Adaptively Coupled Domain Decomposition Method for Multiphase and Multicomponent Porous Media Flows

Shizhe Li, Li Zhao, Chen-Song Zhang
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Abstract

Numerical simulation of large-scale multiphase and multicomponent flow in porous media is a significant field of interest in the petroleum industry. The fully implicit approach is favored in reservoir simulation due to its numerical stability and relaxed constraints on time-step sizes. However, this method requires solving a large nonlinear system at each time step, making the development of efficient and convergent numerical methods crucial for accelerating the nonlinear solvers. In this paper, we present an adaptively coupled subdomain framework based on the domain decomposition method. The solution methods developed within this framework effectively handle strong nonlinearities in global problems by addressing subproblems in the coupled regions. Furthermore, we propose several adaptive coupling strategies and develop a method for leveraging initial guesses to accelerate the solution of nonlinear problems, thereby improving the convergence and parallel performance of nonlinear solvers. A series of numerical experiments validate the effectiveness of the proposed framework. Additionally, by utilizing tens of thousands of processors, we demonstrate the scalability of this approach through a large-scale reservoir simulation with over 2 billion degrees of freedom.
多相和多组分多孔介质流动的自适应耦合领域分解法
多孔介质中大规模多相和多组分流动的数值模拟是石油工业的一个重要领域。由于其数值稳定性和对时间步长的宽松限制,完全隐式方法在储层模拟中备受青睐。然而,这种方法需要在每个时间步求解一个大型非线性系统,因此开发高效、收敛的数值方法对于加速非线性求解至关重要。在本文中,我们提出了一种基于域分解方法的自适应耦合子域框架。在此框架内开发的求解方法通过解决耦合区域中的子问题,有效地处理了全局问题中的强非线性问题。此外,我们还提出了几种自适应耦合策略,并开发了一种利用初始猜测加速非线性问题求解的方法,从而提高了非线性求解器的收敛性和并行性能。一系列数值实验验证了所提框架的有效性。此外,通过利用数万个处理器,我们通过一个超过 20 亿自由度的大规模储层模拟,证明了这种方法的可扩展性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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