Chin.Phys.Lett.  2015, Vol. 34 Issue (03): 030501    DOI: 10.1088/0256-307X/34/3/030501
GENERAL |
Mathematical Constraints in Multiscale Subgrid-Scale Modeling of Nonlinear Systems
Le Fang1,2, Ming-Wei Ge3**
1Laboratory of Mathematics and Physics, Ecole Centrale de P閗in, Beihang University, Beijing 100191
2Co-Innovation Center for Advanced Aero-Engine, Beihang University, Beijing 100191
3School of Renewable Energy, North China Electric Power University, Beijing 102206
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Abstract To shed light on the subgrid-scale (SGS) modeling methodology of nonlinear systems such as the Navier–Stokes turbulence, we define the concepts of assumption and restriction in the modeling procedure, which are shown by generalized derivation of three general mathematical constraints for different combinations of restrictions. These constraints are verified numerically in a one-dimensional nonlinear advection equation. This study is expected to inspire future research on the SGS modeling methodology of nonlinear systems.
Received: 21 October 2016      Published: 14 March 2017
PACS:  05.45.Pq (Numerical simulations of chaotic systems)  
  47.11.St (Multi-scale methods)  
  05.20.Gg (Classical ensemble theory)  
  47.27.eb (Statistical theories and models)  
Fund: Supported by the National Natural Science Foundation of China under Grant Nos 11572025, 11202013 and 51420105008.
Issue Date: 14 March 2017
Cite this article:   
Le Fang,Ming-Wei Ge 2015 Chin.Phys.Lett. 34 030501
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http://cpl.iphy.ac.cn/newweb/10.1088/0256-307X/34/3/030501       OR      http://cpl.iphy.ac.cn/newweb/Y2015/V34/I03/030501
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Le Fang
Ming-Wei Ge
[1]Fang L, Shao L and Bertoglio J P 2014 Sci. Chin. Phys. Mech. Astron. 57 2188
[2]Park N, Yoo J Y and Choi H 2005 Phys. Fluids 17 015103
[3]Cui G X, Xu C X, Fang L, Shao L and Zhang Z S 2007 J. Fluid Mech. 582 377
[4]Fang L, Shao L, Bertoglio J P, Cui G X, Xu C X and Zhang Z S 2009 Phys. Fluids 21 065108
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[17]Shi Y P, Xiao Z L and Chen S Y 2008 Phys. Fluids 20 011701
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