Verification and comparison of four numerical schemes for a 1D viscoelastic blood flow model

Abstract

A reliable and fast numerical scheme is crucial for the 1D simulation of blood flow in compliant vessels. In this paper, a 1D blood flow model is incorporated with a Kelvin–Voigt viscoelastic arterial wall. This leads to a nonlinear hyperbolic–parabolic system, which is then solved with four numerical schemes, namely: MacCormack, Taylor–Galerkin, monotonic upwind scheme for conservation law and local discontinuous Galerkin. The numerical schemes are tested on a single vessel, a simple bifurcation and a network with 55 arteries. The numerical solutions are checked favorably against analytical, semi-analytical solutions or clinical observations. Among the numerical schemes, comparisons are made in four important aspects: accuracy, ability to capture shock-like phenomena, computational speed and implementation complexity. The suitable conditions for the application of each scheme are discussed.

Keywords::

• blood flow
• 1D flow modeling
• vascular network
• numerical simulation

Acknowledgements

We wish to gratefully thank Jean-Frédéric Gerbeau (INRIA) for helpful discussion and implementation of the Taylor–Galerkin scheme, and Olivier Delestre (Université de Nice Sophia-Antipolis) for FV scheme. We are also very grateful to the anonymous reviewers, whose comments helped us a lot to improve this paper.

Notes

^1. Email: [email protected]

^2. Email: [email protected]

Additional information

Funding

This work was supported by French state funds managed by CALSIMLAB and the ANR within the Investissements d'Avenir programme under reference ANR-11-IDEX-0004-02. The first author would also like to thank the partial financial aid of China Scholarship Council.