An implicit high-order spectral difference approach for large eddy simulation

M. Parsani*, G. Ghorbaniasl, C. Lacor, E. Turkel

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

48 Scopus citations


The filtered fluid dynamic equations are discretized in space by a high-order spectral difference (SD) method coupled with large eddy simulation (LES) approach. The subgrid-scale stress tensor is modelled by the wall-adapting local eddy-viscosity model (WALE). We solve the unsteady equations by advancing in time using a second-order backward difference formulae (BDF2) scheme. The nonlinear algebraic system arising from the time discretization is solved with the nonlinear lower-upper symmetric Gauss-Seidel (LU-SGS) algorithm. In order to study the sensitivity of the method, first, the implicit solver is used to compute the two-dimensional (2D) laminar flow around a NACA0012 airfoil at Re=5×105 with zero angle of attack. Afterwards, the accuracy and the reliability of the solver are tested by solving the 2D " turbulent" flow around a square cylinder at Re=104 and Re= 2.2×104. The results show a good agreement with the experimental data and the reference solutions.

Original languageEnglish (US)
Pages (from-to)5373-5393
Number of pages21
JournalJournal of Computational Physics
Issue number14
StatePublished - Jul 2010
Externally publishedYes


  • High-order spectral difference method
  • Implicit LU-SGS algorithm
  • Large eddy simulation
  • Wall-adapting local eddy-viscosity model

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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