The minimum entropy principle for compressible fluid flows in a nozzle with discontinuous cross-section
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 42 (2008) no. 3, p. 425-442

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.

DOI : https://doi.org/10.1051/m2an:2008011
Classification:  35L65,  76N10,  76L05
Keywords: Euler equations, conservation law, shock wave, nozzle flow, source term, entropy solution
@article{M2AN_2008__42_3_425_0,
     author = {Kr\"oner, Dietmar and Lefloch, Philippe G. and Thanh, Mai-Duc},
     title = {The minimum entropy principle for compressible fluid flows in a nozzle with discontinuous cross-section},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {42},
     number = {3},
     year = {2008},
     pages = {425-442},
     doi = {10.1051/m2an:2008011},
     zbl = {1139.76048},
     mrnumber = {2423793},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2008__42_3_425_0}
}
The minimum entropy principle for compressible fluid flows in a nozzle with discontinuous cross-section. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 42 (2008) no. 3, pp. 425-442. doi : 10.1051/m2an:2008011. http://www.numdam.org/item/M2AN_2008__42_3_425_0/

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