Fernando F. Grinstein and Christer Fureby European Conference on Computational Fluid Dynamics ECCOMAS CFD 2006 P. Wesseling, E. Oñate, J. Périaux (Eds) © TU Delft, Delft The Netherland, 2006 RECENT PROGRESS ON FLUX-LIMITING BASED IMPLICIT LARGE EDDY SIMULATION Fernando F. Grinstein 1 and Christer Fureby 2 1 Applied Physics Division, Los Alamos National Laboratory, MS-F699, Los Alamos, NM 87545, USA e-mail: fgrinstein@lanl.gov 2 The Swedish Defence Research Agency, FOI, SE-172 90, Stockholm, Sweden e-mail: fureby@foi.se Key Words: LES, implicit LES, limiting, non-oscillatory, modified equation Abstract. We review our recent progress in understanding the theoretical basis of Implicit Large Eddy Simulation (ILES) and fundamental features relating to its performance. We use the Modified Equation Analysis (MEA) to show that the leading order truncation error terms intro- duced by a particular class of hybrid methods provide implicit Subgrid Scale (SGS) models simi- lar in form to those of conventional mixed SGS models. Major properties of the implicit SGS model are related to: (i) the choice of high- and low-order schemes – where the former is well- behaved in smooth flow regions and the latter is well-behaved near sharp gradients; (ii) the choice of flux-limiter which determines how these schemes are blended locally, depending on the flow; (iii) the balance of the dissipation and dispersion contributions to the numerical solution, which depend on the design details of each numerical method. The possibility of achieving ILES performance enhancements through improved design of the SGS physics capturing capabilities of the high resolution methods is emphasized in this context. Results from recent tests of the per- formance of various hybrid algorithms suitable for ILES is then demonstrated in the case of the Taylor-Green vortex (TGV) problem. The results show robustness of ILES in capturing estab- lished theoretical findings for transition and turbulence decay, in terms of the characteristic evo- lution of the kinetic energy dissipation, energy spectra, and enstrophy. 1 INTRODUCTION In nearly every area of fluid mechanics, our understanding is inhibited by the presence of turbulence. Although many experimental and theoretical studies in the past have significantly helped to increase our physical understanding, a predictive closed theory of turbulent flows has not yet been established and is unlikely to emerge in the foreseeable future. Moreover, even with the capabilities of today’s supercomputers, it is not possible to compute high-Reynolds (Re) number turbulent flows directly, by fully resolving all relevant scales of motions in space and time. Instead, at least part of the unsteady turbulent motion must be approximated, to make these calculations feasible. The grand challenge is to develop simulation models that although may not be explicitly incorporating all dynamic scales will still give accurate and reliable results for at least the larger energy-containing scales of flow motion. The current drive is towards Large Eddy Simulation (LES) in which the large scale struc- tures are resolved, the smaller flow features (presumably more isotropic and universal) are fil-