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Numerical approximation of the Smagorinsky model by a two‐level method

2007; Wiley; Volume: 7; Issue: 1 Linguagem: Inglês

10.1002/pamm.200700754

1617-7061

Jeff Borggaard, Traian Iliescu, Hyesuk Lee, John Paul Roop, Hyunjin Son,

Advanced Numerical Methods in Computational Mathematics

Abstract A two‐level method for discretizing the Smagorinsky model for the numerical simulation of turbulent flows is proposed. In the two‐level algorithm, the solution to the fully nonlinear coarse mesh problem is utilized in a single‐step linear fine mesh problem. When modeling parameters are chosen appropriately, the error in the two‐level algorithm is comparable to the error in solving the fully nonlinear problem on the fine mesh. We provide an a priori error estimate for the two‐level method, which yields appropriate scalings between the coarse and fine mesh‐sizes ( H and h , respectively), and the radius of the spatial filter used in the Smagorinsky model ( δ ). In addition, we provide an algorithm in which a coarse mesh correction is performed to further enhance the accuracy. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)