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Advances in Numerical Analysis
Volume 2009 (2009), Article ID 370289, 13 pages
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.
- P. Gresho and R. Sani, Incompressible Flow and the Finite Element Method, vol. 2, John Wiley & Sons, New York, NY, USA, 1998.
- U. Frisch, Turbulence, Cambridge University Press, Cambridge, UK, 1995.
- H. K. Moffatt and A. Tsinober, “Helicity in laminar and turbulent flow,” Annual Review of Fluid Mechanics, vol. 24, no. 1, pp. 281–312, 1992.
- Q. Chen, S. Chen, and G. L. Eyink, “The joint cascade of energy and helicity in three-dimensional turbulence,” Physics of Fluids, vol. 15, no. 2, pp. 361–374, 2003.
- C. Foias, D. D. Holm, and E. S. Titi, “The Navier-Stokes-alpha model of fluid turbulence,” Physica D, vol. 152-153, pp. 505–519, 2001.
- L. G. Rebholz, “A family of new, high order NS- models arising from helicity correction in Leray turbulence models,” Journal of Mathematical Analysis and Applications, vol. 342, no. 1, pp. 246–254, 2008.
- N. A. Adams and S. Stolz, “On the approximate deconvolution procedure for LES,” Physics of Fluids, vol. 2, pp. 1699–1701, 1999.
- N. A. Adams and S. Stolz, “Deconvolution methods for subgrid-scale approximation in large eddy simulation,” Modern Simulation Strategies for Turbulent Flow, 2001.
- S. Stolz, N. A. Adams, and L. Kleiser, “An approximate deconvolution model for large-eddy simulation with application to incompressible wall-bounded flows,” Physics of Fluids, vol. 13, no. 4, pp. 997–1015, 2001.
- L. G. Rebholz, “Conservation laws of turbulence models,” Journal of Mathematical Analysis and Applications, vol. 326, no. 1, pp. 33–45, 2007.
- W. J. Layton, C. C. Manica, M. Neda, and L. G. Rebholz, “Helicity and energy conservation and dissipation in approximate deconvolution les models of turbulence,” Advances and Applications in Fluid Mechanics, vol. 4, no. 1, pp. 1–46, 2008.
- W. Layton, C. Manica, M. Neda, and L. Rebholz, “Numerical analysis and computational comparisons of the NS- and NS- regularizations,” to appear in Computer Methods in Applied Mechanics and Engineering.
- W. Layton, I. Stanculescu, and C. Trenchea, “Theory of the NS- model: a complement to the NS- model,” submitted.
- J.-G. Liu and W.-C. Wang, “Energy and helicity preserving schemes for hydro- and magnetohydro-dynamics flows with symmetry,” Journal of Computational Physics, vol. 200, no. 1, pp. 8–33, 2004.
- L. G. Rebholz, “An energy- and helicity-conserving finite element scheme for the Navier-Stokes equations,” SIAM Journal on Numerical Analysis, vol. 45, no. 4, pp. 1622–1638, 2007.
- W. Miles and L. Rebholz, “An enhanced physics based scheme for the NS- turbulence model,” to appear in Numerical Methods for Partial Differential Equations.
- L. C. Berselli, T. Iliescu, and W. J. Layton, Mathematics of Large Eddy Simulation of Turbulent Flows, Scientific Computation, Springer, Berlin, Germany, 2006.
- V. Girault and P.-A. Raviart, Finite Element Methods for Navier-Stokes Equations: Theory and Algorithm, vol. 5 of Springer Series in Computational Mathematics, Springer, Berlin, Germany, 1986.
- W. Layton, Introduction to the Numerical Analysis of Incompressible Viscous Flows, vol. 6 of Computational Science & Engineering, SIAM, Philadelphia, Pa, USA, 2008.
- S. C. Brenner and L. R. Scott, The Mathematical Theory of Finite Element Methods, vol. 15 of Texts in Applied Mathematics, Springer, New York, NY, USA, 1994.
- W. Layton, C. C. Manica, M. Neda, and L. G. Rebholz, “Numerical analysis and computational testing of a high accuracy Leray-deconvolution model of turbulence,” Numerical Methods for Partial Differential Equations, vol. 24, no. 2, pp. 555–582, 2008.
- W. Layton and M. Neda, “Truncation of scales by time relaxation,” Journal of Mathematical Analysis and Applications, vol. 325, no. 2, pp. 788–807, 2007.
- C. C. Manica and S. Kaya Merdan, “Convergence analysis of the finite element method for a fundamental model in turbulence,” Tech. Rep., University of Pittsburgh, 2006.