A bounded artificial viscosity large eddy simulation model

In this paper, we present a rigorous numerical analysis for a bounded artificial viscosity model (τ =μδσ α(δ∥▽ su∥F) ▽s u) for the numerical simulation of turbulent flows. In practice, the commonly used Smagorinsky model (τ =(cs δ)2 u∥▽su∥F) ▽s 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 strategics strongly rely upon a priori knowledge of the flow regime. The bounded artificial viscosity model relics on a highly nonlinear, but monotone and smooth, semilincar 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. © 2009 Society for Industrial and Applied Mathematics.