(untitled) (Advances in Applied Mathematics and Mechanics, 2018)
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.