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

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.