A benchmark study of numerical schemes for one-dimensional arterial blood flow modelling

Etienne Boileau, Perumal Nithiarasu*, Pablo J. Blanco, Lucas O. Mueller, Fredrik Eikeland Fossan, Leif Rune Hellevik, Wouter P. Donders, Wouter Huberts, Marie Willemet, Jordi Alastruey

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


Haemodynamical simulations using one-dimensional (1D) computational models exhibit many of the features of the systemic circulation under normal and diseased conditions. Recent interest in verifying 1Dnumerical schemes has led to the development of alternative experimental setups and the use of three-dimensionalnumerical models to acquire data not easily measured in vivo. In most studies to date, only one particular 1Dscheme is tested. In this paper, we present a systematic comparison of six commonly used numerical schemes for 1Dblood flow modelling: discontinuous Galerkin, locally conservative Galerkin, Galerkin least-squares finite element method, finite volume method, finite difference MacCormack method and a simplified trapezium rule method. Comparisons are made in a series of six benchmark test cases with an increasing degree of complexity. The accuracy of the numerical schemes is assessed by comparison with theoretical results, three-dimensionalnumerical data in compatible domains with distensible walls or experimental data in a network of silicone tubes. Results show a good agreement among all numerical schemes and their ability to capture the main features of pressure, flow and area waveforms in large arteries. All the information used in this study, including the input data for all benchmark cases, experimental data where available and numerical solutions for each scheme, is made publicly available online, providing a comprehensive reference data set to support the development of 1Dmodels and numerical schemes.
Original languageEnglish
Article numbere02732
Number of pages33
JournalInternational Journal for Numerical Methods in Biomedical Engineering
Issue number10
Publication statusPublished - Oct 2015


  • 1D arterial haemodynamics
  • 1D numerical schemes
  • benchmark test cases
  • pulse wave propagation

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