This paper presents the numerical solution of immiscible two-phase flows in porous media, obtained by a first-order finite element method equipped with mass-lumping and flux up-winding. The unknowns are the physical phase pressure and phase saturation. Our numerical experiments confirm that the method converges optimally for manufactured solutions. For both structured and unstructured meshes, we observe the high-accuracy wetting saturation profile that ensures minimal numerical diffusion at the front. Performing several examples of quarter-five spot problems in two and three dimensions, we show that the method can easily handle heterogeneities in the permeability field. Two distinct features that make the method appealing to reservoir simulators are: (i) maximum principle is satisfied, and (ii) mass balance is locally conserved.

翻译：本文展示了在多孔介质中不强迫的两阶段流动的数值解决方案,该介质是通过配备大规模排挤和通量向上流的第一级有限元素方法获得的。未知数是物理阶段压力和相向饱和度。我们的数字实验证实,该方法在制造解决方案方面是最佳结合的。对于结构化和无结构化的介质,我们观察高精确度湿饱和度剖面图,以确保在前面最小的数值扩散。在两个和三个维度上执行几个25分点问题的例子,我们显示该方法可以很容易地处理可渗透性领域的异质。使水库模拟器具有吸引力的两个不同特征是:(一) 符合最高原则,和(二) 质量平衡是当地保护的。