A Well-Balanced Discontinuous Galerkin Method for the Blood Flow Model

Abstract

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.