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Stability and convergence of some parallel iterative subgrid stabilized algorithms for the steady Navier-Stokes equations

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Abstract

Based on finite element discretization and a fully overlapping domain decomposition, we propose and study some parallel iterative subgrid stabilized algorithms for the simulation of the steady Navier-Stokes equations with high Reynolds numbers, where the quadratic equal-order elements are used for the velocity and pressure approximations, and the subgrid-scale model based on an elliptic projection is employed to penalize instability introduced by the dominant convective term in the Navier-Stokes system. In the present algorithms, each subproblem is defined in the whole domain with the vast majority of the degrees of freedom associated with the particular subdomain that it is responsible for and hence can be solved in parallel with other subproblems. All of the subproblems are nonlinear and are independently solved by some iterative methods. Stability and convergence of the proposed parallel iterative algorithms are analyzed under some (strong) uniqueness conditions. Furthermore, new results of stopping criteria for nonlinear iterations are derived. Numerical examples which verify the effectiveness of the proposed algorithms are given.

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Acknowledgements

The authors would like to thank the anonymous referees for their valuable suggestions and comments, which led to an improvement of the paper.

Funding

The work was supported by the Natural Science Foundation of China (No. 11361016), Cooperative Program of Guizhou Provincial Department of Science and Technology, China (No. Qian Ke He LH [2015]7042), and the Natural Science Foundation of Chongqing Municipality, China (No. cstc2021jcyj-msxmX1044).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Southwest University, Chongqing, 400715, People’s Republic of China

    Bo Zheng & Yueqiang Shang

  2. School of Mathematics Science, Zunyi Normal College, Zunyi, 563002, People’s Republic of China

    Jin Qin

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  1. Bo Zheng
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  2. Jin Qin
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  3. Yueqiang Shang
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Correspondence to Yueqiang Shang.

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Zheng, B., Qin, J. & Shang, Y. Stability and convergence of some parallel iterative subgrid stabilized algorithms for the steady Navier-Stokes equations. Adv Comput Math 48, 35 (2022). https://doi.org/10.1007/s10444-022-09950-6

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