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An example of low Mach (Froude) number effects for compressible flows with nonconstant density (height) limit

Published online by Cambridge University Press:  15 June 2005

Didier Bresch ,
Marguerite Gisclon  and
Chi-Kun Lin
Didier Bresch
Affiliation:
LMC-IMAG, (CNRS, INPG, UJF, INRIA) 38051 Grenoble Cedex, France. didier.bresch@imag.fr
Marguerite Gisclon
Affiliation:
Université de Savoie, LAMA, UMR CNRS 5127, 73376 Le Bourget-du-lac, France. marguerite.gisclon@univ-savoie.fr
Chi-Kun Lin
Affiliation:
Department of Mathematics, National Cheng Kung University, Tianan 701 Taiwan. cklin@mail.ncku.edu.tw
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Abstract

The purpose of this work is to study an example of low Mach (Froude) number limit of compressible flows when the initial density (height) is almost equal to a function depending on x. This allows us to connect the viscous shallow water equation and the viscous lake equations. More precisely, we study this asymptotic with well prepared data in a periodic domain looking at the influence of the variability of the depth. The result concerns weak solutions. In a second part, we discuss the general low Mach number limit for standard compressible flows given in P.–L. Lions' book that means with constant viscosity coefficients.

Keywords

Compressible flowsNavier-Stokes equationslow Mach (Froude) Number limit shallow-water equationslake equationsnonconstant density.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 39 , Issue 3: Special issue on Low Mach Number Flows Conference , May 2005 , pp. 477 - 486
Copyright
© EDP Sciences, SMAI, 2005

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