A modified compact numerical algorithm to solve 2D Navier-Stokes equation

Abstract

In this paper a modified fourth order compact scheme for solving unsteady 2-D Navier-stokes equation in stream function-vorticity formulation is proposed. The proposed scheme involves domain transformation and the governing cartesian equations are transformed to body fitted coordinate system. Explicit Euler’s forward discretization in time and central difference in space are applied except for few nodes adjacent to the computational boundaries. The scheme is tested on two benchmark problems Taylor vortex flow, Burgraff flow. The results in numerical form are compared with exact solutions and are in excellent agreement.