TY - JOUR
T1 - An Efficient High Order Well-Balanced Finite Difference WENO Scheme for the Blood Flow Model
AU - Qian , Shouguo
AU - Li , Gang
AU - Lv , Xianqing
AU - Shao , Fengjing
JO - Advances in Applied Mathematics and Mechanics
VL - 1
SP - 22
EP - 40
PY - 2018
DA - 2018/10
SN - 10
DO - http://doi.org/10.4208/aamm.OA-2016-0151
UR - https://global-sci.org/intro/article_detail/aamm/10499.html
KW - Blood flow model, finite difference scheme, WENO scheme, high order accuracy, well-balanced property.
AB - <p style="text-align: justify;">The blood flow model admits the steady state, in which the flux gradient is
non-zero and is exactly balanced by the source term. In this paper, we present a high
order well-balanced finite difference weighted essentially non-oscillatory (WENO)
scheme, which exactly preserves the steady state. In order to maintain the well-balanced
property, we propose to reformulate the equation and apply a novel source
term approximation. Extensive numerical experiments are carried out to verify the
performances of the current scheme such as the maintenance of well-balanced property,
the ability to capture the perturbations of such steady state and the genuine high
order accuracy for smooth solutions.</p>