Convergence of Discontinuous Galerkin Methods for Incompressible Two-Phase Flow in Heterogeneous Media
Convergence of Discontinuous Galerkin Methods for Incompressible Two-Phase Flow in Heterogeneous Media
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DOI：
10.1137/120898358
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发表时间：
2013-12
期刊：
影响因子：
--
通讯作者：
Jisheng Kou;Shuyu Sun
中科院分区：
文献类型：
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作者：
Jisheng Kou;Shuyu Sun
提出了一类具有内部惩罚的间断伽辽金方法，用于研究具有毛细管压力的非均匀多孔介质中的不可压缩两相流。制定了两相流全耦合系统的半离散近似方案。在高度非均质渗透介质中，由于毛细管压力不同，饱和度是不连续的，因此，所提出的方法将毛细管压力纳入压力方程而不是饱和度方程中。通过引入稳定性和误差估计的耦合方法，而不是传统的压力和饱和度单独分析，方案在空间和时间上的稳定性以及先验马力误差估计在压力的 $L^2(H^1)$ 和饱和度的 $L^\infty(L^2)$ 和 $L^2(H^1)$ 中给出。引入两次离散化方案来有效计算离散解。
A class of discontinuous Galerkin methods with interior penalties is presented for incompressible two-phase flow in heterogeneous porous media with capillary pressures. The semidiscrete approximate schemes for fully coupled system of two-phase flow are formulated. In highly heterogeneous permeable media, the saturation is discontinuous due to different capillary pressures, and therefore, the proposed methods incorporate the capillary pressures in the pressure equation instead of saturation equation. By introducing a coupling approach for stability and error estimates instead of the conventional separate analysis for pressure and saturation, the stability of the schemes in space and time and a priori hp error estimates are presented in the $L^2(H^1)$ for pressure and in the $L^\infty(L^2)$ and $L^2(H^1)$ for saturation. Two time discretization schemes are introduced for effectively computing the discrete solutions.