This paper presents and analyzes a discontinuous Galerkin method for the compressible three-phase flow problem in porous media. We use a first order time extrapolation which allows us to solve the equations implicitly and sequentially. We show that the discrete problem is well-posed, and obtain a priori error estimates. Our numerical results validate the theoretical results, i.e. the algorithm converges with first order, under different setups that involve variable density and effects of gravity.

翻译：本文介绍并分析了一种不连续的 Galerkin 方法, 用于在多孔介质中压缩三相流程问题。 我们使用第一个顺序时间的外推法, 从而可以默认和连续地解答方程式。 我们显示离散问题已经得到了很好的定位, 并获得了先验误差估计。 我们的数字结果证实了理论结果, 即算法与第一顺序相融合, 由不同结构组成, 涉及可变密度和重力效应。