Geodesic
The minimum entropy principle for compressible fluid flows in a nozzle with discontinuous cross-section
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 42 (2008) no. 3, pp. 425-442

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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 : 10.1051/m2an:2008011
Classification : 35L65, 76N10, 76L05
Keywords: Euler equations, conservation law, shock wave, nozzle flow, source term, entropy solution 
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     title = {The minimum entropy principle for compressible fluid flows in a nozzle with discontinuous cross-section},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {425--442},
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Kröner, Dietmar; Lefloch, Philippe G.; Thanh, Mai-Duc. The minimum entropy principle for compressible fluid flows in a nozzle with discontinuous cross-section. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 42 (2008) no. 3, pp. 425-442. doi: 10.1051/m2an:2008011

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