The Well-balanced Numerical Method Of The Blood Flow Model

The high order numerical simulations of the blood flow model in arteries is significant to medical and life science researches.This blood flow model belongs to a typical hyperbolic equilibrium system,and this model admits the steady state solutions because the gradient of flux is non-zero and is exactly balanced by the source term.At the discrete level,well-balanced method can maintain the balance between the gradient of flux and the source term.We start with review the basic steps of discontinuous Galerkin method and finite volume scheme to solve the hyperbolic conservation laws in this paper.In order to solve this blood flow model,we design a high order discontinuous Galerkin method and a high order finite volume WENO scheme in this paper by a novel source term approximation and well-balanced numerical fluxes,and the two numerical methods can maintain the well-balanced property at the discrete level.At last,we demonstrate the performance of the two methods by carrying out extensive numerical experiments.Theoretical analysis and a large number of numerical experiments show that the two numerical methods designed in this paper can not only maintain the well-balanced property but also have high order accuracy,and can also maintain good resolutions for smooth and discontinuous solutions in coarser grids.