The minimum entropy principle for compressible fluid flows in a nozzle with discontinuous cross-section
Institute of Applied Mathematics, University of Freiburg,
Hermann-Herder Str. 10, 79104 Freiburg, Germany. Dietmar.Kroener@mathematik.uni-freiburg.de
2 Laboratoire Jacques-Louis Lions & Centre National de la Recherche Scientifique, Université de Paris VI, 4 Place Jussieu, 75252 Paris, France. LeFloch@ann.jussieu.fr
3 Department of Mathematics, International University, Quarter 6, Linh Trung Ward, Thu Duc District, Ho Chi Minh City, Vietnam. MDThanh@hcmiu.edu.vn
Revised: 3 November 2007
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.
Mathematics Subject Classification: 35L65 / 76N10 / 76L05
Key words: Euler equations / conservation law / shock wave / nozzle flow / source term / entropy solution.
© EDP Sciences, SMAI, 2008