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

Lizhen Chen, Tao Tang, Chuanju Xu*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review


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.

Original languageEnglish
Article number4
Number of pages20
JournalAdvances in Aerodynamics
Issue number1
Early online date17 Jan 2022
Publication statusPublished - Dec 2022

Scopus Subject Areas

  • Civil and Structural Engineering
  • Aerospace Engineering
  • Mechanical Engineering
  • Renewable Energy, Sustainability and the Environment
  • Modelling and Simulation

User-Defined Keywords

  • Navier-Stokes equations
  • Spectral vanishing viscosity
  • Triangular spectral element method


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