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A Bounded Artificial Viscosity Large Eddy Simulation Model

2009; Society for Industrial and Applied Mathematics; Volume: 47; Issue: 1 Linguagem: Inglês

10.1137/060656164

1095-7170

Jeff Borggaard, Traian Iliescu, John Paul Roop,

Computational Fluid Dynamics and Aerodynamics

In this paper, we present a rigorous numerical analysis for a bounded artificial viscosity model ($\tau=\mu\delta^\sigma a(\delta\|\nabla^s\bm{u}\|_F)\nabla^s\bm{u})$ for the numerical simulation of turbulent flows. In practice, the commonly used Smagorinsky model ($\tau=(c_s\delta)^2\|\nabla^s\bm{u}\|_F\,\nabla^s\bm{u}$) is overly dissipative and yields unphysical results. To date, several methods for "clipping" the Smagorinsky viscosity have proven useful in improving the physical characteristics of the simulated flow. However, such heuristic strategies strongly rely upon a priori knowledge of the flow regime. The bounded artificial viscosity model relies on a highly nonlinear, but monotone and smooth, semilinear elliptic form for the artificial viscosity. For this model, we have introduced a variational computational strategy, provided finite element error convergence estimates, and included several computational examples indicating its improvement on the overly diffusive Smagorinsky model.