The Finite Difference WENO Format Of The Blood Model

The blood flow model maintains the steady state solutions,in which the flux gradients are non-zero but exactly balanced by the source term.It is a challenging task to design genuinely high order accurate numerical schemes which preserve exactly these steady state solutions.In this paper,we design high order finite difference well-balanced weighted essentially non-oscillatory(WENO)schemes.In order to maintain the well-balanced property,we first do the special handling of the source terms,then the spatial derivatives of the flux gradients and source terms are approximated by a linear finite difference operator,finally we get the semi-discrete schemes.We consider a WENO scheme with a global Lax-Friedrichs flux splitting,for the temporal discretization,we apply the third order Runge-Kutta methods.Rigorous theoretical analysis as well as extensive numerical results all indicate that the resulting schemes maintain the well-balanced property,verify high order accuracy,and keep good resolution for smooth and discontinuous solutions.