AuthorA. E. Tejada-Martinez
TitleDynamic Subgrid-Scale Modeling for Large-Eddy Simulation of Turbulent Flows with a Stabilized Finite Element Method
SchoolRensselaer Polytechnic Institute
AbstractThis thesis is concerned with large-eddy simulation (LES) of turbulent flows in which the large scales of the flow are resolved numerically, while their interactions with the small scales or subgrid-scales are modeled. The goal is to understand and better model the dynamics of the subgrid-scales. In the simulations considered here, the subgrid-scales are represented by a physical LES model, namely the popular dynamic Smagorinsky model (or simply dynamic model), as well as by a numerical model in the form of the well-known streamline upwind / Petrov-Galerkin (SUPG) stabilization for finite element discretiza-tions of advection-diffusion systems. The latter is not a physical model, as its purpose is to provide sufficient algorithmic dissipation for a stable, consistent, and convergent numerical method. In the first part of this work, various finite element-based , low-pass, spatial test filters, required for computing the dynamic model, are proposed and analyzed. A number of simulations of decaying isotropic turbulence are performed to understand the dependence of the dynamic model on the test filter of choice. From these numerical experiments, key assumptions are extracted leading to the derivation of two new dynamic models in which the sole model parameter is computed dynamically. The second of these models is parameter-free. Traditionally, the dynamic model parameter has been taken as a constant. Both new dynamic models are tested on decaying isotropic turbulence and the parameter-free model is also tested on turbulent channel flow. In the latter part of this work, the interaction between the physical and numerical models is studied by analyzing energy dissipation associated to these two. Based on this study, a modified dynamic model is proposed, characterized by a coupling between the previously mentioned physical model and the numerical model. The modified dynamic model is shown to be successful in simulations of turbulent channel flow. The physical models proposed herein provide accounting of the numerical methods implicit filtering characteristics as well as discounting of the numerical method's dissipative nature.
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