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

Swansea University Author: ATAOLLAH GHAVAMIAN

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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...

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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
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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-e&#xFB00;ective 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 di&#xFB00;erent 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 o&#xFB00;er the possibility of tackling speci&#xFB01;c applications in which mesh-based techniques may not be e&#xFB03;cient (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 &#xFB01;nite 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 &#xFB01;rst order hyperbolic conservation laws for isothermal elastodynamics was presented in [3&#x2013;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 &#xFB01;rst 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 &#x3B7; or total energy density E by which the Total Lagrangian entropy-based and total energy-based formulations {p, F , H, J, &#x3B7; 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 arti&#xFB01;cial 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 e&#xFB03;cient in nearly incompressible thermo-elasticity in comparison with classical &#xFB01;nite element displacement-based approaches. 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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 College of Engineering Engineering 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
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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 2021-11-08T04:32:45Z
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