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A high-order stabilised ALE finite element formulation for the Euler equations on deformable domains

Rubén Sevilla Orcid Logo, Antonio Gil Orcid Logo, Michael Weberstadt

Computers & Structures, Volume: 181, Pages: 89 - 102

Swansea University Authors: Rubén Sevilla Orcid Logo, Antonio Gil Orcid Logo

Abstract

This paper presents a high-order accurate stabilised finite element formulation for the simulation of transient inviscid flow problems in deformable domains. This work represents an extension of the methodology described in Sevilla et al. (2013), where a high-order stabilised finite element formulat...

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Published in: Computers & Structures
ISSN: 0045-7949
Published: 2017
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URI: https://cronfa.swan.ac.uk/Record/cronfa30908
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spelling 2017-07-07T11:13:35.6723076 v2 30908 2016-11-03 A high-order stabilised ALE finite element formulation for the Euler equations on deformable domains b542c87f1b891262844e95a682f045b6 0000-0002-0061-6214 Rubén Sevilla Rubén Sevilla true false 1f5666865d1c6de9469f8b7d0d6d30e2 0000-0001-7753-1414 Antonio Gil Antonio Gil true false 2016-11-03 CIVL This paper presents a high-order accurate stabilised finite element formulation for the simulation of transient inviscid flow problems in deformable domains. This work represents an extension of the methodology described in Sevilla et al. (2013), where a high-order stabilised finite element formulation was used as an efficient alternative for the simulation of steady flow problems of aerodynamic interest. The proposed methodology combines the Streamline Upwind/Petrov-Galerkin method with the generalised-α method and employs an Arbitrary Lagrangian Eulerian (ALE) description to account for the motion of the underlying mesh. Two computational frameworks, based on the use of reference and spatial variables are presented, discussed and thoroughly compared. In the process, a tailor-made discrete geometric conservation law is derived in order to ensure that a uniform flow field is exactly reproduced. Several numerical examples are presented in order to illustrate the performance of the proposed methodology. The results demonstrate the optimal approximation properties of both spatial and temporal discretisations as well as the crucial benefits, in terms of accuracy, of the exact satisfaction of the discrete geometric conservation law. In addition, the behaviour of the proposed high-order formulation is analysed in terms of the chosen stabilisation parameter. Finally, the benefits of using high-order approximations for the simulation of inviscid flows in moving domains are discussed by comparing low and high-order approximations for the solution of the Euler equations on a deformable domain. Journal Article Computers & Structures 181 89 102 0045-7949 31 3 2017 2017-03-31 10.1016/j.compstruc.2016.11.019 COLLEGE NANME Civil Engineering COLLEGE CODE CIVL Swansea University 2017-07-07T11:13:35.6723076 2016-11-03T09:07:37.8750575 College of Engineering Engineering Rubén Sevilla 0000-0002-0061-6214 1 Antonio Gil 0000-0001-7753-1414 2 Michael Weberstadt 3 0030908-07022017151245.pdf sevilla2016v5.pdf 2017-02-07T15:12:45.6270000 Output 1816900 application/pdf Version of Record true 2017-02-07T00:00:00.0000000 false
title A high-order stabilised ALE finite element formulation for the Euler equations on deformable domains
spellingShingle A high-order stabilised ALE finite element formulation for the Euler equations on deformable domains
Rubén Sevilla
Antonio Gil
title_short A high-order stabilised ALE finite element formulation for the Euler equations on deformable domains
title_full A high-order stabilised ALE finite element formulation for the Euler equations on deformable domains
title_fullStr A high-order stabilised ALE finite element formulation for the Euler equations on deformable domains
title_full_unstemmed A high-order stabilised ALE finite element formulation for the Euler equations on deformable domains
title_sort A high-order stabilised ALE finite element formulation for the Euler equations on deformable domains
author_id_str_mv b542c87f1b891262844e95a682f045b6
1f5666865d1c6de9469f8b7d0d6d30e2
author_id_fullname_str_mv b542c87f1b891262844e95a682f045b6_***_Rubén Sevilla
1f5666865d1c6de9469f8b7d0d6d30e2_***_Antonio Gil
author Rubén Sevilla
Antonio Gil
author2 Rubén Sevilla
Antonio Gil
Michael Weberstadt
format Journal article
container_title Computers & Structures
container_volume 181
container_start_page 89
publishDate 2017
institution Swansea University
issn 0045-7949
doi_str_mv 10.1016/j.compstruc.2016.11.019
college_str College of Engineering
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hierarchy_top_title College of Engineering
hierarchy_parent_id collegeofengineering
hierarchy_parent_title College of Engineering
department_str Engineering{{{_:::_}}}College of Engineering{{{_:::_}}}Engineering
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description This paper presents a high-order accurate stabilised finite element formulation for the simulation of transient inviscid flow problems in deformable domains. This work represents an extension of the methodology described in Sevilla et al. (2013), where a high-order stabilised finite element formulation was used as an efficient alternative for the simulation of steady flow problems of aerodynamic interest. The proposed methodology combines the Streamline Upwind/Petrov-Galerkin method with the generalised-α method and employs an Arbitrary Lagrangian Eulerian (ALE) description to account for the motion of the underlying mesh. Two computational frameworks, based on the use of reference and spatial variables are presented, discussed and thoroughly compared. In the process, a tailor-made discrete geometric conservation law is derived in order to ensure that a uniform flow field is exactly reproduced. Several numerical examples are presented in order to illustrate the performance of the proposed methodology. The results demonstrate the optimal approximation properties of both spatial and temporal discretisations as well as the crucial benefits, in terms of accuracy, of the exact satisfaction of the discrete geometric conservation law. In addition, the behaviour of the proposed high-order formulation is analysed in terms of the chosen stabilisation parameter. Finally, the benefits of using high-order approximations for the simulation of inviscid flows in moving domains are discussed by comparing low and high-order approximations for the solution of the Euler equations on a deformable domain.
published_date 2017-03-31T03:42:38Z
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