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A variationally consistent Streamline Upwind Petrov–Galerkin Smooth Particle Hydrodynamics algorithm for large strain solid dynamics

Chun Hean Lee Orcid Logo, Antonio Gil Orcid Logo, Osama Hassan, Javier Bonet, Sivakumar Kulasegaram

Computer Methods in Applied Mechanics and Engineering, Volume: 318, Pages: 514 - 536

Swansea University Authors: Chun Hean Lee Orcid Logo, Antonio Gil Orcid Logo, Osama Hassan

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DOI (Published version): 10.1016/j.cma.2017.02.002

Abstract

This paper presents a new Smooth Particle Hydrodynamics (SPH) computational framework for explicit fast solid dynamics. The proposed methodology explores the use of the Streamline Upwind Petrov Galerkin (SUPG) stabilisation methodology as an alternative to the Jameson-Schmidt-Turkel (JST) stabilisat...

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Published in: Computer Methods in Applied Mechanics and Engineering
ISSN: 0045-7825
Published: 2017
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URI: https://cronfa.swan.ac.uk/Record/cronfa31873
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The proposed methodology explores the use of the Streamline Upwind Petrov Galerkin (SUPG) stabilisation methodology as an alternative to the Jameson-Schmidt-Turkel (JST) stabilisation recently presented by the authors in Lee et al. (2016) in the context of a conservation law formulation of fast solid dynamics. The work introduced in this paper puts forward three advantageous features over the recent JST-SPH framework. First, the variationally consistent nature of the SUPG stabilisation allows for the introduction of a locally preserving angular momentum procedure which can be solved in a monolithic manner in conjunction with the rest of the system equations. This differs from the JST-SPH framework, where an a posteriori projection procedure was required to ensure global angular momentum preservation. Second, evaluation of expensive harmonic and bi-harmonic operators, necessary for the JST stabilisation, is circumvented in the new SUPG-SPH framework. Third, the SUPG-SPH framework is more accurate (for the same number of degrees of freedom) than its JST-SPH counterpart and its accuracy is comparable to that of the robust (but computationally more demanding) Petrov Galerkin Finite Element Method (PG-FEM) technique explored by the authors in Lee, Gil and Bonet (2014), Gil et al. (2014), Gil et al. (2016), Bonet et al. (2015), as shown in the numerical examples included. A series of numerical examples are analysed in order to benchmark and assess the robustness and effectiveness of the proposed algorithm. 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spelling 2021-01-14T12:49:15.6874613 v2 31873 2017-02-06 A variationally consistent Streamline Upwind Petrov–Galerkin Smooth Particle Hydrodynamics algorithm for large strain solid dynamics e3024bdeee2dee48376c2a76b7147f2f 0000-0003-1102-3729 Chun Hean Lee Chun Hean Lee true false 1f5666865d1c6de9469f8b7d0d6d30e2 0000-0001-7753-1414 Antonio Gil Antonio Gil true false 527e97a89bb2be48a3963d11d4e18328 Osama Hassan Osama Hassan true false 2017-02-06 FGSEN This paper presents a new Smooth Particle Hydrodynamics (SPH) computational framework for explicit fast solid dynamics. The proposed methodology explores the use of the Streamline Upwind Petrov Galerkin (SUPG) stabilisation methodology as an alternative to the Jameson-Schmidt-Turkel (JST) stabilisation recently presented by the authors in Lee et al. (2016) in the context of a conservation law formulation of fast solid dynamics. The work introduced in this paper puts forward three advantageous features over the recent JST-SPH framework. First, the variationally consistent nature of the SUPG stabilisation allows for the introduction of a locally preserving angular momentum procedure which can be solved in a monolithic manner in conjunction with the rest of the system equations. This differs from the JST-SPH framework, where an a posteriori projection procedure was required to ensure global angular momentum preservation. Second, evaluation of expensive harmonic and bi-harmonic operators, necessary for the JST stabilisation, is circumvented in the new SUPG-SPH framework. Third, the SUPG-SPH framework is more accurate (for the same number of degrees of freedom) than its JST-SPH counterpart and its accuracy is comparable to that of the robust (but computationally more demanding) Petrov Galerkin Finite Element Method (PG-FEM) technique explored by the authors in Lee, Gil and Bonet (2014), Gil et al. (2014), Gil et al. (2016), Bonet et al. (2015), as shown in the numerical examples included. A series of numerical examples are analysed in order to benchmark and assess the robustness and effectiveness of the proposed algorithm. The resulting SUPG-SPH framework is therefore accurate, robust and computationally