Study of 2-D laminar separated flow using unsteady incompressible Navier-Stokes equations

The unsteady incompressible Navier-Stokes equations are formulated in terms of vorticity and stream function in generalized coordinates to facilitate the analysis of internal viscous flows within general geometries. The numerical method solves the conservation form of the vorticity transport equation using the alternating direction implicit method while the stream-function equation is solved by an efficient implementation of the block Gaussian elimination technique. The overall method is applied to the model problem of flow over a backward-facing step in a doubly infinite two-dimensional channel. The convection-dominated separated-flow region near the backstep as well as the farfield-field diffusion-dominated region are resolved. The time-asymptotic steady-state flow solutions are obtained in the entire laminar-flow regime for this model problem.