A new dynamic two-parameter mixed model for large-eddy simulation

Abstract

A new dynamic subgrid-scale (SGS) mixed model is proposed for large-eddy simulation of turbulent flows. This model is based on the decomposition of the SGS stress terms into the modified Leonard, modified cross and modified SGS Reynolds stress terms. In this model, the modified Leonard term is computed explicitly. The modified cross term and modified SGS Reynolds stress are assumed to be proportional to a new term, the form of which is comparable to the generalized central moment, derived as an extension of the filtered Bardina model proposed by Horiuti [J. Phys. Soc. Jpn. 66, 91 (1997)]. Using a linear combination of this new term with the Smagorinsky model for the modified SGS Reynolds stress, the proposed model contains two model parameters, which are computed dynamically. Two formulations for the test-filtered SGS stress reported by Zang et al. [Phys. Fluids A 5, 3186 (1993)] and Vreman et al. [Phys. Fluids 6, 4057 (1994)] are compared, and the compatibility of the SGS models with the standard dynamic SGS model procedure is discussed. The proposed model is assessed for incompressible channel and mixing layer flows, in comparison with the dynamic Smagorinsky model of Germano et al. [Phys. Fluids A 3, 1760 (1991)], the dynamic mixed model of Zang et al. and the dynamic two-parameter mixed model of Salvetti and Banerjee [Phys. Fluids 7, 2831 (1995)]. In the “a priori” test, the proposed model gave the closest agreement with the modified cross term as well as the modified SGS Reynolds stress term. It is shown that the proposed term represents a more general model of the SGS stress than the modified Leonard term and yields a more accurate approximation. These SGS models are tested further in actual LES of channel and mixing layer flows (“a posteriori” test). The results were consistent with those of the “a priori” tests; the proposed model yielded the most accurate results. In the proposed model, the SGS quantities were predominantly represented using the new term, and the contribution of the Smagorinsky model was minimal. The two parameters contained in the model were determined locally in space on a point-by-point basis.

Effects of subgrid-scale modeling on time correlations in large eddy simulation

“…The Smagorinsky model 1 is the classic eddy viscosity model. Although it is no longer often applied in its original form, it is the basis of much more commonly used models like the dynamic model, 2 various ''mixed'' models, 3,4 and more specialized spectral SGS models for homogeneous turbulence. 5,6 Eddy viscosity models attempt to describe the transfer of energy between the resolved and unresolved scales.…”

Toward the development of an anisotropy-resolving subgrid-scale model for large eddy simulation

“…Since the success of LES depends strongly on the accurate representation of the SGS stresses, a number of research groups have proposed several kinds of SGS models for τ i j (see for example, Germano et al, 1991;Lilly, 1992;Zang et al, 1993;Vreman et al, 1994;Salvetti and Banerjee, 1995;Horiuti, 1997;Sarghini et al, 1999;Morinishi and Vasilyev, 2001). Although these models have provided encouraging results, there still remain several aspects to be further improved.…”

Large eddy simulation of turbulent channel flows by the rational large eddy simulation model

“…We note that, for both types of model, the best results in actual LES simulations were obtained by using the dynamic mixed procedure. 23,28 In fact, it has been noted before 9,23,24,28 that there are strong ties between the gradient model and the scale-similarity model: the first term in the Taylor series expansion of the scale-similarity model is indeed the gradient model. As noted by Winckelmans et al, 23 however, the other terms in the expansion are different.…”

“…Some of these limitations are circumvented by using a dynamic procedure in calculating the Smagorinsky constant, yielding the dynamic subgrid-scale eddy-viscosity model introduced by Germano et al, 7 and used in many studies. 8,9 Another class of LES models is the scale-similarity one. The scale-similarity model, introduced by Bardina et al, 6 postulates that the full structure of the velocity field at scales below the filter width is similar to that at scales above the filter width.…”