Locally conservative Galerkin and finite volume methods for two-phase flow in porous media

In this paper we propose a locally conservative Galerkin (LCG) finite element method for two-phase flow simulations in heterogeneous porous media. The main idea of the method is to use the property of local conservation at steady state conditions in order to define a numerical flux at element boundaries. It provides a way to apply standard Galerkin finite element method in two-phase flow simulations in porous media. The LCG method has all the advantages of the standard finite element method while explicitly conserving fluxes over each element. All the examples presented show that the formulation employed is accurate and robust, while using less CPU time than finite volume method.