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Entropy-Preserving Coupling Conditions for One-dimensional Euler Systems at Junctions

  • This paper is concerned with a set of novel coupling conditions for the 3x3 one-dimensional Euler system with source terms at a junction of pipes with possibly different cross-sectional areas. Beside conservation of mass, we require the equality of the total enthalpy at the junction and that the specific entropy for pipes with outgoing flow equals the convex combination of all entropies that belong to pipes with incoming flow. These conditions ensure energy as well as entropy conservation at the junction. We prove the existence and uniqueness of solutions to the generalised Riemann problem at a junction in the neighbourhood of constant stationary states which belong to the subsonic region. This provides the basis for the well-posedness of the homogeneous and inhomogeneous Cauchy problems for initial data with sufficiently small total variation.

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Metadaten
Author:Jens Lang, Pascal Mindt
DOI:https://doi.org/10.3934/nhm.2018008
Document Type:Article
Language:English
Date of Publication (online):2017/04/13
Date of first Publication:2017/11/13
Release Date:2017/11/13
Volume:Networks and Heterogeneous Media
Issue:Vol. 13
Page Number:14
First Page:177
Last Page:190
Subprojects:B01