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Lagrangian Averaging for Compressible Fluids

Bhat, H. S. and Fetecau, R. C. and Marsden, J. E. and Mohseni, K. and West, M. (2005) Lagrangian Averaging for Compressible Fluids. Multiscale Modeling and Simulation, 3 (4). pp. 818-837. ISSN 1540-3459. http://resolver.caltech.edu/CaltechAUTHORS:BHAmms05

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Abstract

This paper extends the derivation of the Lagrangian averaged Euler (LAE-α) equations to the case of barotropic compressible flows. The aim of Lagrangian averaging is to regularize the compressible Euler equations by adding dispersion instead of artificial viscosity. Along the way, the derivation of the isotropic and anisotropic LAE-α equations is simplified and clarified. The derivation in this paper involves averaging over a tube of trajectories η^ε centered around a given Lagrangian flow η. With this tube framework, the LAE-α equations are derived by following a simple procedure: start with a given action, Taylor expand in terms of small-scale fluid fluctuations ξ, truncate, average, and then model those terms that are nonlinear functions of ξ. Closure of the equations is provided through the use of flow rules, which prescribe the evolution of the fluctuations along the mean flow.


Item Type:Article
Additional Information:©2005 Society for Industrial and Applied Mathematics. Received by the editors November 10, 2003; accepted for publication (in revised form) August 10, 2004; published electronically March 17, 2005. This research was partially supported by AFOSR contract F49620-02-1-0176. The research of the first author [H.S.B.] was supported by the National Science Foundation through a Graduate Research Fellowship. We extend our sincerest thanks to Steve Shkoller, Darryl Holm, and Marcel Oliver for helpful discussions and criticism on a wide array of issues central to this paper.
Subject Keywords:averaged Lagrangians; inviscid compressible fluids
Record Number:CaltechAUTHORS:BHAmms05
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:BHAmms05
Alternative URL:http://dx.doi.org/10.1137/030601739
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9105
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:29 Oct 2007
Last Modified:26 Dec 2012 09:45

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