A fractal model for large eddy simulation of turbulent flow

A new class of subgrid closures for large eddy simulation (LES) of turbulence is developed, based on the construction of synthetic, fractal subgrid-scale fields. The relevant mathematical tool, fractal interpolation, allows to interpolate the resolved velocity with fields that have fluctuations down to much smaller scales and to compute the required stresses explicitly. In one dimension, the approach is used in the context of the coarse-grained Burgers equation. Then, fractal interpolation is extended to three dimensions and is used to formulate a subgrid model for the filtered Navier-Stokes equations, The model is applied to LES of both steady and freely decaying isotropic turbulence. We find that the assumption of fractality per se is not enough to yield physically meaningful results, and we explore several variants of the model in which the rules to generate the synthetic fields explicitly incorporate the condition that energy dissipation take place. In one dimension, this is accomplished by means of an additional transport equation that allows to dynamically determine the fractal dimension. In three dimensions, good results are obtained only once the fractal dimension is allowed to vary in different eigendirections of the resolved strain-rate tensor so as to (nearly) maximize energy dissipation. (C) 1999 Elsevier Science B.V. All rights reserved.