A fast auxiliary space preconditioner for numerical reservoir simulations

Xiaozhe Hu, Wei Liu, Guan Qin, Jinchao Xu, Yan Yan, Chen Song Zhang

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Scopus citations


The Fast Auxiliary Space Preconditioning (FASP) method is a general framework for constructing effective preconditioners for solving discretized partial differential equations (PDEs). By constructing appropriate auxiliary spaces, FASP transforms a complicated problem into a sequence of simpler solver-friendly systems. In this paper, we present a new FASP preconditioner for petroleum reservoir simulations. According to the analytic characteristics for the pressure and saturation variables in the black oil model, we choose appropriate auxiliary spaces for different parts of the Jacobian systems arising from the fully implicit method (FIM) with coupled implicit wells. By combining the new preconditioner with Krylov subspace methods (such as the GMRes method), we construct an efficient and robust solver, which can be easily generalized to more complicated models like the modified black oil model for simulating polymer flooding. Preliminary numerical experiments demonstrate the advantages of this new preconditioner. Copyright 2011, Society of Petroleum Engineers.
Original languageEnglish (US)
Title of host publicationSociety of Petroleum Engineers - SPE Reservoir Characterisation and Simulation Conference and Exhibition 2011, RCSC 2011
PublisherSociety of Petroleum Engineers
Number of pages10
ISBN (Print)9781618394224
StatePublished - Jan 1 2011
Externally publishedYes


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