Applications of a variational multiscale method for large eddy simulation of turbulent flows on moving/deforming unstructured grids

In this paper, the three-level formulation of a variational multiscale (VMS) large eddy simulation (LES) method for compressible flow computations [B. Koobus, C. Farhat, A variational multiscale method for the large eddy simulation of compressible turbulent flows on unstructured meshes—application to vortex shedding, Comput. Methods Appl. Mech. Eng. 193 (2004) 1367–1384; C. Farhat, A. Rajasekharan, B. Koobus, A dynamic variational multiscale method for large eddy simulations on unstructured meshes, Comput. Methods Appl. Mech. Eng. 195 (2006) 1667–1691] is extended for applications involving moving/deforming grids. A consistent method to improve the VMS-LES method by computing the small scale Smagorinsky constant (Cs′) dynamically [C. Farhat, A. Rajasekharan, B. Koobus, A dynamic variational multiscale method for large eddy simulations on unstructured meshes, Comput. Methods Appl. Mech. Eng. 195 (2006) 1667–1691; A. Rajasekharan, Variationally consistent multiscale formulations and ALE time integrators for large eddy simulation of turbulent flows on dynamic grids, Ph.D. Dissertation, Stanford University, 2008] as the flow develops (dynamic VMS-LES) is also extended for dynamic grid applications. Two applications of VMS-LES for the simulation of separated flow over moving NACA-0012 extruded airfoil is then presented. The first application involves a qualitative simulation exploring the Knoller–Betz effect [K.D. Jones, C.M. Dohring, M.F. Platzer, Experimental and computational investigation of the Knoller–Betz effect, AIAA J. 36(7) (1998) 1240–1246] of the heaving airfoil at high Strouhal number. The second application is that of the pitching airfoil undergoing dynamic stall. The results predicted by the dynamic VMS-LES method are compared to those obtained with other turbulence models and to experimental data and it is found that the dynamic VMS-LES performs better than the other considered static and dynamic LES models.