Introduction to monotone integrated large eddy simulation

Turbulence is proving to be one of nature's most interesting and perplexing problems, challenging theorists, experimentalists, and computationalists equally. On the computational side, direct numerical simulation of idealized turbulence is used to challenge the world's largest computers, even before they are deemed ready for general use. The Earth Simulator, for example, has recently completed a Navier–Stokes solution of turbulence in a periodic box on a 4096 × 4096 × 4096 grid, achieving an effective Reynolds number somewhat in excess of 8000. Such a computation is impossible for nearly every person on the planet. Further, periodic geometry has little attraction for an engineer, and a Reynolds number of 8000 is far too small for most problems of practical importance.

The subject of this chapter is monotone integrated large eddy simulation (LES), or MILES – monotonicity-preserving implicit LES (ILES), a class of practical methods for simulating turbulent high-Reynolds-number flows with complicated, compressible physics and complex geometry. LES has always been the natural way to exploit the full range of computer power available for engineering fluid dynamics. When the dynamics of the energy-containing scales in a complex flow can be resolved, it is a mistake to average them out. Doing so limits the accuracy of the results, because uniform convergence to the physically correct answer, insofar as one exists, is automatically voided at the scale where the averaging has been performed. Even if the computational grid is refined repeatedly, the answer can get no better. At the same time, the overall resolution of a computation suffers when many computational degrees of freedom are expended unnecessarily on unresolved scales.