NOVEL FINITE DIFFERENCE SCHEME FOR THE NUMERICAL SOLUTION OF TWO-DIMENSIONAL INCOMPRESSIBLE NAVIER-STOKES EQUATIONS

(Communicated by Jean-Luc Guermond) Abstract. In the present article, a new methodology has been developed to solve two-dimensional (2D) Navier-Stokes equations (NSEs) in new form proposed by Pukhnachev (J. Appl. Mech. Tech. Phys., 45:2 (2004), 167–171) who introduces a new unknown function that is related to the pressure and the stream function. The important distinguish of this formulation from vorticity-stream function form of NSEs is that stream function satisfies to the transport equation and the new unknown function satisfies to the elliptic equation. The scheme and algorithm treat the equations as a coupled system which allows one to satisfy two conditions for stream function with no condition on the new function. The numerical algorithm is applied to the lid-driven cavity flow as the benchmark problem. The characteristics of this flow are adequately represented by the new numerical model. Key Words. Navier-Stokes equations, incompressible viscous flow, finite-difference scheme