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

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

数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (2): 391-427.doi: 10.1016/S0252-9602(10)60056-2

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

Gui-Qiang G. Chen, Weihua Ruan

School of Mathematical Sciences, Fudan University, |Shanghai 200433, China; Mathematical Institute, University of Oxford, 24-29 St Giles, Oxford, OX1 3LB, UK; Department of Mathematics, Northwestern |University, Evanston, IL 60208-2730, USA； Department of Mathematics, Computer Science and Statistics, |Purdue University Calumet, Hammond, IN 46323-2094, USA

收稿日期:2009-11-14 出版日期:2010-03-20 发布日期:2010-03-20
基金资助:
Gui-Qiang Chen's research was supported in part by the National Science Foundation under Grants DMS-0935967, DMS-0807551, DMS-0720925, and DMS-0505473, the Natural Science Foundation of China under Grant NSFC-10728101, and the Royal Society-Wolfson Research Merit Award (UK).

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

Gui-Qiang G. Chen, Weihua Ruan

School of Mathematical Sciences, Fudan University, |Shanghai 200433, China; Mathematical Institute, University of Oxford, 24-29 St Giles, Oxford, OX1 3LB, UK; Department of Mathematics, Northwestern |University, Evanston, IL 60208-2730, USA； Department of Mathematics, Computer Science and Statistics, |Purdue University Calumet, Hammond, IN 46323-2094, USA

Received:2009-11-14 Online:2010-03-20 Published:2010-03-20
Supported by:
Gui-Qiang Chen's research was supported in part by the National Science Foundation under Grants DMS-0935967, DMS-0807551, DMS-0720925, and DMS-0505473, the Natural Science Foundation of China under Grant NSFC-10728101, and the Royal Society-Wolfson Research Merit Award (UK).

摘要/Abstract

摘要：

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.

关键词: conservation laws, hyperbolic system, fluid flow, blood flow, , vessel, , hyperbolicity, Riemann problem, Riemann solution, wave

Abstract:

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

中图分类号:

35L65

Gui-Qiang G. Chen, Weihua Ruan. A HYPERBOLIC SYSTEM OF CONSERVATION LAWS FOR FLUID FLOWS THROUGH COMPLIANT XISYMMETRIC VESSELS[J]. 数学物理学报(英文版), 2010, 30(2): 391-427.

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

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

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