Application of the numerical density-enthalpy method to the multi-phase flow through a porous medium

In this paper we apply a new method to solve multi-phase fluid flow problem for 1D and 2D fluid systems. This method is developed at TNO and presented in [1] for spatially homogeneous systems. We call this method the numerical density-enthalpy method (or ρ-h method) because density-enthalpy phase diagrams (or ρ-h diagrams) play an important role in it. Finite elements are used for spatial discretization along with the streamline upwind PetrovGalerkin method. In contrast to conventional methods, the ρ-h method eliminates the requirement of separate sets of equations for various phases and necessitates fewer parametric assumptions. Therefore, it is aimed at a simple formulation and at an increase of efficiency.