Fourth - order nite di erence simulation of a di erentially heated cavity

We present benchmark simulations for the 8:1 di erentially heated cavity problem, the focus of a special session at the rst MIT conference on Computational Fluid and Solid Mechanics in June 2001. The numerical scheme is a fourth-order nite di erence method based on the vorticity-stream function formulation of the Boussinesq equations. The momentum equation is discretized by a compact scheme with the no-slip boundary condition enforced using a local vorticity boundary condition. Long-stencil discretizations are used for the temperature transport equation with one-sided extrapolation applied near the boundary. The time stepping scheme for both equations is classical fourth-order Runge–Kutta. The main step is the solution of two discrete Poisson-like equations at each Runge–Kutta time stage, which are solved using FFT-based methods. Copyright ? 2002 John Wiley & Sons, Ltd.