TY - JOUR
T1 - The Riemann problem for a blood flow model in arteries
AU - Sheng, Wancheng
AU - Zhang, Qinglong
AU - Zheng, Yuxi
N1 - Funding Information:
This work was supported by NSFC 11371240 and 11771274. Zhang was also supported by the State Scholarship Fund from China Scholarship Council (201706890042). The authors gratefully acknowledge Professor Jiequan Li for his enthusiastic help.
Publisher Copyright:
© 2020 Global-Science Press
PY - 2020
Y1 - 2020
N2 - In this paper, the Riemann solutions of a reduced 6×6 blood flow model in medium-sized 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.
AB - In this paper, the Riemann solutions of a reduced 6×6 blood flow model in medium-sized 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.
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U2 - 10.4208/cicp.OA-2018-0220
DO - 10.4208/cicp.OA-2018-0220
M3 - Article
AN - SCOPUS:85073821793
SN - 1815-2406
VL - 27
SP - 227
EP - 250
JO - Communications in Computational Physics
JF - Communications in Computational Physics
IS - 1
ER -