## Abstract

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=5×10^{5} 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=10^{4} and Re= 2.2×10^{4}. The results show a good agreement with the experimental data and the reference solutions.

Original language | English (US) |
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Pages (from-to) | 5373-5393 |

Number of pages | 21 |

Journal | Journal of Computational Physics |

Volume | 229 |

Issue number | 14 |

DOIs | |

State | Published - Jan 1 2010 |

## Keywords

- 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)
- Physics and Astronomy(all)
- Computer Science Applications
- Computational Mathematics
- Applied Mathematics