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Research | Open Access

Efficient SVV stabilized triangular spectral element methods for incompressible flows of high Reynolds numbers

Lizhen Chen1, Tao Tang2,3, Chuanju Xu4()
Beijing Computational Science Research Center, Beijing, 100193, People’s Republic of China
Division of Science and Technology, BNU-HKBU United International College, Zhuhai, Guangdong, People’s Republic of China
Guangdong Provincial Key Laboratory of Computational Science and Material Design, Southern University of Science and Technology, Shenzhen, People’s Republic of China
School of Mathematical Sciences, and Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing, Xiamen University, Xiamen, 361005, People’s Republic of China
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Abstract

In this paper, we propose a spectral vanishing viscosity method for the triangular spectral element computation of high Reynolds number incompressible flows. This can be regarded as an extension of a similar stabilization technique for the standard spectral element method. The difficulty of this extension lies in the fact that a suitable definition of spectral vanishing viscosity operator in non-structured elements does not exist, and it is not clear that if a suitably defined spectral vanishing viscosity provides desirable dissipation for the artificially accumulated energy. The main contribution of the paper includes: 1) a well-defined spectral vanishing viscosity operator is proposed for non-standard spectral element methods for the Navier-Stokes equations based on triangular or tetrahedron partitions; 2) an evaluation technique is introduced to efficiently implement the stabilization term without extra computational cost; 3) the accuracy and efficiency of the proposed method is carefully examined through several numerical examples. Our numerical results show that the proposed method not only preserves the exponential convergence, but also produces improved accuracy when applied to the unsteady Navier-Stokes equations having smooth solutions. Especially, the stabilized triangular spectral element method efficiently stabilizes the simulation of high Reynolds incompressible flows.

Keywords

Navier-Stokes equationsTriangular spectral element methodSpectral vanishing viscosity

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Advances in Aerodynamics
Volume 4 Issue 1,
December 2022
Pages 4-4
DOI: 10.1186/s42774-021-00090-x
Cite this article:
Chen L, Tang T, Xu C. Efficient SVV stabilized triangular spectral element methods for incompressible flows of high Reynolds numbers. Advances in Aerodynamics, 2022, 4(1): 4. https://doi.org/10.1186/s42774-021-00090-x
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