Parallel multilevel domain decomposition preconditioners for monolithic solution of non-isothermal flow in reservoir simulation

Mei Zhang, Haijian Yang, Shuhong Wu, Shuyu Sun

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


In reservoir simulation, the non-isothermal flow adds a conservation of the energy equation with the involvement of a temperature variable to the complicated physics dynamics, which brings a higher nonlinearity of the corresponding PDE system and therefore exhibits significantly additional challenges on the linear preconditioner of the simulator. However, the commonly used block preconditioning techniques mostly focus on the isothermal petroleum model and do not have a specific treatment of the energy conservation equation for the non-isothermal flow. In this study, we propose and develop a family of multilevel restricted additive Schwarz (MRAS) preconditioners on parallel computers for the fully implicit solution of the non-isothermal flow in porous media. The proposed parallel reservoir simulator incorporates the restricted additive Schwarz preconditioner into a general multilevel preconditioning framework with the use of the domain decomposition technique and the multigrid method, which allows us to flexibly construct several types of multilevel Schwarz preconditioners by using the additive or multiplicative strategies. In particular, it follows the fully implicit discretization scheme for the monolithic solution, and therefore is unconditionally stable with the relaxation of the time step size by the stability condition. We numerically show that the proposed approach is highly robust and efficient for solving some non-isothermal flow problems with high nonlinearity, and good parallel scalabilities are obtained on a supercomputer with a large number of processors.
Original languageEnglish (US)
Pages (from-to)105183
JournalComputers and Fluids
StatePublished - Oct 15 2021

Bibliographical note

KAUST Repository Item: Exported on 2021-10-26
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 reviewers 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. 11971006 and No. 11871069), the Hunan Province Natural Science Foundation of China (No. 2020JJ2002), and the PetroChina Innovation Foundation of China (No. 2019D-5007-0213). The fourth author also greatly thank for the support from King Abdullah University of Science and Technology (KAUST, Saudi Arabia through the grants BAS/1/1351-01, URF/1/4074-01, and URF/1/3769-01.

ASJC Scopus subject areas

  • General Engineering
  • General Computer Science


Dive into the research topics of 'Parallel multilevel domain decomposition preconditioners for monolithic solution of non-isothermal flow in reservoir simulation'. Together they form a unique fingerprint.

Cite this