On the numerical solution to two fluid models via a cell centered finite volume method

A new method for the discretization of nonlinear systems of partial differe ntial equations occurring in the numerical simulation of two phase flows is proposed. This method is based on a cell centered finite volume discretiza tion on possibly unstructured meshes and aims to approximate three-dimensio nal stationary and evolution problems in arbitrary geometries, We are able to consider conservative and non-conservative systems of equations and the method belongs to the class of shock-capturing upwind ones. In the paper we put the emphasis on the treatment of terms involving first-order derivativ es since we deal with the change of type (hyperbolic to non-hyperbolic). On e of the features of the method is that it does not rely a priori on the hy perbolic character of the convection operator. The method is illustrated on a classical numerical benchmark and we refer to the bibliography concernin g various and numerous applications in the context of two phase flows. (C) 2001 Editions scientifiques et medicales Elsevier SAS.