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Coarse analysis of multiscale systems: diffuser flows, charged particle motion, and connections to averaging theory 
Abstract 
We describe a technique for the efficient … We describe a technique for the efficient computation of the dominantscale dynamics of a fluid
system when only a highfidelity simulation is available. Such a technique is desirable when governing equations for the dominant scales are unavailable, when model reduction is impractical, or
when the original highfidelity computation is expensive. We adopt the coarse analysis framework
proposed by I. G. Kevrekidis (Comm. Math. Sci. 2003), where a computational superstructure is
designed to use shorttime, highfidelity simulations to extract the dominant features for a multi
scale system. We apply this technique to compute the dominant features of the compressible flow
through a planar diffuser. We apply the proper orthogonal decomposition to classify the dominant
and subdominant scales of diffuser flows. We derive a suitable coarse pro jective AdamsBashforth
time integration routine and apply it to compute averaged diffuser flows. The results include accu
rate tracking of the dominantscale dynamics for a range of parameter values for the computational
superstructure. These results demonstrate that coarse analysis methods are useful for solving fluid
flow problems of a multiscale nature.
<p>
In order to elucidate the behavior of coarse analysis techniques, we make comparisons to averaging
theory. To this end, we derive governing equations for the average motion of charged particles in
a magnetic field in a number of different settings. First, we apply a novel procedure, inspired by WKB theory and Whitham averaging, to average the variational principle. The resulting equations
are equivalent to the guiding center equations for charged particle motion; this marks an instance
where averaging and variational principles commute. Secondly, we apply Lagrangian averaging
techniques, previously applied in fluid mechanics, to derive averaged equations. Making comparisons to the WKB/Whithamstyle derivation allows for the necessary closure of the Lagrangian
averaging formulation. We also discuss the Hamiltonian setting and show that averaged Hamiltonian systems may be derivable using concepts from coarse analysis. Finally, we apply a prototypical
coarse analysis procedure to the system of charged particles and generate tra jectories that resemble
guiding center tra jectories. We make connections to perturbation theory to derive guidelines for the
design of coarse analysis techniques and comment on the prototypical coarse analysis application. prototypical coarse analysis application. +


Authors  Jimmy Fung + 
ID  2005 + 
Source  PhD Dissertation, Caltech Aeronautics, May 2005 + 
Tag  jf05phd + 
Title  Coarse analysis of multiscale systems: diffuser flows, charged particle motion, and connections to averaging theory + 
Type  PhD Dissertation + 
Categories  Papers 
Modification date This property is a special property in this wiki.

15 May 2016 06:18:04 + 
URL This property is a special property in this wiki.

http://www.cds.caltech.edu/~murray/preprints/jf05phd.pdf + 
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Coarse analysis of multiscale systems: diffuser flows, charged particle motion, and connections to averaging theory +  Title 
