Lagrangian averaging for the 1D compressible Euler equations

Harish  S. Bhat; Razvan C. Fetecau

doi:10.3934/dcdsb.2006.6.979

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2006, Volume 6, Issue 5: 979-1000. Doi: 10.3934/dcdsb.2006.6.979

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Lagrangian averaging for the 1D compressible Euler equations

Harish S. Bhat^1, and
Razvan C. Fetecau^2,

1.
Applied Physics and Applied Mathematics, Columbia University, New York NY 10027
2.
Department of Mathematics, Stanford University, Stanford CA 94305-2125

Received: May 31, 2005

Revised: February 28, 2006

Published: August 2006

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Abstract

We consider a $1$-dimensional Lagrangian averaged model for an inviscid compressible fluid. As previously introduced in the literature, such equations are designed to model the effect of fluctuations upon the mean flow in compressible fluids. This paper presents a traveling wave analysis and a numerical study for such a model. The discussion is centered around two issues. One relates to the intriguing wave motions supported by this model. The other is the appropriateness of using Lagrangian-averaged models for compressible flow to approximate shock wave solutions of the compressible Euler equations.

Keywords:

Lagrangian averaging,
compressible fluids.

Mathematics Subject Classification: 37K05, 76N99, 37N10.

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