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Javier Bonet - One of the best experts on this subject based on the ideXlab platform.
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A parameter-free total Lagrangian Smooth Particle Hydrodynamics algorithm applied to problems with free surfaces
Computational Particle Mechanics, 2021Co-Authors: Kenny W. Q. Low, Antonio J Gil, Chun Hean Lee, Jibran Haider, Javier BonetAbstract:This paper presents a new Smooth Particle Hydrodynamics computational framework for the solution of inviscid free surface flow problems. The formulation is based on the Total Lagrangian description of a system of first-order conservation laws written in terms of the linear momentum and the Jacobian of the deformation. One of the aims of this paper is to explore the use of Total Lagrangian description in the case of large deformations but without topological changes. In this case, the evaluation of spatial integrals is carried out with respect to the initial undeformed configuration, yielding an extremely efficient formulation where the need for continuous Particle neighbouring search is completely circumvented. To guarantee stability from the SPH discretisation point of view, consistently derived Riemann-based numerical dissipation is suitably introduced where global numerical entropy production is demonstrated via a novel technique in terms of the time rate of the Hamiltonian of the system. Since the kernel derivatives presented in this work are fixed in the reference configuration, the non-physical clumping mechanism is completely removed. To fulfil conservation of the global angular momentum, a posteriori (least-squares) projection procedure is introduced. Finally, a wide spectrum of dedicated prototype problems is thoroughly examined. Through these tests, the SPH methodology overcomes by construction a number of persistent numerical drawbacks (e.g. hour-glassing, pressure instability, global conservation and/or completeness issues) commonly found in SPH literature, without resorting to the use of any ad-hoc user-defined artificial stabilisation parameters. Crucially, the overall SPH algorithm yields equal second order of convergence for both velocities and pressure.
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a variationally consistent streamline upwind petrov galerkin Smooth Particle Hydrodynamics algorithm for large strain solid dynamics
Computer Methods in Applied Mechanics and Engineering, 2017Co-Authors: Chun Hean Lee, Javier Bonet, Antonio J Gil, Osama I Hassan, Sivakumar KulasegaramAbstract: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 et al. (2014), Gil et al. (2014,2016), 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.
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a new jameson schmidt turkel Smooth Particle Hydrodynamics algorithm for large strain explicit fast dynamics
Computer Methods in Applied Mechanics and Engineering, 2016Co-Authors: Chun Hean Lee, Giorgio Greto, Sivakumar Kulasegaram, Antonio J Gil, Javier BonetAbstract:This paper presents a new Smooth Particle Hydrodynamics (SPH) computational framework for large strain explicit solid dynamics. A mixed-based set of Total Lagrangian conservation laws (Bonet et al., 2015; Gil et al., 2016) is presented in terms of the linear momentum and an extended set of geometric strain measures, comprised of the deformation gradient, its co-factor and the Jacobian. Taking advantage of this representation, the main aim of this paper is the adaptation of the very efficient Jameson–Schmidt–Turkel (JST) algorithm (Jameson et al., 1981) extensively used in computational fluid dynamics, to a SPH based discretisation of the mixed-based set of conservation laws, with three key distinct novelties. First, a conservative JST-based SPH computational framework is presented with emphasis in nearly incompressible materials. Second, the suppression of numerical instabilities associated with the non-physical zero-energy modes is addressed through a well-established stabilisation procedure. Third, the use of a discrete angular momentum projection algorithm is presented in conjunction with a monolithic Total Variation Diminishing Runge–Kutta time integrator in order to guarantee the global conservation of angular momentum. For completeness, exact enforcement of essential boundary conditions is incorporated through the use of a Lagrange multiplier projection technique. A series of challenging numerical examples (e.g. in the near incompressibility regime) are examined in order to assess the robustness and accuracy of the proposed algorithm. The obtained results are benchmarked against a wide spectrum of alternative numerical strategies.
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a stabilised total lagrangian corrected Smooth Particle Hydrodynamics technique in large strain explicit fast solid dynamics
VII European Congress on Computational Methods in Applied Sciences and Engineering, 2016Co-Authors: Giorgio Greto, Sivakumar Kulasegaram, Chun Hean Lee, Antonio J Gil, Javier BonetAbstract:An explicit Total Lagrangian mixed momentum/strains formulation [1-5], in the form of a system of first order conservation laws, has been recently proposed to overcome the shortcomings posed by the traditional second order displacement-based formulation, namely: (1) bending and volumetric locking difficulties; (2) hydrostatic pressure fluctuations; and (3) reduced order of convergence for derived variables. Following the work of Bonet and Kulasegaram [6, 7], the main objective of this paper is the adaptation of Corrected Smooth Particle Hydrodynamics (CSPH) in the context of Total Lagrangian mixed formulation. Appropriate nodally conservative Jameson-Schmidt-Turkel (JST) stabilisation is introduced by taking advantage of the conservation laws. This mixed linear momentum-deformation gradient technique performs extremely well in nearly incompressible bending dominated scenarios [1, 2] without the appearance of spurious pressure oscillations. Additionally, as both linear momentum and deformation gradient are used as primary variables of the system, equal order of approximation should be achieved in both fields. A series of numerical examples are carried out to assess the applicability and robustness of the proposed algorithm.
