A subgrid-scale model based on the estimation of unresolved scales of turbulence

Abstract

A new method for large eddy simulations is described and evaluated. In the proposed method the primary modeled quantity is the unfiltered velocity field appearing in the definition of the subgrid-scale stress tensor. An estimate of the unfiltered velocity is obtained by expanding the resolved large-scale velocity field to subgrid-scales two times smaller than the grid scale. The estimation procedure consists of two steps. The first step utilizes properties of a filtering operation and the representation of quantities in terms of basis functions such as Fourier polynomials. In the second step, the phases associated with the newly computed smaller scales are adjusted in order to correspond to the small-scale phases generated by nonlinear interactions of the large-scale field. The estimated velocity field is expressed entirely in terms of the known, resolved velocity field without any adjustable constants. The modeling procedure is evaluated in a priori analyses using direct numerical simulation results of channel flow at low Reynolds number and in actual large eddy simulations of channel flow at two different Reynolds numbers. In all cases, the new model performs better than or comparable to classical eddy viscosity models for the majority of physical quantities. In particular, all components of the subgrid-scale stress tensor are predicted accurately and the procedure naturally accounts for backscatter without any adverse effects on the numerical stability.