Turbulence: Subgrid-Scale Modeling

From Scholarpedia

Author: Prof. Charles Meneveau, Johns Hopkins University

Prof. Charles Meneveau accepted the invitation on 26 April 2009 (self-imposed deadline: 26 December 2009).

Turbulent flows are characterized by complicated motions occurring simultaneously at many length-scales. Accurate computer modeling based on the Navier-Stokes equations requires that the computational grid system cover all the relevant scales, which is prohibitive in many applications. Often, simulations may capture only a range of large-scale eddies. Such simulations, called Large Eddy Simulations (LES), require models to represent the effects of unresolved eddies that fall below the grid. This is the subject of subgrid-scale modeling in turbulence and is the subject of this article.

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Contents 1 Subsection b 2 Subsection c 3 Section d 3.1 Subsection e 3.2 Subsection f 3.3 Citing references 4 References 5 Further reading 6 External links 7 See also

Subsection b

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(1)

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Subsection c

Refer to figures and equations as Fig. and Eq. (1).

Section d

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  This is useful though to provide code

Subsection e

Subsection f

Citing references

Groups of authors larger than 2 can be cited with "et al.".

• As proven in (Albero A, 1999).
• As Albero (2009) said.
• As proven in (Albero and Bocca, 2001)
• As proven by Albero and Bocca (2001)
• As proven by Albero et al. (2003)
• As proven by Albero, Bocca and Cuoco (2003)
• As proven by Albero et al. (2007a), confirmed by Albero et al. (2007b) and discarded by Albero et al. (2007c)
• As proven in (Albero A, 1999).
• As proven by Albero and Bocca (2001).

References

• Albero, Antony (1999). Pizza Margherita. Journal of pizza eaters 19(3): 13. arXiv:0808.000
• Albero, Antonio and Bocca, Bill (2001). Pizza Capricciosa. Journal of pizza eaters 27: 121-127. arXiv:0808.000
• Albero, Antonio; Bocca, Bill and Cuoco, C T (2003). Pizza Quattro Stagioni. Journal of pizza eaters 34(4): 12.
• Albero, Antonio; Bocca, Bill; Cuoco, C T and Dude, David B (2007a). Pizza Napoletana. Journal of pizza eaters 37: 121-127.
• Albero, Antonio; Bocca, Bill; Cuoco, C T; Dude, David and Elica, E Q (2007b). Pizza Marinara. Journal of pizza eaters 43(4): 1-13.
• Albero, Antonio et al. (2008). Pizza Piccante. Journal of pizza eaters 45(5): 1-13.
• Alto, Antony (1999). La Pizza! Mangiare bene, Volume 3. Albero and Bacca editors. Food Publishers, Genoa.
• Alto, Antony and Bocca, Bill (2000). La Pasta! Mangiare bene. Albero editor. Food Publishers, Genoa. Chapter 1.
• Alto, Antony; Bocca, Bill and Cuoco, C T (2002). Pizza: prepare it yourself. Food Publishers, Genoa. Page 22. ISBN 1-234-99929-0.
• Alto, Antony; Bocca, Bill; Cuoco, C T and Dude, David B (2005a). Italian Pizza. Food Publishers, Genoa.
• Alto, Antony; Bocca, Bill; Cuoco, C T; Dude, David B and Elica, E Q (2005b). Napolitan Pizza. Food Publishers, Genoa.
• Alto, Antony et al. (2005c). American Pizza. Food Publishers, Genoa.

Further reading

• Magro, C T (2008). Pizza: a danger for health? Food Publishers, Paris. page 22. ISBN 1-234-90929-0. This reference is unreliable in conclusions, but quite accurate in its introduction.
• Izhikevich, E M (2007). Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting The MIT Press, Cambridge, MA. ISBN 0262090430. This book offers an introduction to nonlinear dynamical systems theory for researchers and graduate students in neuroscience.

External links

Eugene M. Izhikevich website

See also

Brain, Neuron, Scholarpedia:Instructions for authors

Invited by:

Dr. Oleg Schilling, Lawrence Livermore National Laboratory, Livermore, CA 94551