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

Didier Bresch; Marguerite Gisclon; Chi-Kun Lin

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2005)

  • Volume: 39, Issue: 3, page 477-486
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Bresch, Didier, Gisclon, Marguerite, and Lin, Chi-Kun. "An example of low Mach (Froude) number effects for compressible flows with nonconstant density (height) limit." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 39.3 (2005): 477-486. <http://eudml.org/doc/244834>.

@article{Bresch2005,
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.},
author = {Bresch, Didier, Gisclon, Marguerite, Lin, Chi-Kun},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {compressible flows; Navier-Stokes equations; low Mach (Froude) number limit shallow-water equations; lake equations; nonconstant density; viscous shallow water equation; viscous lake equations; well prepared data; weak solutions},
language = {eng},
number = {3},
pages = {477-486},
publisher = {EDP-Sciences},
title = {An example of low Mach (Froude) number effects for compressible flows with nonconstant density (height) limit},
url = {http://eudml.org/doc/244834},
volume = {39},
year = {2005},
}

TY - JOUR
AU - Bresch, Didier
AU - Gisclon, Marguerite
AU - Lin, Chi-Kun
TI - An example of low Mach (Froude) number effects for compressible flows with nonconstant density (height) limit
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2005
PB - EDP-Sciences
VL - 39
IS - 3
SP - 477
EP - 486
AB - 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.
LA - eng
KW - compressible flows; Navier-Stokes equations; low Mach (Froude) number limit shallow-water equations; lake equations; nonconstant density; viscous shallow water equation; viscous lake equations; well prepared data; weak solutions
UR - http://eudml.org/doc/244834
ER -

References

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