A Methodology for Simulations of Complex Turbulent Flows

Abstract

A new flow simulation methodology (FSM) for computing turbulent shear flows is presented. The development of FSM was initiated in close collaboration with C. Speziale (then at Boston University). The centerpiece of FSM is a strategy to provide the proper amount of modeling of the subgrid scales. The strategy is implemented by use of a “contribution function” which is dependent on the local and instantaneous “physical” resolution in the computation. This physical resolution is obtained during the actual simulation by comparing the size of the smallest relevant scales to the local grid size used in the computation. The contribution function is designed such that it provides no modeling if the computation is locally well resolved so that the computation approaches a direct numerical simulation in the fine grid limit, or provides modeling of all scales in the coarse grid limit and thus approaches an unsteady RANS calculation. In between these resolution limits, the contribution function adjusts the necessary modeling for the unresolved scales while the larger (resolved) scales are computed as in traditional large-eddy simulations (LES). However, a LES that is based on the present strategy is distinctly different from traditional LES in that the required amount of modeling is determined by physical considerations, and that state-of-the-art turbulence models (as developed for Reynolds-averaged Navier-Stokes) can be employed for modeling of the unresolved scales. Thus, in contrast to traditional LES based on the Smagorinsky model, with FSM a consistent approach (in the local sense) to the coarse grid and fine grid limits is possible. As a consequence of this, FSM should require much fewer grid points for a given calculation than traditional LES or, for a given grid size, should allow computations for larger Reynolds numbers. In the present paper, the fundamental aspects of FSM are presented and discussed. Several examples are provided. The examples were chosen such that they expose, on the one hand, the inherent difficulties of simulating complex wall bounded flows, and on the other hand demonstrate the potential of the FSM approach.