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Application of auxiliary space preconditioning in field-scale reservoir simulation. (English) Zbl 1305.86001

Summary: 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.

MSC:

86-08 Computational methods for problems pertaining to geophysics
86A20 Potentials, prospecting
65N22 Numerical solution of discretized equations for boundary value problems involving PDEs
65F08 Preconditioners for iterative methods
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs

Software:

IPARS
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Full Text: DOI

References:

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