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

被引：0

作者：

GuiQiang GChen School of Mathematical SciencesFudan UniversityShanghai China ^{[200433
]}

Mathematical InstituteUniversity of Oxford St GilesOxfordOX LBUK ^{[24
,29
,1
,3
]}

Department of MathematicsNorthwestern UniversityEvanstonIL USA Weihua Ruan Department of MathematicsComputer Science and StatisticsPurdue University CalumetHammondIN USA ^{[60208
,2730
,46323
,2094
]}

机构：

来源：

Acta Mathematica Scientia | 2010年 / 30卷 / 02期

关键词：

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

D O I：

暂无

中图分类号：

O357 [粘性流体力学];

学科分类号：

080103 ; 080704 ;

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.

引用

页码：391 / 427

页数：37

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