Fluid turbulence is commonly modeled by the Navier-Stokes equations with a large Reynolds number. However, direct numerical simulations are not possible in practice, so that turbulence modeling is introduced. We study artificial spectral viscosity models that render the simulation of turbulence tractable. We show that the models are well posed and have solutions that converge, in certain parameter limits, to solutions of the Navier-Stokes equations. We also show, using the mathematical analyses, how effective choices for the parameters appearing in the models can be made. Finally, we consider temporal discretizations of the models and investigate their stability. © 2009 Springer Science+Business Media, LLC.
M. Gunzburger et al., "Analysis of Nonlinear Spectral Eddy-Viscosity Models of Turbulence," Journal of Scientific Computing, vol. 45, no. 1 thru 3, pp. 294 - 332, Springer, Oct 2010.
The definitive version is available at https://doi.org/10.1007/s10915-009-9335-8
Mathematics and Statistics
Keywords and Phrases
Eddy-Viscosity Models; Navier-Stokes Equations; Spectral Methods; Turbulence
International Standard Serial Number (ISSN)
Article - Journal
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01 Oct 2010
National Science Foundation, Grant DMS-0606671