A Computational Framework for A First-Order System of Conservation Laws in Thermoelasticity

GHAVAMIAN, ATAOLLAH

doi:10.23889/SUthesis.58574

E-Thesis 446 views 148 downloads

A Computational Framework for A First-Order System of Conservation Laws in Thermoelasticity / ATAOLLAH GHAVAMIAN

Swansea University Author: ATAOLLAH GHAVAMIAN

PDF | E-Thesis – open access

Copyright: The author, Ataollah Ghavamian, 2021.
Download (70.89MB)

DOI (Published version): 10.23889/SUthesis.58574

Abstract

It is evidently not trivial to analytically solve practical engineering problems due to their inherent (geometrical and/or material) nonlinearities. Moreover, experimental testing can be extremely costly, time-consuming and even dangerous, in some cases. In the past few decades, therefore, numerical...

Full description

Published:	Swansea 2021
Institution:	Swansea University
Degree level:	Doctoral
Degree name:	Ph.D
Supervisor:	Gil, Antonio J. ; Stainier, Laurent
URI:	https://cronfa.swan.ac.uk/Record/cronfa58574
Tags:	Add Tag No Tags, Be the first to tag this record!

first_indexed	2021-11-08T12:46:59Z
last_indexed	2021-11-09T04:26:00Z
id	cronfa58574
recordtype	RisThesis
fullrecord	<?xml version="1.0"?><rfc1807><datestamp>2021-11-08T14:46:40.6585255</datestamp><bib-version>v2</bib-version><id>58574</id><entry>2021-11-08</entry><title>A Computational Framework for A First-Order System of Conservation Laws in Thermoelasticity</title><swanseaauthors><author><sid>c89a093f38c241e975e296f986d9ec25</sid><firstname>ATAOLLAH</firstname><surname>GHAVAMIAN</surname><name>ATAOLLAH GHAVAMIAN</name><active>true</active><ethesisStudent>false</ethesisStudent></author></swanseaauthors><date>2021-11-08</date><abstract>It is evidently not trivial to analytically solve practical engineering problems due to their inherent (geometrical and/or material) nonlinearities. Moreover, experimental testing can be extremely costly, time-consuming and even dangerous, in some cases. In the past few decades, therefore, numerical techniques have been progressively developed and utilised in order to investigate complex engineering applications through computer simulations, in a cost-eﬀective manner.An important feature of a numerical methodology is how to approximate a physical domain into a computational domain and that, typically, can be carried out via mesh-based and particle-based approximations, either of which manifest with a diﬀerent range of capabilities. Due to the geometrical complexity of many industrial applications (e.g. biomechanics, shape casting, metal forming, additive manufactur-ing, crash simulations), a growing attraction has been received by tetrahedral mesh generation, thanks to Delaunay and advancing front techniques [1, 2]. Alternatively, particle-based methods can be used as they oﬀer the possibility of tackling speciﬁc applications in which mesh-based techniques may not be eﬃcient (e.g. hyper velocity impact, astrophysics, failure simulations, blast).In the context of fast thermo-elastodynamics, modern commercial packages are typically developed on the basis of second order displacement-based ﬁnite element formulations and, unfortunately, that introduces a series of numerical shortcomings such as reduced order of convergence for strains and stresses in comparison with displacements and the possible onset of numerical instabilities (e.g. detrimental locking, hour-glass modes, spurious pressure oscillations).To rectify these drawbacks, a mixed-based set of ﬁrst order hyperbolic conservation laws for isothermal elastodynamics was presented in [3–6], in terms of the linear momentum p per unit undeformed volume and the minors of the deformation, namely, the deformation gradient F , its co-factor H and its Jacobian J. Taking inspiration of these works [4, 7] and in order to account for irreversible processes, the balance of total energy (also known as the ﬁrst law of thermodynamics) is incorporated to the set of physical laws used to describe the deformation process. This, in general, can be expressed in terms of the entropy density η or total energy density E by which the Total Lagrangian entropy-based and total energy-based formulations {p, F , H, J, η or E} are established, respectively. Interestingly, taking advantage of the conservation formulation framework, it is possible to bridge the gap between solid dynamics and Computational Fluid Dynamics (CFD) by exploiting available CFD techniques in the context of solid dynamics.From a computational standpoint, two distinct and extremely competitive spatial discretisations are employed, namely, mesh-based Vertex-Centred Finite Volume Method (VCFVM) and meshless Smooth Particle Hydrodynamics (SPH). A linear reconstruction procedure together with a slope limiter is