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Application of auxiliary space preconditioning in field-scale reservoir simulation

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, The Pennsylvania State University, University Park, PA, 16802, USA

    XiaoZhe Hu & JinChao Xu

  2. LSEC and NCMIS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    ChenSong Zhang

Authors
  1. XiaoZhe Hu
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  2. JinChao Xu
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  3. ChenSong Zhang
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Correspondence to JinChao Xu.

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Dedicated to Professor Shi Zhong-Ci on the Occasion of his 80th Birthday

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Hu, X., Xu, J. & Zhang, C. Application of auxiliary space preconditioning in field-scale reservoir simulation. Sci. China Math. 56, 2737–2751 (2013). https://doi.org/10.1007/s11425-013-4737-3

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