Numerical approximation of the Smagorinsky model by a two-level method |
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| Authors: | Jeff Borggaard Traian Iliescu Hyesuk Lee John Paul Roop Hyunjin Son |
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| Affiliation: | 1. Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA;2. Department of Mathematical Sciences, Clemson University, Clemson, SC 29634, USA;3. Department of Mathematics, North Carolina A & T State University, Greensboro, NC 27411, USA |
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| 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) |
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