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 wellbalanced
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.
Blood flow model, finite difference scheme, WENO scheme, high order accuracy, well-balanced property.