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Advances in Numerical Analysis
Volume 2009 (2009), Article ID 370289, 13 pages
Research Article

Enhanced Physics-Based Numerical Schemes for Two Classes of Turbulence Models

Department of Mathematical Sciences, Clemson University, Clemson, SC 29634, USA

Received 29 June 2009; Accepted 5 August 2009

Academic Editor: William John Layton

Copyright © 2009 Leo G. Rebholz. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We present enhanced physics-based finite element schemes for two families of turbulence models, the N S - 𝜔 models and the Stolz-Adams approximate deconvolution models. These schemes are delicate extensions of a method created for the Navier-Stokes equations in Rebholz (2007), that achieve high physical fidelity by admitting balances of both energy and helicity that match the true physics. The schemes' development requires carefully chosen discrete curl, discrete Laplacian, and discrete filtering operators, in order to permit the necessary differential operator commutations.