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Volume 22, Issue 2
Homogenization of Incompressible Euler Equations

Thomas Y. Hou, Danping Yang & Ke Wang

J. Comp. Math., 22 (2004), pp. 220-229.

Published online: 2004-04

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  • Abstract

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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COPYRIGHT: © Global Science Press

  • Email address

hou@acm.caltech.edu (Thomas Y. Hou)

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@Article{JCM-22-220, author = {Hou , Thomas Y.Yang , Danping and Wang , Ke}, title = {Homogenization of Incompressible Euler Equations}, journal = {Journal of Computational Mathematics}, year = {2004}, volume = {22}, number = {2}, pages = {220--229}, abstract = {

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.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/10325.html} }
TY - JOUR T1 - Homogenization of Incompressible Euler Equations AU - Hou , Thomas Y. AU - Yang , Danping AU - Wang , Ke JO - Journal of Computational Mathematics VL - 2 SP - 220 EP - 229 PY - 2004 DA - 2004/04 SN - 22 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/10325.html KW - Incompressible flow, Multiscale analysis, Homogenization, Multiscale computation. AB -

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.

Hou , Thomas Y.Yang , Danping and Wang , Ke. (2004). Homogenization of Incompressible Euler Equations. Journal of Computational Mathematics. 22 (2). 220-229. doi:
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