On the interaction between dynamic model dissipation and numerical dissipation due to streamline upwind/Petrov-Galerkin stabilization

Here we investigate the roles of physical and numerical subgrid-scale modeling. The subgrid-scales are represented by a physical large-eddy simulation 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 stabilization for finite element discretizations 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. We study the interaction between the physical and numerical models by analyzing energy dissipation associated to the two. Based on this study, a modification to the dynamic model is proposed as a way to discount the numerical method's algorithmic dissipation from the total subgrid-scale dissipation. The modified dynamic model is shown to be successful in simulations of turbulent channel flow.