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

Published online by Cambridge University Press:  03 April 2008

Dietmar Kröner ,
Philippe G. LeFloch  and
Mai-Duc Thanh
Dietmar Kröner
Affiliation:
Institute of Applied Mathematics, University of Freiburg, Hermann-Herder Str. 10, 79104 Freiburg, Germany. Dietmar.Kroener@mathematik.uni-freiburg.de
Philippe G. LeFloch
Affiliation:
Laboratoire Jacques-Louis Lions & Centre National de la Recherche Scientifique, Université de Paris VI, 4 Place Jussieu, 75252 Paris, France. LeFloch@ann.jussieu.fr
Mai-Duc Thanh
Affiliation:
Department of Mathematics, International University, Quarter 6, Linh Trung Ward, Thu Duc District, Ho Chi Minh City, Vietnam. MDThanh@hcmiu.edu.vn
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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.

Keywords

Euler equationsconservation lawshock wavenozzle flowsource termentropy solution.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 42 , Issue 3 , May 2008 , pp. 425 - 442
Copyright
© EDP Sciences, SMAI, 2008

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