## 1 Introduction  
Two dimensional lid-driven square cavity flow is one of the basic issues of fluid mechanics. Using Navier-Stokes equations, [PERSON] et al. [1] studied two-dimensional lid driven square cavity flow, and fluid was considered as incompressible. Several Reynolds numbers and grid resolutions were considered. A multigrid method for mesh refinement was proposed and tested in their work. [PERSON] and [PERSON] [2] investigated as well the incompressible flow inside a square cavity at different Reynolds numbers and grid resolutions. In their research, they employed reliable numerical techniques of high-order accuracy. These two studies [1, 2] are frequently used as benchmark cases for steady states. The critical Reynolds number characterizing the boundary between steady and unsteady periodic flow in square cavities was reported at 7500 [3, 4], 8000 [5, 6, 7], and 8000-8300 [8]. [PERSON] and [PERSON] [3] numerically investigated the critical Reynolds number, which was observed at 7500. In another work performed by [PERSON] and [PERSON] [7], they employed the Lyapunov exponent at different Reynolds numbers to obtain the critical Reynolds number. They reported a critical Reynolds number of 8000. Via analyzing the phase-space trajectories of velocity v vs. velocity u and the Fourier spectra of velocity u, [PERSON] et al. [4] reported a critical Reynolds number of 7500. [PERSON] et al. [5] solved the eigenvalues of the Jacobian matrix and obtained a critical Reynolds number of 8000. The same value of the critical Reynolds number was reported by [PERSON] et al. [6] using a second-order spectral projection method. Using a novel implicit finite volume method combined with the Arnoldi's one, [PERSON] and [PERSON] [8] employed linear stability analysis to determine the stability properties. They reported a critical Reynolds number between 8000-8300. Some of the studies performed on triangular lid driven cavities are [9; 10; 11; 12; 13; 14; 15; 16; 17; 18]. The flow in an equilateral triangular cavity was initially investigated by [PERSON] et al. [9]. A set of Reynolds numbers ranging from 1 to 500 were studied. They observed that a finer mesh was needed for simulations with high Reynolds numbers, and reported that using an upwind difference scheme would be desirable for solving higher Reynolds numbers cases. Using a multigrid solution procedure for the Navier-Stokes equations, [PERSON] and [PERSON] [10] studied the flow inside lid driven isosceles triangular cavities. For code validation they employed a deep triangular cavity with long hypotenuses. Due to the geometry they used, they observed four vortices hierarchically located along the cavity vertical main axis. The vortex located on the top, moved to the right with the Reynolds number increase, and the smaller lower ones remained in the same location. The flow inside a triangular cavity via using finite differences was studied by [PERSON] and [PERSON] [11]. Different shapes of triangular cavities, including equilateral and scalene geometries were evaluated. Using finite elements, steady viscous flow in triangular cavities was as well studied by [PERSON] et al. [12]. They reported that the secondary recirculations diminished rapidly in size as the stagnant corner angle was increased beyond 40 degrees. Using a very fine mesh, the flow inside lid-driven triangular cavities was investigated by [PERSON] and [PERSON] [13]. The different shapes were tested at Reynolds numbers ranging from 0 to 7500. Mostly due to the small stagnant corner angle, they reported that for an equilateral triangular cavity flow, [PERSON]'s mean-square law was not as successful as it was in square or rectangle cavity flows. Steady flow inside a lid-driven isosceles triangular cavity at Reynolds numbers varying from 100 to 780 was studied by [PERSON] et al. [14]. The top lid moved toward the rectangular corner and in the opposite direction. Experimental and numerical results were performed and compared.