Numerical Analysis of a Two Dimensional Cavity Flow

Abstract

A driven cavity flow of a two dimensional incompressible viscous flow is calculated by finite difference method. A generalized coordinate system is used so that a sufficient number of grid points are distributed near the wall by Thompson's method. In order to satisfy continuity of mass flow rate, Poisson equation of the pressure which is derived from the MAC method is solved. And the three kinds of the third order upwind scheme are applied for the convective term in the Navier-Stokes equation. Furthermore, all calculations which employed the vectorized implicit time marching scheme are carried out on a supercomputer. As the results of computation, differences of the three schemes in the general coordinate at high Reynolds number are shown in this paper.