Numerical Algorithms 34: 117–125, 2003.  2003 Kluwer Academic Publishers. Printed in the Netherlands. Numerical simulation of two-phase flow through heterogeneous porous media M. Afif a and B. Amaziane b,∗ a Université Cadi Ayyad, F.S.S.M., BP 2390, Marrakech, Maroc E-mail: mafif@technologist.com b Université de Pau, LMA–CNRS, FRE2570, Av. de l’Université, 64000 Pau, France E-mail: brahim.amaziane@univ-pau.fr Received 4 December 2001; accepted 4 February 2003 A mixed finite element method is combined to finite volume schemes on structured and un- structured grids for the approximation of the solution of incompressible flow in heterogeneous porous media. A series of numerical examples demonstrates the effectiveness of the method- ology for a coupled system which includes an elliptic equation and a nonlinear degenerate diffusion–convection equation arising in modeling of flow and transport in porous media. Keywords: finite volume method, mixed hybrid finite element, nonlinear convection– diffusion, porous media, unstructured grids AMS subject classification: 76M12, 65M12, 35K65 1. Introduction Multiphase flow of fluids in porous media is physically and chemically complex. It involves heterogeneities in the porous media at many different length scales and com- plicated processes such as diffusion and dispersion. It is well known that the transport term in the flow equations are governed by fluid velocities. Thus accurate numerical simulation requires accurate approximations of these velocities. Often the flow proper- ties of the porous media vary abruptly with sharp changes in lithology. Consequently, the coefficient in the flow equation is quite rough. Flow simulation in petroleum and environmental applications has been extensively studied using finite element methods in the last two decades (see, e.g., [9, and references therein]). Also, discretizations using both finite element and finite volume methods are presented in [7]. More recently, finite volume methods were developed and analyzed for immiscible two-phase flow in porous media in the case where the diffusion term is neglected (see [8, and references therein]). This approach leads to robust schemes applicable for unstructured grids and the approximate solution has various interesting ∗ Corresponding author.