Numerical Solutions of 2-D Steady Incompressible Flow in a Driven Square Cavity Using Stream Function-Vorticity Formulation

Abstract

In this study, a streamfunction-vorticity $(\psi-\xi)$ method is suitably used to investigate the problem of 2-D steady viscous incompressible flow in a driven square cavity with moving top and bottom wall. We used this method to solve the governing equations along with no-slip and slip wall boundary conditions at low Reynolds number. A general algorithm was used for this method in order to compute the numerical solutions for streamfunction $\psi$, vorticityfunction $\xi$ for low Reynolds numbers $Re \leq 100$. We have executed this with the aid of a computer programme developed and run in C++ compiler. We have also proposed the stability criterion of the numerical scheme used. Streamline, vorticity and isobar contours have been depicted at different low Reynolds numbers. For flows at Reynolds number $Re$=100, our numerical solutions are compared with established steady state results and excellent agreement is obtained.