An $h$-Adaptive Operator Splitting Method for Two-Phase Flow in 3D Heterogeneous Porous Media

Chih-Che Chueh, Ned Djilali, Wolfgang Bangerth

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


The simulation of multiphase flow in porous media is a ubiquitous problem in a wide variety of fields, such as fuel cell modeling, oil reservoir simulation, magma dynamics, and tumor modeling. However, it is computationally expensive. This paper presents an interconnected set of algorithms which we show can accelerate computations by more than two orders of magnitude compared to traditional techniques, yet retains the high accuracy necessary for practical applications. Specifically, we base our approach on a new adaptive operator splitting technique driven by an a posteriori criterion to separate the flow from the transport equations, adaptive meshing to reduce the size of the discretized problem, efficient block preconditioned solver techniques for fast solution of the discrete equations, and a recently developed artificial diffusion strategy to stabilize the numerical solution of the transport equation. We demonstrate the accuracy and efficiency of our approach using numerical experiments in one, two, and three dimensions using a program that is made available as part of a large open source library. © 2013 Society for Industrial and Applied Mathematics.
Original languageEnglish (US)
Pages (from-to)B149-B175
Number of pages1
JournalSIAM Journal on Scientific Computing
Issue number1
StatePublished - Jan 2013
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: This author’s work was supported by award KUS-C1-016-04, made by the King Abdullah University of Science and Technology, by the ComputationalInfrastructure in Geodynamics initiative through the NSF under award EAR-0949446 and The Universityof California–Davis, and through an Alfred P. Sloan Research Fellowship.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.


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