Numerical simulations by high order methods for the blood flow model in
arteries have wide applications in medical engineering. This blood flow model admits
the steady state solutions, for which the flux gradient is non-zero, and is exactly balanced
by the source term. In this paper,we design a high order discontinuous Galerkin
method to this model by means of a novel source term approximation as well as well-balanced
numerical fluxes. Rigorous theoretical analysis as well as extensive numerical
results all suggests that the resulting method maintains the well-balanced property,
enjoys high order accuracy and keeps good resolutions for smooth and discontinuous
solutions.
