摘要
We study a class of preconditioners to solve large-scale linear systems arising from fully implicit reservoir simulation.These methods are discussed in the framework of the auxiliary space preconditioning method for generality.Unlike in the case of classical algebraic preconditioning methods,we take several analytical and physical considerations into account.In addition,we choose appropriate auxiliary problems to design the robust solvers herein.More importantly,our methods are user-friendly and general enough to be easily ported to existing petroleum reservoir simulators.We test the efciency and robustness of the proposed method by applying them to a couple of benchmark problems and real-world reservoir problems.The numerical results show that our methods are both efcient and robust for large reservoir models.
We study a class of preconditioners to solve large-scale linear systems arising from fully implicit reservoir simulation. These methods are discussed in the framework of the auxiliary space preconditioning method for generality. Unlike in the case of classical algebraic preconditioning methods, we take several analytical and physical considerations into account. In addition, we choose appropriate auxiliary problems to design the robust solvers herein. More importantly, our methods are user-friendly and general enough to be easily ported to existing petroleum reservoir simulators. We test the efficiency and robustness of the proposed method by applying them to a couple of benchmark problems and real-world reservoir problems. The numerical results show that our methods are both efficient and robust for large reservoir models.
基金
supported by Petro-China Joint Research Funding(Grant No.12HT1050002654)
National Science Foundation of USA(Grant No.DMS-1217142)
the Dean’s Startup Fund
Academy of Mathematics and System Sciences and the State High Tech Development Plan of China(863 Program)(GrantNo.2012AA01A309)
关键词
预处理方法
油藏模拟器
辅助用房
应用
油田
生日
油藏数值模拟
线性系统
reservoir simulation, black-oil model, fully implicit method, auxiliary space preconditioning,algebraic multigrid method, Krylov subspace iterative method