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 (2010)

  • 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 39.3 (2010): 477-486. <http://eudml.org/doc/194271>.

@article{Bresch2010,
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},
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},
month = {3},
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/194271},
volume = {39},
year = {2010},
}

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
DA - 2010/3//
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/194271
ER -

References

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