The four-sided lid driven square cavity using stream function-vorticity formulation

In this paper, an unsteady 2-D incompressible fluid flow with heat and mass transfer in a four-sided lid driven square cavity is investigated numerically. The top, bottom, left, and right walls of the square cavity move to the right, left, downward and upward respectively. All four sides of the cavity move with a uniform velocity. The flow variables are simulated below the critical Reynolds numbers with isothermal and mass-transfer conditions in the square cavity. We have used a streamfunction-vorticity (ψ - ξ) formulation to investigate the fluid flow in terms of flow variables ψ, ξ, T and C at low Reynolds numbers (Re). The Prandtl number (Pr) and Schmidt number (Sc) have been chosen as 6:62 and 10, 50, 100, 150 respectively, in order to calculate the numerical solutions of T and C. The matrix method has been used to evaluate the stability and convergence of the numerical scheme. The conditions obtained from the matrix method have been used to arrive at the numerical solutions with desired accuracy.