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

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  • Xiaofei Wang
  • Jose-Maria Fullana
  • Pierre-Yves Lagrée

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.

Suggested Citation

  • Xiaofei Wang & Jose-Maria Fullana & Pierre-Yves Lagrée, 2015. "Verification and comparison of four numerical schemes for a 1D viscoelastic blood flow model," Computer Methods in Biomechanics and Biomedical Engineering, Taylor & Francis Journals, vol. 18(15), pages 1704-1725, November.
    • Handle: RePEc:taf:gcmbxx:v:18:y:2015:i:15:p:1704-1725
    DOI: 10.1080/10255842.2014.948428
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    Cited by:

    1. Krivovichev, Gerasim V., 2022. "Comparison of inviscid and viscid one-dimensional models of blood flow in arteries," Applied Mathematics and Computation, Elsevier, vol. 418(C).

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