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

2007/12/21 by Dietmar Kroener, Philippe G. LeFloch, Kroener, Dietmar +3
Engineering · Mathematics · #35L65 #76L05 #76N10 #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Gas Dynamics and Kinetic Theory #Navier-Stokes equation solutions #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.0712.3774

openalex publication_date 2007/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 investigate weak solutions in the sense of Dal Maso, LeFloch, and Murat. 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.

Citations

• A Well-Balanced Scheme for the Numerical Processing of Source Terms in Hyperbolic Equations

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