Finite-volume optimal large-eddy simulation of isotropic turbulence

The feasibility of an optimal finite-volume large-eddy simulation (LES) model for isotropic turbulence is evaluated. This modeling approach is based on the approximation of the ideal LES by a stochastic estimate of the fluxes in a finite-volume representation of the Navier-Stokes equation. Stochastic estimation of the fluxes allows for the simultaneous treatment of Navier-Stokes, discretization and subgrid effects, yielding a compact, yet accurate scheme for the large eddy simulation of isotropic turbulence. Both global and local models based on optimal finite-volume LES are developed and used in a priori tests guiding the choice of stencil geometry and model inputs. The most promising models in the a priori exams are tested in actual simulations (i.e., a posteriori) and the results compared with those for filtered direct numerical simulation (DNS) and the dynamic Smagorinsky model. The a posteriori performance of the optimal finite-volume LES models, evaluated by the energy spectrum and third-order structure function, is superior to that of the dynamic Smagorinsky model on a coarse grid. While applicability to other cases is currently limited by the dependence of the present approach on DNS statistical data, research is underway to remove this requirement. (C) 2004 American Institute of Physics.