On the numerical approximation of compressible two phase flows

In this paper, we present a numerical method able to simulate compressible multiphase flows. Its main feature is to be a discrete version of the averaging technique of Drew et coll. It has many numerical properties. In particular, it enables to avoid the difficult problem of discretizing the non conservative terms that appear naturally in the modelization. This method has also additional properties, for example it provides a natural way of constructing entropy satisfying schemes. It also enables to derive models with less unknowns in some limit cases, to construct entropy satisfying pressure and velocity closures. Several numerical illustrations are provided to illustrate the technique. (author)