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Homogenization of incompressible Euler equations

Hou, Thomas Y. and Yang, Dan-ping and Wang, Ke (2004) Homogenization of incompressible Euler equations. Journal of Computational Mathematics, 22 (2). pp. 220-229. ISSN 0254-9409.

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In this paper, we perform a nonlinear multiscale analysis for incompressible Euler equations with rapidly oscillating initial data. The initial condition for velocity field is assumed to have two scales. The fast scale velocity component is periodic and is of order one. One of the important questions is how the two-scale velocity structure propagates in time and whether nonlinear interaction will generate more scales dynamically. By using a Lagrangian framework to describe the propagation of small scale solution, we show that the two-scale structure is preserved dynamically. Moreover, we derive a well-posed homogenized equation for the incompressible Euler equations. Preliminary numerical experiments are presented to demonstrate that the homogenized equation captures the correct averaged solution of the incompressible Euler equation.

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Additional Information:© 2004 Global Science Press. Received January 31, 2004. This work was supported by an NSF grant DMS-0073916, an NSF ITR grant ACI-0204932, Major State Basic Research Program of China grant G1999032803 and the Research Fund for Doctoral Program of High Education by China State Education Ministry.
Funding AgencyGrant Number
Major State Basic Research Program of ChinaG1999032803
China State Education Ministry Research Fund for Doctoral Program of High EducationUNSPECIFIED
Subject Keywords:incompressible flow; multiscale analysis; homogenization; multiscale computation
Issue or Number:2
Classification Code:Mathematics subject classification: 76F25, 76B47, 35L45
Record Number:CaltechAUTHORS:20110819-082640450
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:24952
Deposited By: Tony Diaz
Deposited On:23 Aug 2011 23:19
Last Modified:03 Oct 2019 03:01

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