A high order approximation of hyperbolic conservation laws in networks: Application to one-dimensional blood flow

Abstract

We present a methodology for the high order approximation of hyperbolic conservation laws in networks by using the Dumbser–Enaux–Toro solver and exact solvers for the classical Riemann problem at junctions. The proposed strategy can be applied to any hyperbolic system, conservative or non-conservative, and possibly with flux functions containing discontinuous parameters, as long as an exact or approximate Riemann problem solver is available. The methodology is implemented for a one-dimensional blood flow model that considers discontinuous variations of mechanical and geometrical properties of vessels. The achievement of formal order of accuracy, as well as the robustness of the resulting numerical scheme, is verified through the simulation of both, academic tests and physiological flows.