticity exchange between the two regions by partially merging and realigning them. Boundary conditions for the vorticity are automatically treated by the vortex method. Favorable numerical results have been obtained for the problem of recirculating flow in a square cavity for Reynolds number of 400 and 1000