Scalable semismooth Newton methods with multilevel domain decomposition for subsurface flow and reactive transport in porous media

Tianpei Cheng, Haijian Yang, Chao Yang, Shuyu Sun

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


Large-scale modeling and predictive simulations of the subsurface flow and reactive transport system in porous media is significantly challenging, due to the high nonlinearity of the governing equations and the strong heterogeneity of material coefficients. The design of novel mathematical models and state-of-the-art methods for the flow simulation through porous media typically needs to satisfy the so-called bound-preserving property, i.e., the computed solution should stay inside a physically meaningful range. This paper presents a robust, scalable numerical framework based on the variational inequality formulation and the semismooth Newton method in a fully implicit manner, to model and simulate highly nonlinear flows without violating the boundedness requirement of the solution. Rigorous theoretical analysis for the variational inequality formulation of the problem is provided for facilitating the design of algorithms. Specifically, our approach further enhances the numerical formulation by utilizing a family of multilevel monolithic overlapping Schwarz methods for efficiently preconditioning, and the parallel implementation of the bound-preserving solver is based on the fast and robust domain decomposition technique. Numerical experiments are presented to demonstrate the efficiency and parallel scalability of the solution strategy for both standard benchmarks as well as realistic flow problems involving strong heterogeneity and high nonlinearity. We also show that the proposed framework is more robust and efficient than the commonly used inexact Newton algorithm in terms of the bound-preserving property.
Original languageEnglish (US)
Pages (from-to)111440
JournalJournal of Computational Physics
StatePublished - Jul 14 2022

Bibliographical note

KAUST Repository Item: Exported on 2022-09-14
Acknowledged KAUST grant number(s): BAS/1/1351-01, URF/1/3769-01, URF/1/4074-01
Acknowledgements: The authors would like to express their appreciations to the anonymous reviewer for the invaluable comments that have greatly improved the quality of the manuscript. This work is partially supported by the National Natural Science Foundation of China (No. 12131002 and No. 11971006), the Hunan Province Natural Science Foundation of China (No. 2020JJ2002). The fourth author also greatly thanks for the support from King Abdullah University of Science and Technology (KAUST) through the grants BAS/1/1351-01, URF/1/4074-01, and URF/1/3769-01.

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)
  • Computer Science Applications


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