Active-Set Reduced-Space Methods with Nonlinear Elimination for Two-Phase Flow Problems in Porous Media
Type
ArticleAuthors
Yang, HaijianYang, Chao-he

Sun, Shuyu

KAUST Department
Earth Science and Engineering ProgramPhysical Sciences and Engineering (PSE) Division
Date
2016-07-26Online Publication Date
2016-07-26Print Publication Date
2016-01Permanent link to this record
http://hdl.handle.net/10754/619780
Metadata
Show full item recordAbstract
Fully implicit methods are drawing more attention in scientific and engineering applications due to the allowance of large time steps in extreme-scale simulations. When using a fully implicit method to solve two-phase flow problems in porous media, one major challenge is the solution of the resultant nonlinear system at each time step. To solve such nonlinear systems, traditional nonlinear iterative methods, such as the class of the Newton methods, often fail to achieve the desired convergent rate due to the high nonlinearity of the system and/or the violation of the boundedness requirement of the saturation. In the paper, we reformulate the two-phase model as a variational inequality that naturally ensures the physical feasibility of the saturation variable. The variational inequality is then solved by an active-set reduced-space method with a nonlinear elimination preconditioner to remove the high nonlinear components that often causes the failure of the nonlinear iteration for convergence. To validate the effectiveness of the proposed method, we compare it with the classical implicit pressure-explicit saturation method for two-phase flow problems with strong heterogeneity. The numerical results show that our nonlinear solver overcomes the often severe limits on the time step associated with existing methods, results in superior convergence performance, and achieves reduction in the total computing time by more than one order of magnitude.Citation
Active-Set Reduced-Space Methods with Nonlinear Elimination for Two-Phase Flow Problems in Porous Media 2016, 38 (4):B593 SIAM Journal on Scientific ComputingSponsors
The authors would like to thank the anonymous reviewers for the valuable suggestions leading to the improvement of the paper.Additional Links
http://epubs.siam.org/doi/10.1137/15M1041882ae974a485f413a2113503eed53cd6c53
10.1137/15M1041882