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A two-step stabilized finite element algorithm for the Smagorinsky model

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  • Zheng, Bo
  • Shang, Yueqiang

Abstract

This study considers an efficient two-step stabilized finite element algorithm for the simulation of Smagorinsky model, which involves solving a stabilized nonlinear Smagorinsky problem by the lowest equal-order P1−P1 finite elements and solving a stabilized linear Smagorinsky problem by the quadratic equal-order P2−P2 finite elements. We theoretically and numerically show that the present two-step algorithm can provide an approximate solution with basically the same accuracy as that of solving the stabilized P2−P2 finite element method, and represent a reduction in CPU time.

Suggested Citation

  • Zheng, Bo & Shang, Yueqiang, 2022. "A two-step stabilized finite element algorithm for the Smagorinsky model," Applied Mathematics and Computation, Elsevier, vol. 422(C).
    • Handle: RePEc:eee:apmaco:v:422:y:2022:i:c:s0096300322000571
    DOI: 10.1016/j.amc.2022.126971
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    References listed on IDEAS

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    1. An, Rong & Li, Yuan & Zhang, Yuqing, 2016. "Error estimates of two-level finite element method for Smagorinsky model," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 786-800.
    2. Zheng, Bo & Shang, Yueqiang, 2020. "Local and parallel stabilized finite element algorithms based on the lowest equal-order elements for the steady Navier–Stokes equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 178(C), pages 464-484.
    3. Shi, Dongyang & Li, Minghao & Li, Zhenzhen, 2019. "A nonconforming finite element method for the stationary Smagorinsky model," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 308-319.
    4. Zheng, Bo & Shang, Yueqiang, 2019. "Parallel iterative stabilized finite element algorithms based on the lowest equal-order elements for the stationary Navier–Stokes equations," Applied Mathematics and Computation, Elsevier, vol. 357(C), pages 35-56.
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