employed in order to ensure second order accuracy in space whilst avoiding numerical oscillations in the vicinity of sharp gradients, respectively. Crucially, the discontinuous solution for the conservation variables across (dual) control volume interfaces or between any pair of particles is approximated via an acoustic Riemann solver. In addition, a tailor-made artiﬁcial compressibility algorithm and an angular momentum preservation scheme are also incorporated in order to assess same limiting scenarios.The semi-discrete system of equations is then temporally discretised using a one-step two-stage Total Variation Diminishing (TVD) Runge-Kutta time integrator, providing second order accuracy in time. The geometry is also monolithically updated to be only used for post-processing purposes.Finally, a wide spectrum of challenging examples is presented in order to assess both the performance and applicability of the proposed schemes. The new formulation is proven to be very eﬃcient in nearly incompressible thermo-elasticity in comparison with classical ﬁnite element displacement-based approaches. The proposed computational framework provides a good balance between accuracy and speed of computation.</abstract><type>E-Thesis</type><journal/><volume/><journalNumber/><paginationStart/><paginationEnd/><publisher/><placeOfPublication>Swansea</placeOfPublication><isbnPrint/><isbnElectronic/><issnPrint/><issnElectronic/><keywords>Finite Volume Method, Vertex-Centred scheme, Smooth Particle Hydrodynamics, Riemann solver, Conservation laws, Thermoelasticity</keywords><publishedDay>8</publishedDay><publishedMonth>11</publishedMonth><publishedYear>2021</publishedYear><publishedDate>2021-11-08</publishedDate><doi>10.23889/SUthesis.58574</doi><url/><notes>ORCiD identifier: https://orcid.org/0000-0001-5074-5981</notes><college>COLLEGE NANME</college><CollegeCode>COLLEGE CODE</CollegeCode><institution>Swansea University</institution><supervisor>Gil, Antonio J. ; Stainier, Laurent</supervisor><degreelevel>Doctoral</degreelevel><degreename>Ph.D</degreename><degreesponsorsfunders>European Commission EACEA; EM Joint Doctorate Simulation in Engineering and Entrepreneurship Development (SEED)</degreesponsorsfunders><apcterm/><lastEdited>2021-11-08T14:46:40.6585255</lastEdited><Created>2021-11-08T12:42:25.3883425</Created><path><level id="1">Faculty of Science and Engineering</level><level id="2">School of Engineering and Applied Sciences - Uncategorised</level></path><authors><author><firstname>ATAOLLAH</firstname><surname>GHAVAMIAN</surname><order>1</order></author></authors><documents><document><filename>58574__21447__cda9451ba9c641ac8b93931d07a6119c.pdf</filename><originalFilename>Ghavamian_Ataollah_PhD_Thesis_Final_Redacted_Signature.pdf</originalFilename><uploaded>2021-11-08T13:11:20.4368093</uploaded><type>Output</type><contentLength>74334842</contentLength><contentType>application/pdf</contentType><version>E-Thesis – open access</version><cronfaStatus>true</cronfaStatus><documentNotes>Copyright: The author, Ataollah Ghavamian, 2021.</documentNotes><copyrightCorrect>true</copyrightCorrect><language>eng</language></document></documents><OutputDurs/></rfc1807>
spelling	2021-11-08T14:46:40.6585255 v2 58574 2021-11-08 A Computational Framework for A First-Order System of Conservation Laws in Thermoelasticity c89a093f38c241e975e296f986d9ec25 ATAOLLAH GHAVAMIAN ATAOLLAH GHAVAMIAN true false 2021-11-08 It is evidently not trivial to analytically solve practical engineering problems due to their inherent (geometrical and/or material) nonlinearities. Moreover, experimental testing can be extremely costly, time-consuming and even dangerous, in some cases. In the past few decades, therefore, numerical techniques have been progressively developed and utilised in order to investigate complex engineering applications through computer simulations, in a cost-eﬀective manner.An important feature of a numerical methodology is how to approximate a physical domain into a computational domain and that, typically, can be carried out via mesh-based and particle-based approximations, either of which manifest with a diﬀerent range of capabilities. Due to the geometrical complexity of many industrial applications (e.g. biomechanics, shape casting, metal forming, additive manufactur-ing, crash simulations), a growing attraction has been received by tetrahedral mesh generation, thanks to Delaunay and advancing front techniques [1, 2]. Alternatively, particle-based methods can be used as they oﬀer the possibility of tackling speciﬁc applications in which mesh-based techniques may not be eﬃcient (e.g. hyper velocity impact, astrophysics, failure simulations, blast).In the context of fast thermo-elastodynamics, modern commercial packages