TY - JOUR
T1 - The Riemann Problem for a Blood Flow Model in Arteries
AU - Sheng , Wancheng
AU - Zhang , Qinglong
AU - Zheng , Yuxi
JO - Communications in Computational Physics
VL - 1
SP - 227
EP - 250
PY - 2019
DA - 2019/10
SN - 27
DO - http://doi.org/10.4208/cicp.OA-2018-0220
UR - https://global-sci.org/intro/article_detail/cicp/13320.html
KW - Blood flow, elementary waves, Riemann problem, non-uniqueness, global entropy
condition.
AB - <p style="text-align: justify;">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 non-strictly 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.</p>