The Riemann Problem for a Blood Flow Model in Arteries  

作　　者：Wancheng Sheng Qinglong Zhang Yuxi Zheng 

机构地区：[1]Department of Mathematics,Shanghai University,Shanghai,200444,P.R.China [2]Department of Mathematics,The Pennsylvania State University,University Park,PA 16802,United States

出　　处：《Communications in Computational Physics》2020年第1期227-250,共24页计算物理通讯（英文）

基　　金：supported by NSFC 11371240,11771274;supported by the State Scholarship Fund from China Scholarship Council(201706890042).

摘　　要：In this paper,the Riemann solutions of a reduced 6×6 blood flow model in mediumsized to large vessels are constructed.The model is nonstrictly hyperbolic and non-conservative in nature,which brings two difficulties of the Riemann problem.One is the appearance of resonance while the other one is loss of uniqueness.The elementary waves include shock wave,rarefaction wave,contact discontinuity and stationary wave.The stationary wave is obtained by solving a steady equation.We construct the Riemann solutions especially when the steady equation has no solution for supersonic initial data.We also verify that the global entropy condition proposed by C.Dafermos can be used here to select the physical relevant solution.The Riemann solutions may contribute to the design of numerical schemes,which can apply to the complex blood flows.

关 键 词：Blood flow elementary waves Riemann problem NON-UNIQUENESS global entropy condition 

分 类 号：O17[理学—数学]