are typically developed on the basis of second order displacement-based ﬁnite element formulations and, unfortunately, that introduces a series of numerical shortcomings such as reduced order of convergence for strains and stresses in comparison with displacements and the possible onset of numerical instabilities (e.g. detrimental locking, hour-glass modes, spurious pressure oscillations).To rectify these drawbacks, a mixed-based set of ﬁrst order hyperbolic conservation laws for isothermal elastodynamics was presented in [3–6], in terms of the linear momentum p per unit undeformed volume and the minors of the deformation, namely, the deformation gradient F , its co-factor H and its Jacobian J. Taking inspiration of these works [4, 7] and in order to account for irreversible processes, the balance of total energy (also known as the ﬁrst law of thermodynamics) is incorporated to the set of physical laws used to describe the deformation process. This, in general, can be expressed in terms of the entropy density η or total energy density E by which the Total Lagrangian entropy-based and total energy-based formulations {p, F , H, J, η or E} are established, respectively. Interestingly, taking advantage of the conservation formulation framework, it is possible to bridge the gap between solid dynamics and Computational Fluid Dynamics (CFD) by exploiting available CFD techniques in the context of solid dynamics.From a computational standpoint, two distinct and extremely competitive spatial discretisations are employed, namely, mesh-based Vertex-Centred Finite Volume Method (VCFVM) and meshless Smooth Particle Hydrodynamics (SPH). A linear reconstruction procedure together with a slope limiter is employed in order to ensure second order accuracy in space whilst avoiding numerical oscillations in the vicinity of sharp gradients, respectively. Crucially, the discontinuous solution for the conservation variables across (dual) control volume interfaces or between any pair of particles is approximated via an acoustic Riemann solver. In addition, a tailor-made artiﬁcial compressibility algorithm and an angular momentum preservation scheme are also incorporated in order to assess same limiting scenarios.The semi-discrete system of equations is then temporally discretised using a one-step two-stage Total Variation Diminishing (TVD) Runge-Kutta time integrator, providing second order accuracy in time. The geometry is also monolithically updated to be only used for post-processing purposes.Finally, a wide spectrum of challenging examples is presented in order to assess both the performance and applicability of the proposed schemes. The new formulation is proven to be very eﬃcient in nearly incompressible thermo-elasticity in comparison with classical ﬁnite element displacement-based approaches. The proposed computational framework provides a good balance between accuracy and speed of computation. E-Thesis Swansea Finite Volume Method, Vertex-Centred scheme, Smooth Particle Hydrodynamics, Riemann solver, Conservation laws, Thermoelasticity 8 11 2021 2021-11-08 10.23889/SUthesis.58574 ORCiD identifier: https://orcid.org/0000-0001-5074-5981 COLLEGE NANME COLLEGE CODE Swansea University Gil, Antonio J. ; Stainier, Laurent Doctoral Ph.D European Commission EACEA; EM Joint Doctorate Simulation in Engineering and Entrepreneurship Development (SEED) 2021-11-08T14:46:40.6585255 2021-11-08T12:42:25.3883425 Faculty of Science and Engineering School of Engineering and Applied Sciences - Uncategorised ATAOLLAH GHAVAMIAN 1 58574__21447__cda9451ba9c641ac8b93931d07a6119c.pdf Ghavamian_Ataollah_PhD_Thesis_Final_Redacted_Signature.pdf 2021-11-08T13:11:20.4368093 Output 74334842 application/pdf E-Thesis – open access true Copyright: The author, Ataollah Ghavamian, 2021. true eng
title	A Computational Framework for A First-Order System of Conservation Laws in Thermoelasticity
spellingShingle	A Computational Framework for A First-Order System of Conservation Laws in Thermoelasticity ATAOLLAH GHAVAMIAN
title_short	A Computational Framework for A First-Order System of Conservation Laws in Thermoelasticity
title_full	A Computational Framework for A First-Order System of Conservation Laws in Thermoelasticity
title_fullStr	A Computational Framework for A First-Order System of Conservation Laws in Thermoelasticity
title_full_unstemmed	A Computational Framework for A First-Order System of Conservation Laws in Thermoelasticity
title_sort	A Computational Framework for A First-Order System of Conservation Laws in Thermoelasticity
author_id_str_mv	c89a093f38c241e975e296f986d9ec25
author_id_fullname_str_mv	c89a093f38c241e975e296f986d9ec25_***_ATAOLLAH GHAVAMIAN
author	ATAOLLAH GHAVAMIAN
author2	ATAOLLAH GHAVAMIAN
format	E-Thesis
