Numerical simulation of three‐sided lid‐driven square cavity

Abstract

Abstract In this article, an incompressible, two‐dimensional (2D), time‐dependent Newtonian fluid flow in a square cavity is simulated using finite difference method and alternating direction implicit technique. Navier‐Stokes equations are solved numerically in stream function‐vorticity formulation. In order to verify the numerical solver, the one‐sided lid‐driven cavity is studied and the results are compared with relevant data in the literature. They were in a very good agreement. Furthermore, two distinguished 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, while the left wall is translated upward and the right wall remains stationary. Moreover, in case (2), the upper wall is translated to the right but the lower wall is translated to the left, while the left wall is translated downward and the right wall remains stationary. However, 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 (Re), typically (Re = 100 to 2000). Moreover, the higher the Re, the more main primary vortex approaches the cavity center and the bigger the secondary vortices.

Keywords

• finite difference method
• incompressible flow
• lid‐driven cavity
• Navier‐Stokes equations
• stream function‐vorticity formulation