The minimum entropy principle for compressible fluid flows in a nozzle with discontinuous cross-section

Dietmar Kröner; Philippe G. LeFloch; Mai-Duc Thanh

ESAIM: Mathematical Modelling and Numerical Analysis (2008)

  • Volume: 42, Issue: 3, page 425-442
  • ISSN: 0764-583X

Abstract

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We consider the Euler equations for compressible fluids in a nozzle whose cross-section is variable and may contain discontinuities. We view these equations as a hyperbolic system in nonconservative form and investigate weak solutions in the sense of Dal Maso, LeFloch and Murat [J. Math. Pures Appl.74 (1995) 483–548]. Observing that the entropy equality has a fully conservative form, we derive a minimum entropy principle satisfied by entropy solutions. We then establish the stability of a class of numerical approximations for this system.

How to cite

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Kröner, Dietmar, LeFloch, Philippe G., and Thanh, Mai-Duc. "The minimum entropy principle for compressible fluid flows in a nozzle with discontinuous cross-section." ESAIM: Mathematical Modelling and Numerical Analysis 42.3 (2008): 425-442. <http://eudml.org/doc/250325>.

@article{Kröner2008,
abstract = { We consider the Euler equations for compressible fluids in a nozzle whose cross-section is variable and may contain discontinuities. We view these equations as a hyperbolic system in nonconservative form and investigate weak solutions in the sense of Dal Maso, LeFloch and Murat [J. Math. Pures Appl.74 (1995) 483–548]. Observing that the entropy equality has a fully conservative form, we derive a minimum entropy principle satisfied by entropy solutions. We then establish the stability of a class of numerical approximations for this system. },
author = {Kröner, Dietmar, LeFloch, Philippe G., Thanh, Mai-Duc},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Euler equations; conservation law; shock wave; nozzle flow; source term; entropy solution.; shock wave},
language = {eng},
month = {4},
number = {3},
pages = {425-442},
publisher = {EDP Sciences},
title = {The minimum entropy principle for compressible fluid flows in a nozzle with discontinuous cross-section},
url = {http://eudml.org/doc/250325},
volume = {42},
year = {2008},
}

TY - JOUR
AU - Kröner, Dietmar
AU - LeFloch, Philippe G.
AU - Thanh, Mai-Duc
TI - The minimum entropy principle for compressible fluid flows in a nozzle with discontinuous cross-section
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2008/4//
PB - EDP Sciences
VL - 42
IS - 3
SP - 425
EP - 442
AB - We consider the Euler equations for compressible fluids in a nozzle whose cross-section is variable and may contain discontinuities. We view these equations as a hyperbolic system in nonconservative form and investigate weak solutions in the sense of Dal Maso, LeFloch and Murat [J. Math. Pures Appl.74 (1995) 483–548]. Observing that the entropy equality has a fully conservative form, we derive a minimum entropy principle satisfied by entropy solutions. We then establish the stability of a class of numerical approximations for this system.
LA - eng
KW - Euler equations; conservation law; shock wave; nozzle flow; source term; entropy solution.; shock wave
UR - http://eudml.org/doc/250325
ER -

References

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