Regularization modeling of buoyancy-driven flows

Abstract

Simulation of turbulent flow by means of direct numerical simulation (DNS) and large-eddy simulation (LES) started almost fifty years ago. Probably the earliest paper on the application of LES was by Smagorinksy in the March 1963 issue of Monthly Weather Review. Although Smagorinsky did not mention the term largeeddy simulation explicitly, he proposed a model to represent the effects of smallscale eddies on the large-scale dynamics of the flow, which was treated explicitly. Smagorinsky applied his now famous model to the simulation and study of the dynamics of the general circulation in the earth's atmosphere. Direct numerical simulation of wall-bounded flows started some twenty years later with the well-known 1987 paper in the Journal of Fluid Mechanics by Kim, Moin and Moser on DNS of turbulent channel flow at a bulk Reynolds number of 3300. Although DNS had been applied before on homogeneous, isotropic turbulence and some preliminary studies on under-resolved channel flow had been performed, this paper presented the first fully resolved DNS of a wall-bounded turbulent flow. The large number of citations reported on Web of Science proves the tremendous impact both papers had and still have on research in turbulence. The continuing growth of computational power has increasingly stimulated the usage of DNS and LES, since LES and in some applications even DNS can now be used as a design tool for several practical and industrial problems. This is reflected by the possibility of CFD software packages to perform LES, although this should still be treated with care. On the other hand, for flow in simple geometries, such as channel flow, DNS has been extended to higher and higher Reynolds numbers, which brings the study of fundamental properties of turbulent flow at large Reynolds numbers within reach. These examples highlight the two major reasons for usage of DNS and LES: application-driven research and fundamental research into the nature of turbulence and into turbulence models. The history of this research over the past two decades can well be grasped from the contents of the ERCOFTAC series of Workshops on Direct and Large-Eddy Simulation.