We are concerned with the approximation of solutions to a compressible two-phase flow model in porous media thanks to an enhanced control volume finite element discretization. The originality of the methodology consists in treating the case where the densities are depending on their own pressures without any major restriction neither on the permeability tensor nor on the mesh. Contrary to the ideas of [23], the point of the current scheme relies on a phase-by-phase “sub”-unpwinding approach so that we can recover the coercivity-like property. It allows on a second place for the preservation of the physical bounds on the discrete saturation. The convergence of the numerical scheme is therefore performed using classical compactness arguments. Numerical experiments are presented to exhibit the efficiency and illustrate the qualitative behavior of the implemented method.

由于增强了控制体积有限元离散化，我们关注多孔介质中可压缩两相流模型的近似解。该方法的独创性在于处理密度取决于其自身压力的情况，而对渗透率张量和网格均无任何主要限制。与[23]的想法相反，当前方案的重点在于分阶段“子”展开方法，以便我们可以恢复类似矫顽力的性质。其次，它可以保留离散饱和度上的物理边界。因此，使用经典的紧凑性参数来执行数值方案的收敛。