Numerical computation of lid driven cavity using marker and cell (MAC) method

Abstract

The numerical analysis of lid driven in a square cavity flow is discussed. The two dimensional, incompressible, time dependent Navier-Stokes equations are investigated. The governing equations which contains continuity and momentum equations are derived from conservation of mass and conservation of momentum. The governing equations are first transformed into nondimensional equations. These equations are solved numerically using Marker and Cell (MAC) method in conjunction with fractional step method. Next, the results plotted using Matlab. Numerical results presented include the velocity profiles, pressure and vorticity contours. The velocity profiles is compared with [1]. The results showed that MAC method is suitable for solving the problem since the error is not quite difference. Different Reynolds number are used causing perturbation on vorticity contours. Then, the problem is extended by adding a velocity at the bottom wall of cavity. The pattern of the flow fluid is changed when different direction of velocities is applied to the problem. Linear stability condition must be obeyed in choosing Reynolds number. The smaller the Reynolds number gives more stability to the problem. The very large Reynolds number make diffusive terms becomes zeroes.