FINITE-ELEMENT ANALYSIS OF UNSTEADY 2-DIMENSIONAL NAVIER-STOKES EQUATIONS

This paper reports on the development of a semi-implicit projection-type scheme for solving incompressible Navier-Stokes and energy equations. The numerical scheme employs a finite-element method using a time-splitting method to integrate the two-dimensional full Navier-Stokes and energy equations satisfying continuity constraints to machine accuracy. The fundamental concepts and characteristics of the formulations and the solution methodology used are described in detail. The performance of the method is illustrated by numerical solutions obtained for two-dimensional fluid flows in a square cavity with an impulsively starting lid and with an oscillating lid, considering the effects of heat transfer, Reynolds number, Rayleigh number, and oscillatory Stokes number. The results are compared with those available in the literature and are based on alternative approaches to treat incompressibility and convective acceleration.