Massively parallel simulation of multiphase flows in porous media is challenging due to the highly nonlinear governing equations with the complexity of various modeling features and the significant heterogeneity of material coefficients. In this paper, we introduce a fully implicit discontinuous Galerkin (DG) reservoir simulator designed for parallel computers to handle large-scale multiphase flow simulations. Our approach formulates a fully implicit DG scheme on 3D unstructured grids to discretize the nonlinear governing equations, which take into account capillary effects, permeability heterogeneity, gravity, and injection/production wells. A vertex-based slope limiter within the fully implicit DG framework is adopted to suppress oscillations near discontinuities and ensure the boundedness of the solution. We address the resulting nonlinear systems from the fully implicit discretization using a family of inexact Newton–Krylov algorithms with an analytic Jacobian. Moreover, we employ an unstructured block-type preconditioner with an efficient overlapping additive Schwarz approximation to accelerate the convergence of iterations and enhance the scalability of the simulator. Large-scale simulations of both benchmark and realistic reservoir problems on 3D unstructured grids are conducted to demonstrate the efficiency and scalability of the proposed reservoir simulator.

中文翻译：

---

具有非结构化块预调节器的完全隐式边界保持间断 Galerkin 算法，用于多孔介质中的多相流


由于高度非线性的控制方程、各种建模特征的复杂性以及材料系数的显著异质性，因此多孔介质中多相流的大规模并行仿真具有挑战性。在本文中，我们介绍了一种完全隐式非间断 Galerkin （DG） 储层模拟器，该模拟器专为并行计算机设计，用于处理大规模多相流模拟。我们的方法在 3D 非结构化网格上制定了一个完全隐式的 DG 方案，以离散非线性控制方程，其中考虑了毛细管效应、渗透率非均质性、重力和注入/生产井。在完全隐式 DG 框架中采用基于顶点的斜率限制器来抑制不连续性附近的振荡并确保解的有界性。我们使用一系列不精确的 Newton-Krylov 算法和解析雅可比矩阵来解决从完全隐式离散化中得到的非线性系统。此外，我们采用了具有高效重叠加法 Schwarz 近似的非结构化块型预条件器来加速迭代的收敛并增强模拟器的可扩展性。在 3D 非结构化网格上对基准和实际储层问题进行了大规模仿真，以证明所提出的储层模拟器的效率和可扩展性。