Simulation of Three-Sided Lid-Driven Cavity

In this paper, an incompressible, two-dimensional (2D), time-dependent, and laminar Newtonian fluid flow in a square cavity is simulated in order to investigate vortex dynamics in cavities. Navier-Stokes equations in vorticity-stream function formulation are solved numerically using the finite difference method (FDM) and alternating direction implicit (ADI) technique as they are computationally effective. Two original, distinguished, and unexplored cases of the three-sided lid-driven cavity have been investigated. In case (1) the upper and lower walls are translated to the right whereas the left wall is translated upward and the right wall remains stationary. Furthermore, in case (2) the upper wall is translated to the right but the lower wall is translated to the left whereas the left wall is translated downward and the right wall remains stationary. Moreover, the speed magnitude is unity for all moving walls. However, a MATLAB code is developed, used, and validated by studying the one-sided lid-driven cavity. The results were in a very good agreement. Besides, stream function and vorticity values in addition to the location of primary and secondary vortices’ centers inside the square cavity have been revealed at low and intermediate Reynolds numbers, typically (Re=100 to 2000). Moreover, as Reynolds number increases, more secondary vortices are generated near the cavity corners and the main primary vortex approaches the cavity center.