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 seek weak solutions in the sense of \textit{G. Dal Maso, Ph. G. LeFloch} and \textit{F. Murat} [J. Math. Pures Appl., IX. Sér. 74, No. 6, 483–548 (1995; Zbl 0853.35068)]. 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.