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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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New SAV-pressure correction methods for the Navier-Stokes equations: stability and error analysis
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by Xiaoli Li, Jie Shen and Zhengguang Liu HTML | PDF
Math. Comp. 91 (2022), 141-167 Request permission

Abstract:

We construct new first- and second-order pressure correctionschemes using the scalar auxiliary variable approach for the Navier-Stokes equations. These schemes are linear, decoupled and only require solving a sequence of Poisson type equations at each time step. Furthermore, they are unconditionally energy stable. We also establish rigorous error estimates in the two dimensional case for the velocity and pressure approximation of the first-order scheme without any condition on the time step.
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Additional Information
  • Xiaoli Li
  • Affiliation: School of Mathematics, Shandong University, Jinan, Shandong 250100, People’s Republic of China
  • MR Author ID: 1152951
  • Email: xiaolisdu@163.com
  • Jie Shen
  • Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
  • MR Author ID: 257933
  • ORCID: 0000-0002-4885-5732
  • Email: shen7@purdue.edu
  • Zhengguang Liu
  • Affiliation: School of Mathematics and Statistics, Shandong Normal University, Jinan, Shandong 250358, People’s Republic of China
  • ORCID: 0000-0002-3345-2148
  • Email: liuzhgsdu@yahoo.com
  • Received by editor(s): May 3, 2020
  • Received by editor(s) in revised form: February 3, 2021
  • Published electronically: October 5, 2021
  • Additional Notes: The work of the first author was supported by the National Natural Science Foundation of China grants 11901489, 11971407. The work of the second author was supported in part by NSF grant DMS-2012585 and AFOSR grant FA9550-20-1-0309. The work of the third author was supported by the National Natural Science Foundation of China grant 12001336 and China Postdoctoral Science Foundation grant 2020M672111
  • © Copyright 2021 American Mathematical Society
  • Journal: Math. Comp. 91 (2022), 141-167
  • MSC (2020): Primary 35Q30, 65M12, 65J15
  • DOI: https://doi.org/10.1090/mcom/3651
  • MathSciNet review: 4350535