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Novel semi-implicit, locally conservative Galerkin (SILCG) methods: Application to blood flow in a systemic circulation

Hayder Hasan, Alberto Coccarelli Orcid Logo, Perumal Nithiarasu Orcid Logo

Computer Methods in Applied Mechanics and Engineering, Volume: 332, Pages: 217 - 233

Swansea University Authors: Hayder Hasan, Alberto Coccarelli Orcid Logo, Perumal Nithiarasu Orcid Logo

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DOI (Published version): 10.1016/j.cma.2017.12.017

Abstract

Three novel, locally conservative Galerkin (LCG) methods in their semi-implicit form are proposed for 1D blood flow modelling in arterial networks. These semi-implicit discretizations are: the second order Taylor expansion (SILCG-TE) method, the streamline upwind Petrov–Galerkin (SILCG-SUPG) procedu...

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Published in: Computer Methods in Applied Mechanics and Engineering
ISSN: 0045-7825
Published: 2018
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URI: https://cronfa.swan.ac.uk/Record/cronfa37572
first_indexed 2017-12-12T19:49:28Z
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spelling 2022-11-09T15:01:18.4485279 v2 37572 2017-12-12 Novel semi-implicit, locally conservative Galerkin (SILCG) methods: Application to blood flow in a systemic circulation 5bc44c87491bc2dbdee27829a20f6342 Hayder Hasan Hayder Hasan true false 06fd3332e5eb3cf4bb4e75a24f49149d 0000-0003-1511-9015 Alberto Coccarelli Alberto Coccarelli true false 3b28bf59358fc2b9bd9a46897dbfc92d 0000-0002-4901-2980 Perumal Nithiarasu Perumal Nithiarasu true false 2017-12-12 Three novel, locally conservative Galerkin (LCG) methods in their semi-implicit form are proposed for 1D blood flow modelling in arterial networks. These semi-implicit discretizations are: the second order Taylor expansion (SILCG-TE) method, the streamline upwind Petrov–Galerkin (SILCG-SUPG) procedure and the forward in time and central in space (SILCG-FTCS) method. In the LCG method, enforcement of the flux continuity condition at the element interfaces allows to solve the discretized system of equations at element level. For problems with a large number of degrees of freedoms, this offers a significant advantage over the standard continuous Galerkin (CG) procedure. The well established fully explicit LCG method is used for assessing the accuracy of the proposed new methods. Results presented in this work demonstrate that the proposed SILCG methods are stable and as accurate as the explicit LCG method. Among the three methods proposed, the SILCG-FTCS method requires considerably lower number of iterations per element, and thus requires lowest amount of CPU time. On the other hand, the SILCG-TE and SILCG-SUPG methods are stable and accurate for larger time step sizes. Although the standard Newton method requires evaluation of both the Jacobian matrix and the residual for every single iteration, which may be expensive for standard implicit solvers, the computed results show that the maximum number of iterations per element for SILCG-TE and SILCG-SUPG is less than unity (less than 0.3 and 0.7 respectively). Also, numerical experiments show that the Jacobian matrix can be calculated only once per time step, allowing to save a significant amount of computational time. Journal Article Computer Methods in Applied Mechanics and Engineering 332 217 233 0045-7825 Semi-implicit; Locally conservative Galerkin (SILCG) methods; SILCG-TE; SILCG-SUPG and SILCG-FTCS methods; Elastic tubes; Systemic circulation; Arterial flow 15 4 2018 2018-04-15 10.1016/j.cma.2017.12.017 COLLEGE NANME COLLEGE CODE Swansea University 2022-11-09T15:01:18.4485279 2017-12-12T16:01:37.2263979 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering Hayder Hasan 1 Alberto Coccarelli 0000-0003-1511-9015 2 Perumal Nithiarasu 0000-0002-4901-2980 3 0037572-02012018120533.pdf hasan2017v2.pdf 2018-01-02T12:05:33.0570000 Output 10367041 application/pdf Accepted Manuscript true 2018-12-19T00:00:00.0000000 Released with a Creative Commons Attribution Non-Commercial No Derivatives License (CC-BY-NC-ND). true eng
title Novel semi-implicit, locally conservative Galerkin (SILCG) methods: Application to blood flow in a systemic circulation
spellingShingle Novel semi-implicit, locally conservative Galerkin (SILCG) methods: Application to blood flow in a systemic circulation
Hayder Hasan
Alberto Coccarelli
Perumal Nithiarasu
title_short Novel semi-implicit, locally conservative Galerkin (SILCG) methods: Application to blood flow in a systemic circulation
title_full Novel semi-implicit, locally conservative Galerkin (SILCG) methods: Application to blood flow in a systemic circulation
title_fullStr Novel semi-implicit, locally conservative Galerkin (SILCG) methods: Application to blood flow in a systemic circulation
title_full_unstemmed Novel semi-implicit, locally conservative Galerkin (SILCG) methods: Application to blood flow in a systemic circulation
title_sort Novel semi-implicit, locally conservative Galerkin (SILCG) methods: Application to blood flow in a systemic circulation
author_id_str_mv 5bc44c87491bc2dbdee27829a20f6342
06fd3332e5eb3cf4bb4e75a24f49149d
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author_id_fullname_str_mv 5bc44c87491bc2dbdee27829a20f6342_***_Hayder Hasan
06fd3332e5eb3cf4bb4e75a24f49149d_***_Alberto Coccarelli
3b28bf59358fc2b9bd9a46897dbfc92d_***_Perumal Nithiarasu
author Hayder Hasan
Alberto Coccarelli
Perumal Nithiarasu
author2 Hayder Hasan
Alberto Coccarelli
Perumal Nithiarasu
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container_title Computer Methods in Applied Mechanics and Engineering
container_volume 332
container_start_page 217
publishDate 2018
institution Swansea University
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doi_str_mv 10.1016/j.cma.2017.12.017
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department_str School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering
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description Three novel, locally conservative Galerkin (LCG) methods in their semi-implicit form are proposed for 1D blood flow modelling in arterial networks. These semi-implicit discretizations are: the second order Taylor expansion (SILCG-TE) method, the streamline upwind Petrov–Galerkin (SILCG-SUPG) procedure and the forward in time and central in space (SILCG-FTCS) method. In the LCG method, enforcement of the flux continuity condition at the element interfaces allows to solve the discretized system of equations at element level. For problems with a large number of degrees of freedoms, this offers a significant advantage over the standard continuous Galerkin (CG) procedure. The well established fully explicit LCG method is used for assessing the accuracy of the proposed new methods. Results presented in this work demonstrate that the proposed SILCG methods are stable and as accurate as the explicit LCG method. Among the three methods proposed, the SILCG-FTCS method requires considerably lower number of iterations per element, and thus requires lowest amount of CPU time. On the other hand, the SILCG-TE and SILCG-SUPG methods are stable and accurate for larger time step sizes. Although the standard Newton method requires evaluation of both the Jacobian matrix and the residual for every single iteration, which may be expensive for standard implicit solvers, the computed results show that the maximum number of iterations per element for SILCG-TE and SILCG-SUPG is less than unity (less than 0.3 and 0.7 respectively). Also, numerical experiments show that the Jacobian matrix can be calculated only once per time step, allowing to save a significant amount of computational time.
published_date 2018-04-15T08:29:42Z
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