Analysis of Model Variance for Ensemble Based Turbulence Modeling
Abstract
This report develops an ensemble or statistical eddy viscosity model. The model is parameterized by an ensemble of solutions of an ensemble-Leray regularization. The combined approach of ensemble time stepping and ensemble eddy viscosity modeling allows direct parametrization of the turbulent viscosity coefficient. We prove unconditional stability and that the model's solution approaches statistical equilibrium as t → ∞ the model's variance converges to zero as t → ∞. The ensemble method is used to interrogate a rotating flow, testing its predictability by computing effective averaged Lyapunov exponents.
Recommended Citation
N. Jiang et al., "Analysis of Model Variance for Ensemble Based Turbulence Modeling," Computational Methods in Applied Mathematics, vol. 15, no. 2, pp. 173 - 188, De Gruyter, Apr 2015.
The definitive version is available at https://doi.org/10.1515/cmam-2014-0029
Department(s)
Mathematics and Statistics
Keywords and Phrases
Lyapunov methods; Turbulence; Turbulence models; Eddy viscosity; Eddy viscosity model; Ensemble; Leray Regularization; Solution approach; Statistical equilibrium; Turbulent viscosity; Unconditional stability; Viscosity; Turbulence Modeling
International Standard Serial Number (ISSN)
1609-4840; 1609-9389
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2015 De Gruyter, All rights reserved.
Publication Date
01 Apr 2015
Comments
Funding: Nan Jiang and William Layton were partially supported by NSF grants DMS 1216465 and AFOSR FA9550-12-1-0191. Songul Kaya was supported by TUBITAK.