This paper presents a numerical study of immiscible, compressible two-phase flows in porous media, that takes into account heterogeneity, gravity, anisotropy, and injection/production wells. We formulate a fully implicit stable discontinuous Galerkin solver for this system that is accurate, that respects the maximum principle for the approximation of saturation, and that is locally mass conservative. To completely eliminate the overshoot and undershoot phenomena, we construct a flux limiter that produces bound-preserving elementwise average of the saturation. The addition of a slope limiter allows to recover a pointwise bound-preserving discrete saturation. Numerical results show that both maximum principle and monotonicity of the solution are satisfied. The proposed flux limiter does not impact the local mass error and the number of nonlinear solver iterations.

翻译：本文对多孔介质中非混相、可压缩两相流进行数值研究，考虑了非均质性、重力、各向异性及注入/生产井的影响。我们为该体系构建了全隐式稳定间断伽辽金求解器，该求解器具有高精度、满足饱和度近似的最大值原理，并保持局部质量守恒。为完全消除过冲和下冲现象，我们构造了一个通量限制器，可生成保界的单元平均饱和度。结合斜率限制器可恢复逐点保界的离散饱和度。数值结果表明，解的最大值原理和单调性均得到满足。所提出的通量限制器不影响局部质量误差及非线性求解器迭代次数。