Realizable Versus Non-Realizable Dynamic Subgrid-Scale Stress Models

Stefan Heinz∗ and Harish Gopalan 1000 East University Avenue, Department of Mathematics, University of Wyoming, Laramie 82071, USA Abstract The existence of many different dynamic large eddy simulation (LES) methods leads to questions about the theoretical foundation of dynamic LES methods. It was shown recently that the use of stochastic analysis enables a theoretically well based systematic derivation of a realizable linear dynamic model (LDM) and a realizable nonlinear dynamic model (NDM). A-priori and a-posteriori analyses of turbulent channel flow are used here to study the characteristic properties of these dynamic models. The LDM and NDM are compared with other dynamic models: the non-stabilized and stabilized dynamic Smagorinsky model (DSM), which is used in many applications of LES, and Wang-Bergstrom’s dynamic model (WBDM), which represents an extension of the DSM. The DSM and WBDM do not represent realizable models because they are not derived as consequences of a realizable stochastic process. The comparisons reported here show that the LDM and NDM are based on a dynamic model formulation that avoids shortcomings of existing concepts. The LDM and NDM account for backscatter, and they are computationally stable without any modification. The LDM and NDM represent the instantaneous small scale structure of turbulence very well. Compared to the DSM and WBDM, respectively, the LDM and NDM are computationally more efficient.