  The blood flow model maintains the steady state solutions, in which the flux
gradients are non-zero but exactly balanced by the source term. In this paper,
we design high order finite difference weighted non-oscillatory (WENO) schemes
to this model with such well-balanced property and at the same time keeping
genuine high order accuracy. Rigorous theoretical analysis as well as extensive
numerical results all indicate that the resulting schemes verify high order
accuracy, maintain the well-balanced property, and keep good resolution for
smooth and discontinuous solutions.