efficient, three key desired features that will allow the authors in forthcoming publications to explore its applicability in large scale simulations. Journal Article Computer Methods in Applied Mechanics and Engineering 318 514 536 0045-7825 Conservation laws; SPH; Instability; SUPG; Fast dynamics; Incompressibility 1 5 2017 2017-05-01 10.1016/j.cma.2017.02.002 COLLEGE NANME Science and Engineering - Faculty COLLEGE CODE FGSEN Swansea University 2021-01-14T12:49:15.6874613 2017-02-06T13:34:50.0594570 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering Chun Hean Lee 0000-0003-1102-3729 1 Antonio Gil 0000-0001-7753-1414 2 Osama Hassan 3 Javier Bonet 4 Sivakumar Kulasegaram 5 31873__4737__e108cddfc2f4470db996128a25d7ffac.pdf lee2017.pdf 2017-02-06T13:36:41.3830000 Output 8478594 application/pdf Accepted Manuscript true 2018-02-10T00:00:00.0000000 Released under the terms of a Creative Commons Attribution Non-Commercial No Derivatives License (CC-BY-NC-ND). true eng
title A variationally consistent Streamline Upwind Petrov–Galerkin Smooth Particle Hydrodynamics algorithm for large strain solid dynamics
spellingShingle A variationally consistent Streamline Upwind Petrov–Galerkin Smooth Particle Hydrodynamics algorithm for large strain solid dynamics
Chun Hean Lee
Antonio Gil
Osama Hassan
title_short A variationally consistent Streamline Upwind Petrov–Galerkin Smooth Particle Hydrodynamics algorithm for large strain solid dynamics
title_full A variationally consistent Streamline Upwind Petrov–Galerkin Smooth Particle Hydrodynamics algorithm for large strain solid dynamics
title_fullStr A variationally consistent Streamline Upwind Petrov–Galerkin Smooth Particle Hydrodynamics algorithm for large strain solid dynamics
title_full_unstemmed A variationally consistent Streamline Upwind Petrov–Galerkin Smooth Particle Hydrodynamics algorithm for large strain solid dynamics
title_sort A variationally consistent Streamline Upwind Petrov–Galerkin Smooth Particle Hydrodynamics algorithm for large strain solid dynamics
author_id_str_mv e3024bdeee2dee48376c2a76b7147f2f
1f5666865d1c6de9469f8b7d0d6d30e2
527e97a89bb2be48a3963d11d4e18328
author_id_fullname_str_mv e3024bdeee2dee48376c2a76b7147f2f_***_Chun Hean Lee
1f5666865d1c6de9469f8b7d0d6d30e2_***_Antonio Gil
527e97a89bb2be48a3963d11d4e18328_***_Osama Hassan
author Chun Hean Lee
Antonio Gil
Osama Hassan
author2 Chun Hean Lee
Antonio Gil
Osama Hassan
Javier Bonet
Sivakumar Kulasegaram
format Journal article
container_title Computer Methods in Applied Mechanics and Engineering
container_volume 318
container_start_page 514
publishDate 2017
institution Swansea University
issn 0045-7825
doi_str_mv 10.1016/j.cma.2017.02.002
college_str Faculty of Science and Engineering
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hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
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 This paper presents a new Smooth Particle Hydrodynamics (SPH) computational framework for explicit fast solid dynamics. The proposed methodology explores the use of the Streamline Upwind Petrov Galerkin (SUPG) stabilisation methodology as an alternative to the Jameson-Schmidt-Turkel (JST) stabilisation recently presented by the authors in Lee et al. (2016) in the context of a conservation law formulation of fast solid dynamics. The work introduced in this paper puts forward three advantageous features over the recent JST-SPH framework. First, the variationally consistent nature of the SUPG stabilisation allows for the introduction of a locally preserving angular momentum procedure which can be solved in a monolithic manner in conjunction with the rest of the system equations. This differs from the JST-SPH framework, where an a posteriori projection procedure was required to ensure global angular momentum preservation. Second, evaluation of expensive harmonic and bi-harmonic operators, necessary for the JST stabilisation, is circumvented in the new SUPG-SPH framework. Third, the SUPG-SPH framework is more accurate (for the same number of degrees of freedom) than its JST-SPH counterpart and its accuracy is comparable to that of the robust (but computationally more demanding) Petrov Galerkin Finite Element Method (PG-FEM) technique explored by the authors in Lee, Gil and Bonet (2014), Gil et al. (2014), Gil et al. (2016), Bonet et al. (2015), as shown in the numerical examples included. A series of numerical examples are analysed in order to benchmark and assess the robustness and effectiveness of the proposed algorithm. The resulting SUPG-SPH framework is therefore accurate, robust and computationally efficient, three key desired features that will allow the authors in forthcoming publications to explore its applicability in large scale simulations.
published_date 2017-05-01T03:38:59Z
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score 11.037581

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