Simplified blood flow model with discontinuous vessel properties: Analysis and exact solutions

Abstract

We formulate a simplified one-dimensional time-dependent non-linear mathematical model for blood flow in vessels with discontinuous material properties. The resulting 3×3 hyperbolic system is analysed and the associated Riemann problem is solved exactly, including tube collapse. Our exact solutions constitute useful reference solutions for assessing the performance of numerical methods intended for simulating more general situations. In addition the presented model may be a useful starting point for numerical calculations involving rapid and discontinuous material properties variations. © Springer-Verlag Italia 2012.