An Efficient High Order Well-Balanced Finite Difference WENO Scheme for the Blood Flow Model (Advances in Applied Mathematics and Mechanics, 2018)
The blood flow model admits the steady state, in which the flux gradient isnon-zero and is exactly balanced by the source term. In this paper, we present a highorder well-balanced finite difference weighted essentially non-oscillatory (WENO)scheme, which exactly preserves the steady state. In order to maintain the well-balancedproperty, we propose to reformulate the equation and apply a novel sourceterm approximation. Extensive numerical experiments are carried out to verify theperformances 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 highorder accuracy for smooth solutions.