publishDate	2021
institution	Swansea University
doi_str_mv	10.23889/SUthesis.58574
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 - Uncategorised{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Engineering and Applied Sciences - Uncategorised
document_store_str	1
active_str	0
description	It is evidently not trivial to analytically solve practical engineering problems due to their inherent (geometrical and/or material) nonlinearities. Moreover, experimental testing can be extremely costly, time-consuming and even dangerous, in some cases. In the past few decades, therefore, numerical techniques have been progressively developed and utilised in order to investigate complex engineering applications through computer simulations, in a cost-eﬀective manner.An important feature of a numerical methodology is how to approximate a physical domain into a computational domain and that, typically, can be carried out via mesh-based and particle-based approximations, either of which manifest with a diﬀerent range of capabilities. Due to the geometrical complexity of many industrial applications (e.g. biomechanics, shape casting, metal forming, additive manufactur-ing, crash simulations), a growing attraction has been received by tetrahedral mesh generation, thanks to Delaunay and advancing front techniques [1, 2]. Alternatively, particle-based methods can be used as they oﬀer the possibility of tackling speciﬁc applications in which mesh-based techniques may not be eﬃcient (e.g. hyper velocity impact, astrophysics, failure simulations, blast).In the context of fast thermo-elastodynamics, modern commercial packages are typically developed on the basis of second order displacement-based ﬁnite element formulations and, unfortunately, that introduces a series of numerical shortcomings such as reduced order of convergence for strains and stresses in comparison with displacements and the possible onset of numerical instabilities (e.g. detrimental locking, hour-glass modes, spurious pressure oscillations).To rectify these drawbacks, a mixed-based set of ﬁrst order hyperbolic conservation laws for isothermal elastodynamics was presented in [3–6], in terms of the linear momentum p per unit undeformed volume and the minors of the deformation, namely, the deformation gradient F , its co-factor H and its Jacobian J. Taking inspiration of these works [4, 7] and in order to account for irreversible processes, the balance of total energy (also known as the ﬁrst law of thermodynamics) is incorporated to the set of physical laws used to describe the deformation process. This, in general, can be expressed in terms of the entropy density η or total energy density E by which the Total Lagrangian entropy-based and total energy-based formulations {p, F , H, J, η or E} are established, respectively. Interestingly, taking advantage of the conservation formulation framework, it is possible to bridge the gap between solid dynamics and Computational Fluid Dynamics (CFD) by exploiting available CFD techniques in the context of solid dynamics.From a computational standpoint, two distinct and extremely competitive spatial discretisations are employed, namely, mesh-based Vertex-Centred Finite Volume Method (VCFVM) and meshless Smooth Particle Hydrodynamics (SPH). A linear reconstruction procedure together with a slope limiter is employed in order to ensure second order accuracy in space whilst avoiding numerical oscillations in the vicinity of sharp gradients, respectively. Crucially, the discontinuous solution for the conservation variables across (dual) control volume interfaces or between any pair of particles is approximated via an acoustic Riemann solver. In addition, a tailor-made artiﬁcial compressibility algorithm and an angular momentum preservation scheme are also incorporated in order to assess same limiting scenarios.The semi-discrete system of equations is then temporally discretised using a one-step two-stage Total Variation Diminishing (TVD) Runge-Kutta time integrator, providing second order accuracy in time. The geometry is also monolithically updated to be only used for post-processing purposes.Finally, a wide spectrum of challenging examples is presented in order to assess both the performance and applicability of the proposed schemes. The new formulation is proven to be very eﬃcient in nearly incompressible thermo-elasticity in comparison with classical ﬁnite element displacement-based approaches. The proposed computational framework provides a good balance between accuracy and speed of computation.
published_date	2021-11-08T04:15:12Z
_version_	1763754023683358720
score	11.036706

A Computational Framework for A First-Order System of Conservation Laws in Thermoelasticity / ATAOLLAH GHAVAMIAN

Similar Items