Fourth‐order finite difference simulation of a differentially heated cavity

We present benchmark simulations for the 8: 1 differentially heated cavity problem, the focus of a special session at the first MIT conference on Computational Fluid and Solid Mechanics in June 2001. The numerical scheme is a fourth‐order finite difference 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.