Hou, Tom and Yang, Danping and Ran, Hongyu (2006) Multiscale computation of isotropic homogeneous turbulent flow. In: Inverse problems, multi-scale analysis, and effective medium theory. Contemporary Mathematics Series (408). American Mathematical Society , Providence, RI, pp. 111-135. ISBN 0-8218-3968-3 http://resolver.caltech.edu/CaltechAUTHORS:20110602-094821767
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In this article we perform a systematic multi-scale analysis and computation for incompressible Euler equations and Navier-Stokes Equations in both 2D and 3D. The initial condition for velocity field has multiple length scales. By reparameterizing them in the Fourier space, we can formally organize the initial condition into two scales with the fast scale component being periodic. By making an appropriate multiscale expansion for the velocity field, we show that the two-scale structure is preserved dynamically. Moreover, we derive a well-posed homogenized equation for the incompressible Euler equations in the Eulerian formulations. Numerical experiments are presented to demonstrate that the homogenized equations indeed capture the correct averaged solution of the incompressible Euler and Navier Stokes equations. Moreover, our multiscale analysis reveals some interesting structure for the Reynolds stress terms, which provides a theoretical base for establishing an effective LES type of model for incompressible fluid flows.
|Item Type:||Book Section|
|Additional Information:||© 2006 American Mathematical Society. The first and the third author was supported in part by an NSF grant DMS-0073916 and an NSF ITR grant ACI-0204932. The second author was supported in part by an NSF grant DMS-0073916, the National Basic Research Program of P. R. China under the grant 2005CB321703, and Natural Science Foundation of China under the Grant 10441005, 10571108.|
|Subject Keywords:||Multiscale analysis, Euler equations, turbulence|
|Classification Code:||1991 Mathematics Subject Classification. Primary 54C40, 14E20; Secondary 46E25, 20C20.|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Tony Diaz|
|Deposited On:||17 Jun 2011 17:15|
|Last Modified:||26 Dec 2012 13:16|
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