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

Kröner, Dietmar; Lefloch, Philippe G.; Thanh, Mai-Duc

ESAIM: Modélisation mathématique et analyse numérique, Tome 42 (2008) no. 3, pp. 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.

Classification : 35L65, 76N10, 76L05
Mots clés : Euler equations, conservation law, shock wave, nozzle flow, source term, entropy solution

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