Approximation of variable density incompressible 1ows by means of 3nite elements and 3nite volumes

This work describes a projection method for approximating incompressible viscous 1ows of nonuniform density. It is shown that unconditional stability in time is possible provided two projections are performed per time step. A 3nite element implementation and a 3nite volume one are described and compared. The performance of the two methods are tested on a Rayleigh–Taylor instability. We show that the considered problem has no inviscid smooth limit; hence con3rming a conjecture by BirkhoA stating that the inviscid problem is not well-posed. Furthermore, we show that at even moderate Reynolds numbers, this problem is extremely sensitive to mesh re3nement and to the numerical method adopted. Copyright ? 2001 John Wiley & Sons, Ltd.