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Dynamic modeling of α in the isotropic lagrangian averaged navier-stokes-α equations

Zhao, Hongwu and Mohseni, Kamran and Marsden, Jerrold E. (2004) Dynamic modeling of α in the isotropic lagrangian averaged navier-stokes-α equations. In: Proceedings of the ASME Fluids Engineering Division--2004 $h [electronic resource] : presented at 2004 ASME International Mechanical Engineering Congress and Exposition : November 13-19, 2004, Anaheim, California, USA. FED (Series). No.260. ASME , New York, pp. 1-9. ISBN 0791847098 http://resolver.caltech.edu/CaltechAUTHORS:20101026-142628970

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Abstract

A dynamic procedure for the Lagrangian Averaged Navier- Stokes-α (LANS-α) equations is developed where the variation in the parameter α in the direction of anisotropy is determined in a self-consistent way from data contained in the simulation itself. In order to derive this model, the incompressible Navier-Stokes equations are Helmholtz-filtered at the grid and a test filter levels. A Germano type identity is derived by comparing the filtered subgrid scale stress terms with those given in the LANS-α equations. Assuming constant α in homogenous directions of the flow and averaging in these directions, results in a nonlinear equation for the parameter α, which determines the variation of α in the non-homogeneous directions or in time. Consequently, the parameter α is calculated during the simulation instead of a pre-defined value. As an initial test, the dynamic LANS-α model is used to compute isotropic homogenous forced and decaying turbulence, where α is constant over the computational domain, but is allowed to vary in time. The resulting simulations are compared with direct numerical simulations and with the LANS-α simulations using fixed value of α. As expected, α is found to change rapidly during the first eddy turn-over time during the simulations. It is also observed that by using the dynamic LANS-α procedure a more accurate simulation of the isotropic homogeneous turbulence is achieved. The energy spectra and the total kinetic energy decay are captured more accurately as compared with the LANS-α simulations using a fixed α. The current results suggest some promising applications of this dynamic LANS-α model, such as to a spatially varying turbulent flow, which we hope to undertake in future research.


Item Type:Book Section
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http://www.cds.caltech.edu/~marsden/bib/2004/12-ZhMoMa2004/ZhMoMa2004.pdfAuthorUNSPECIFIED
http://dx.doi.org/10.1115/IMECE2004-61591 DOIUNSPECIFIED
Additional Information:© 2004 by ASME. The research in this paper was partially supported by the AFOSR contract F49620-02-1-0176. The authors would like to thank B. Kosovic for his initial help in the derivation of the dynamic model and T. Lund for helpful discussions.
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AFOSRF49620-02-1-0176
Record Number:CaltechAUTHORS:20101026-142628970
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20101026-142628970
Official Citation:Dynamic Modeling of alpha in the Isotropic Lagrangian Averaged Navier-Stokes-alpha Equations Hongwu Zhao, Kamran Mohseni, and Jerrold E. Marsden, ASME Conf. Proc. 2004, 695 (2004), DOI:10.1115/IMECE2004-61591
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:20545
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:02 Dec 2010 00:21
Last Modified:26 Dec 2012 12:33

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