2D thermal/isothermal incompressible viscous flows

2D thermal and isothermal time-dependent incompressible viscous flows are presented in rectangular domains governed by the Boussinesq approximation and Navier-Stokes equations in the stream function-vorticity formulation. The results are obtained with a simple numerical scheme based on a fixed point iterative process applied to the non-linear elliptic systems that result after a second-order time discretization. The iterative process leads to the solution of uncoupled, well-conditioned, symmetric linear elliptic problems. Thermal and isothermal examples are associated with the unregularized, driven cavity problem and correspond to several aspect ratios of the cavity. Some results are presented as validation examples and others, to the best of our knowledge, are reported for the first time. The parameters involved in the numerical experiments are the Reynolds number Re, the Grashof number Gr and the aspect ratio. All the results shown correspond to steady state flows obtained from the unsteady problem. Copyright (c) 2005 John Wiley & Sons, Ltd.