TY - JOUR
T1 - A High Order Well-Balanced Finite Volume WENO Scheme for a Blood Flow Model in Arteries 
AU - Zhonghua Yao, Gang Li & Jinmei Gao
JO - East Asian Journal on Applied Mathematics
VL - 4
SP - 852
EP - 866
PY - 2018
DA - 2018/02
SN - 7
DO - http://doi.org/10.4208/eajam.181016.300517f
UR - https://global-sci.org/intro/article_detail/eajam/10725.html
KW - Blood flow model, finite volume scheme, WENO scheme, well-balanced property, high order accuracy, source term.
AB - <p style="text-align: justify;">The numerical simulations for the blood flow in arteries by high order accurate
schemes have a wide range of applications in medical engineering. The blood flow
model admits the steady state solutions, in which the flux gradient is non-zero and is
exactly balanced by the source term. In this paper, we present a high order finite volume
weighted essentially non-oscillatory (WENO) scheme, which preserves the steady
state solutions and maintains genuine high order accuracy for general solutions. The
well-balanced property is obtained by a novel source term reformulation and discretisation,
combined with well-balanced numerical fluxes. Extensive numerical experiments
are carried out to verify well-balanced property, high order accuracy, as well as good
resolution for smooth and discontinuous solutions.</p>