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 -

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.