Large Eddy Simulation based on the Residual-based Variational Multiscale Method and Lagrangian Dynamic Smagorinsky Model

Abstract

In this work, we focus on large eddy simulation (LES) using the finite element method. The use of finite elements is beneficial due to their flexibility for complex problems (e.g., complex geometry, high-order discretizations, adaptivity, parallelization). In order to achieve this, we combine aspects of the residual-based variational multiscale (RBVMS) approach, which provides the basis for stabilized finite element methods, and the dynamic Smagorinsky eddy-viscosity model. For the Smagorinsky model, we employ two dynamic procedures: one that employs spatial averaging over homogeneous directions (which is applicable to turbulent flows with statistical homogeneity) and the other is based on Lagrangian, or fluid pathline, averaging (which is applicable to inhomogeneous turbulent flows). In this study, we consider three models. One model is solely based on the RBVMS approach. The other two models combine the cross-stress terms due to the RBVMS model with the dynamic Smagorinsky eddy-viscosity model for the Reynolds stress terms. In the two combined models, we employ a different type of averaging in each model. We present results using these models on two cases: turbulent channel flow (Reτ = 590) and flow over a cylinder (ReD = 3, 900). For the turbulent channel flow, all models provide similar predictions while for the flow over a cylinder, the combined model provides a better prediction.