A HYPERBOLIC SYSTEM OF CONSERVATION LAWS FOR FLUID FLOWS THROUGH COMPLIANT AXISYMMETRIC VESSELS

Journal article

We are concerned with the derivation and analysis of one-dimensional hyperbolic systems of conservation laws modelling uid ows such as the blood ow through compliant axisymmetric vessels. Early models derived are nonconservative and/or nonhomogeneous with measure source terms, which are endowed with infinitely many Riemann solutions for some Riemann data. In this paper, we derive a one-dimensional hyperbolic system that is conservative and homogeneous. Moreover, there exists a unique global Riemann solution for the Riemann problem for two vessels with arbitrarily large Riemann data, under a natural stability entropy criterion. The Riemann solutions may consist of four waves for some cases. The system can also be written as a 3×3 system for which strict hyperbolicity fails and the standing waves can be regarded as the contact discontinuities corresponding to the second family with zero eigenvalue. © 2010 Wuhan Institute of Physics and Mathematics.

Authors: Chen, G; Ruan, W

• Publication status: Published
• Journal: ACTA MATHEMATICA SCIENTIA
• Volume: 30
• Issue: 2
• Pages: 391-427
• Publication date: 2010-03-01
• DOI: 10.1016/S0252-9602(10)60056-2
• ISSN: 0252-9602
• Language: English
• Keywords: conservation laws; blood flow; standing wave; shock wave; hyperbolic system; wave curve; vessel; Riemann solution; hyperbolicity; fluid flow; Riemann problem; rarefaction wave; stability