Approximation of variable density incompressible flows by means of finite elements and finite volumes
Résumé
This work describes a projection method for approximating incompressible viscous flows of nonuniform density. It is shown that unconditional stability in time is possible provided two projections are performed per time step. A finite element implementation and a finite 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 confirming a conjecture by Birkho 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 refinement and to the numerical method adopted.