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On the interaction between dynamic model dissipation and numerical dissipation due to streamline upwind/Petrov-Galerkin stabilization. (English) Zbl 1091.76027

Summary: 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.

MSC:

76F65 Direct numerical and large eddy simulation of turbulence
76D05 Navier-Stokes equations for incompressible viscous fluids
76M10 Finite element methods applied to problems in fluid mechanics
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