Computation of the two-dimensinal incompressible Navier-Stokes equations using an implicit factored method

An implicit factored scheme was used for solving the two-dimensional incompressible Navier-Stokes equations. Pseudo compressibility was introduced in the continuity equation. The non-conservation form was chosen for stability. Von Neumann stability analysis with a model scalr equation showed that the present scheme remains stable under arbitrary coordinate transformations, without adding any numerical dissipation term. Calculation was made for a backward-facing step flow with the Reynolds number Re = (U peak times H/nu = 58), where H is a step height. Convergence was obtained after about 300 iterations, using a non-dimensional time step delta t = 1.0. The calculated results show a reasonable tendency, except that small oscillations appear in the pressure distribution near the corner point. This phenomenon needs to be further investigated.