Well-balanced high-order solver for blood flow in networks of vessels with variable properties

ABSTRACT We present a well‐balanced, high‐order non‐linear numerical scheme for solving a hyperbolic system that models one‐dimensional flow in blood vessels with variable mechanical and geometrical properties along their length. Using a suitable set of test problems with exact solution, we rigorously assess the performance of the scheme. In particular, we assess the well‐balanced property and the effective order of accuracy through an empirical convergence rate study. Schemes of up to fifth order of accuracy in both space and time are implemented and assessed. The numerical methodology is then extended to realistic networks of elastic vessels and is validated against published state‐of‐the‐art numerical solutions and experimental measurements. It is envisaged that the present scheme will constitute the building block for a closed, global model for the human circulation system involving arteries, veins, capillaries and cerebrospinal fluid. Copyright © 2013 John Wiley & Sons, Ltd. We present a well‐balanced, high‐order non‐linear numerical scheme for solving one‐dimensional blood flow in vessels with variable properties. Using a suitable set of test problems with exact solution, we rigorously assess the well‐balanced property, the effective order of accuracy and the ability to solve unsteady problems. The numerical methodology is then validated against published state‐of‐the‐art numerical solutions and experimental measurements. The efficiency and robustness of the present scheme makes it suitable for modelling both arteries and veins.