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An implicit solver for 1D arterial network models

Jason Carson, Raoul Van Loon, Raoul van Loon Orcid Logo

International Journal for Numerical Methods in Biomedical Engineering, Volume: 33, Issue: 7

Swansea University Author: Raoul van Loon Orcid Logo

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DOI (Published version): 10.1002/cnm.2837

Abstract

In this study the one dimensional blood flow equations are solved using a newly proposed enhanced trapezoidal rule method ETM, which is an extension to the simplified trapezoidal rule method STM. At vessel junctions the conservation of mass and conservation of total pressure are held as system const...

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Published in: International Journal for Numerical Methods in Biomedical Engineering
ISSN: 2040-7939
Published: 2016
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URI: https://cronfa.swan.ac.uk/Record/cronfa30518
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spelling 2020-06-25T12:18:02.3469505 v2 30518 2016-10-10 An implicit solver for 1D arterial network models 880b30f90841a022f1e5bac32fb12193 0000-0003-3581-5827 Raoul van Loon Raoul van Loon true false 2016-10-10 MEDE In this study the one dimensional blood flow equations are solved using a newly proposed enhanced trapezoidal rule method ETM, which is an extension to the simplified trapezoidal rule method STM. At vessel junctions the conservation of mass and conservation of total pressure are held as system constraints using Lagrange multipliers that can be physically interpreted as external flow rates. The ETM scheme is compared with published arterial network benchmark problems and a dam break problem. Strengths of the ETM scheme include being simple to implement, intuitive connection to lumped parameter models, and no restrictive stability criteria such as the CFL number. The ETM scheme does not require the use of characteristics at vessel junctions, or for inlet and outlet boundary conditions. The ETM forms an implicit system of equations which requires only one global solve per time step for pressure, followed by flow rate update on the elemental system of equations, thus no iterations are required per time step. Consistent results are found for all benchmark cases and for a 56 vessel arterial network problem it gives very satisfactory solutions at a spatial and time discretisation that results in a maximum CFL of 3, taking 4.44 seconds per cardiac cycle. By increasing the time step and element size to produce a maximum CFL number of 15 the method takes only 0.39 seconds per cardiac cycle with only a small compromise on accuracy. Journal Article International Journal for Numerical Methods in Biomedical Engineering 33 7 2040-7939 31 12 2016 2016-12-31 10.1002/cnm.2837 COLLEGE NANME Biomedical Engineering COLLEGE CODE MEDE Swansea University 2020-06-25T12:18:02.3469505 2016-10-10T09:09:31.7416067 Faculty of Science and Engineering School of Engineering and Applied Sciences - Biomedical Engineering Jason Carson 1 Raoul Van&nbsp;Loon 2 Raoul van Loon 0000-0003-3581-5827 3 0030518-1011201680650AM.pdf carson2016(2).pdf 2016-10-11T08:06:50.9570000 Output 860751 application/pdf Accepted Manuscript true 2017-10-06T00:00:00.0000000 false
title An implicit solver for 1D arterial network models
spellingShingle An implicit solver for 1D arterial network models
Raoul van Loon
title_short An implicit solver for 1D arterial network models
title_full An implicit solver for 1D arterial network models
title_fullStr An implicit solver for 1D arterial network models
title_full_unstemmed An implicit solver for 1D arterial network models
title_sort An implicit solver for 1D arterial network models
author_id_str_mv 880b30f90841a022f1e5bac32fb12193
author_id_fullname_str_mv 880b30f90841a022f1e5bac32fb12193_***_Raoul van Loon
author Raoul van Loon
author2 Jason Carson
Raoul Van&nbsp;Loon
Raoul van Loon
format Journal article
container_title International Journal for Numerical Methods in Biomedical Engineering
container_volume 33
container_issue 7
publishDate 2016
institution Swansea University
issn 2040-7939
doi_str_mv 10.1002/cnm.2837
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Engineering and Applied Sciences - Biomedical Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Engineering and Applied Sciences - Biomedical Engineering
document_store_str 1
active_str 0
description In this study the one dimensional blood flow equations are solved using a newly proposed enhanced trapezoidal rule method ETM, which is an extension to the simplified trapezoidal rule method STM. At vessel junctions the conservation of mass and conservation of total pressure are held as system constraints using Lagrange multipliers that can be physically interpreted as external flow rates. The ETM scheme is compared with published arterial network benchmark problems and a dam break problem. Strengths of the ETM scheme include being simple to implement, intuitive connection to lumped parameter models, and no restrictive stability criteria such as the CFL number. The ETM scheme does not require the use of characteristics at vessel junctions, or for inlet and outlet boundary conditions. The ETM forms an implicit system of equations which requires only one global solve per time step for pressure, followed by flow rate update on the elemental system of equations, thus no iterations are required per time step. Consistent results are found for all benchmark cases and for a 56 vessel arterial network problem it gives very satisfactory solutions at a spatial and time discretisation that results in a maximum CFL of 3, taking 4.44 seconds per cardiac cycle. By increasing the time step and element size to produce a maximum CFL number of 15 the method takes only 0.39 seconds per cardiac cycle with only a small compromise on accuracy.
published_date 2016-12-31T03:37:07Z
_version_ 1763751626952146944
score 11.016593

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