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

doi:10.1016/S0252-9602(10)60056-2

Abstract

Abstract:

We are concerned with the derivation and analysis of one-dimensional hyperbolic systems of conservation laws modelling fluid flows such as the blood flow 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.

Key words: conservation laws, hyperbolic system, fluid flow, blood flow, , vessel, , hyperbolicity, Riemann problem, Riemann solution, wave
curve, shock wave; , rarefaction wave; , standing wave; , stability

CLC Number:

35L65

Gui-Qiang G. Chen, Weihua Ruan. A HYPERBOLIC SYSTEM OF CONSERVATION LAWS FOR FLUID FLOWS THROUGH COMPLIANT XISYMMETRIC VESSELS[J].Acta mathematica scientia,Series B, 2010, 30(2): 391-427.

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