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 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: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {425--442},
year = {2008},
publisher = {EDP Sciences},
volume = {42},
number = {3},
doi = {10.1051/m2an:2008011},
mrnumber = {2423793},
zbl = {1139.76048},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an:2008011/}
}
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: Modélisation mathématique et analyse numérique PY - 2008 SP - 425 EP - 442 VL - 42 IS - 3 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/m2an:2008011/ DO - 10.1051/m2an:2008011 LA - en ID - M2AN_2008__42_3_425_0 ER -
%0 Journal Article %A Kröner, Dietmar %A Lefloch, Philippe G. %A Thanh, Mai-Duc %T The minimum entropy principle for compressible fluid flows in a nozzle with discontinuous cross-section %J ESAIM: Modélisation mathématique et analyse numérique %D 2008 %P 425-442 %V 42 %N 3 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/m2an:2008011/ %R 10.1051/m2an:2008011 %G en %F M2AN_2008__42_3_425_0
Kröner, Dietmar; Lefloch, Philippe G.; Thanh, Mai-Duc. The minimum entropy principle for compressible fluid flows in a nozzle with discontinuous cross-section. ESAIM: Modélisation mathématique et analyse numérique, Tome 42 (2008) no. 3, pp. 425-442. doi: 10.1051/m2an:2008011
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