The present paper proposes a numerical method for the solution of the two-dimensional incompressible viscous flow problems. Numerical technique is described for a general set of equations, namely the BOUSSINESQ equations. The momentum and energy equations are solved by the modified FLIC method, while the pressure equation is solved by the finite element method.
The present method is applied to two examples: one is the flow in a rectangular cavity driven by the uniform translation of the top wall, while the other is the flow in a square cavity driven by buoyancy forces that caused by temperature differences. The results thus obtained are compared with those obtained by the other conventional methods to demonstrate the validity of the present approach.
The problems treated in the present paper are limited to two-dimensional flow. However, an extension of the present technique to threedimensional flow is straight forward, although it is inevitably accompanied by an increase of computing time.