TY - JOUR
T1 - A benchmark study of numerical schemes for one-dimensional arterial blood flow modelling
AU - Nithiarasu, Perumal
AU - Blanco, Pablo J
AU - Müller, Lucas O
AU - Fossan, Fredrik Eikeland
AU - Hellevik, Leif Rune
AU - Donders, Wouter P
AU - Huberts, Wouter
AU - Willemet, Marie
AU - Alastruey, Jordi
N1 - This article is protected by copyright. All rights reserved. Copyright © 2015 John Wiley & Sons, Ltd.
PY - 2015/10
Y1 - 2015/10
N2 - Haemodynamical simulations using one-dimensional (1-D) computational models exhibit many of the features of the systemic circulation under normal and diseased conditions. Recent interest in verifying 1-D numerical schemes has led to the development of alternative experimental setups and the use of 3-D numerical models to acquire data not easily measured in vivo. In most studies to date, only one particular 1-D scheme is tested. In this paper we present a systematic comparison of six commonly used numerical schemes for 1-D blood flow modelling: discontinuous Galerkin (DCG), locally conservative Galerkin (LCG), Galerkin least-squares finite element method (FEM), finite volume method (FVM), finite difference MacCormack method (McC), and a simplified trapezium rule method (STM). 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 against theoretical results, 3-D numerical 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 1-D models and numerical schemes.
AB - Haemodynamical simulations using one-dimensional (1-D) computational models exhibit many of the features of the systemic circulation under normal and diseased conditions. Recent interest in verifying 1-D numerical schemes has led to the development of alternative experimental setups and the use of 3-D numerical models to acquire data not easily measured in vivo. In most studies to date, only one particular 1-D scheme is tested. In this paper we present a systematic comparison of six commonly used numerical schemes for 1-D blood flow modelling: discontinuous Galerkin (DCG), locally conservative Galerkin (LCG), Galerkin least-squares finite element method (FEM), finite volume method (FVM), finite difference MacCormack method (McC), and a simplified trapezium rule method (STM). 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 against theoretical results, 3-D numerical 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 1-D models and numerical schemes.
U2 - 10.1002/cnm.2732
DO - 10.1002/cnm.2732
M3 - Article
C2 - 26100764
SN - 2040-7939
VL - 31
JO - International Journal For Numerical Methods In Biomedical Engineering
JF - International Journal For Numerical Methods In Biomedical Engineering
IS - 10
M1 - e02732
ER -