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Alternative total Lagrangian formulations for corrected Smooth Particle Hydrodynamics (CSPH) methods in large strain dynamics problems
Revue Européenne des Éléments Finis, 2012Co-Authors: Javier Bonet, Sivakumar KulasegaramAbstract:This paper discusses alternative Lagrangian formulations for Smooth Particle Hydrodynamics method. These Lagrangian formulations are here employed in solving large strain problems that involve elasto-plastic and hyperelastic materials. It has previously been shown in the literature that the Lagrangian formulation for continuum eliminates the problem of tension instability which is generally coupled with Eulerian continuum formulation of Smooth Particle Hydrodynamics and other meshless methods. This paper presents the details of the methodologies used in formulating Lagrangian Smooth Particle Hydrodynamics method and their characteristics.
Sivakumar Kulasegaram - One of the best experts on this subject based on the ideXlab platform.
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simulation of self compacting concrete in an l box using Smooth Particle Hydrodynamics
Magazine of Concrete Research, 2017Co-Authors: Muna M Alrubaye, Sivakumar Kulasegaram, Bhushan Lal KarihalooAbstract:The three-dimensional Lagrangian-Particle-based Smooth Particle Hydrodynamics methodology was used to simulate the flow characteristics of self-compacting concrete (SCC) mixes in an L-box test. A Bingham-type constitutive model was coupled with the Lagrangian momentum and continuity equations to simulate the flow. The simulations of SCC focused on the flow times, the free-surface profile and the distribution of large aggregates (larger than or equal to 8 mm) during the flow. The numerical simulation results were compared with actual L-box tests carried out on several SCC mixes. The comparison revealed that the methodology is very well suited to predicting the flow behaviour of SCC in terms of passing and filling abilities and the distribution of large aggregates.
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a variationally consistent streamline upwind petrov galerkin Smooth Particle Hydrodynamics algorithm for large strain solid dynamics
Computer Methods in Applied Mechanics and Engineering, 2017Co-Authors: Chun Hean Lee, Javier Bonet, Antonio J Gil, Osama I Hassan, Sivakumar KulasegaramAbstract: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 et al. (2014), Gil et al. (2014,2016), 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.
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recent developments in modelling self compacting concrete flow using Smooth Particle Hydrodynamics method
2017Co-Authors: Sivakumar Kulasegaram, Bhushan Lal KarihalooAbstract:Due to the demand forhighly durable concrete structures, self-compacting concrete (SCC)with its unique characteristics (flow-ability,passing ability and stability) has been developed, and is increasinglyreplacing vibrated concrete (VC) in variousstructural applications.SCC, which is characterised in its fresh state by high flow-ability andrheological stability, has excellent applicability for structural elements withcomplicated shapes and congested reinforcement. It has rationalisedthe construction process by offeringseveral economic and technical advantages over VC.Since the main characteristic of SCC is its flow-ability, its freshproperty cannot be thoroughly comprehended without understandingits rheology. The quality control and accurate prediction of the SCCrheology are crucial for the success of its production. The accurateprediction of the SCC flowing behaviour is not a simple task, particularlyin the presence of heavy reinforcement, complex formwork shapes andlarge size of aggregate. In this regard, the indispensable and inexpensiveapproach offering considerable potentialis the numerical simulation of SCC flow. This approach will deepenthe understanding of the SCC mixflow behaviour and evaluate its ability to meet the necessary self-compactingcriteria of passing ability and segregation resistance (i.e. homogeneousdistribution of coarse Particles in the matrix). From a computational point of view,the Smooth Particle Hydrodynamics(SPH), being a mesh-free Particle method, offersconsiderable potential in modelling SCC flow. Identifying SCC as a homogeneous fluid that consists of Particlesof different sizes and shapes, SPHis an idealcomputational method to represent its rheological behaviourwithan acceptable level of accuracy.This methodology hasbeen used and proved to beefficient and accurate in modelling the flow and monitoring the movementof large aggregates and/or short steel fibres of SCC in the coneslump flow,L-box and J-ring tests [1–3].The SPH simulation methodology also provides a useful tool for predicting the yield stress (τy) of SCCmixes accurately in an inverse manner from the flow spread [4]. Thisis particularly relevant to the characterisation of an SCC mix becausethe measurement of τyby rheometers is inconsistent and fraught with inaccuracies.In addition, computational simulationscan also assist inproportioning SCC mixes, thus improving on the traditional trial anderror SCC mix design.This paperwill presentthestate of the artmodelling of SCC mix flow using SPHapproach. This methodology will provide a thoroughunderstanding of whether or notan SCC mix can satisfy self-compatibility criteriaduring slump flow, L-box, J-ring and V-funnel tests. The accuracyof the SPHpredictionswill bebenchmarked against the observations made in the laboratory tests.
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a new jameson schmidt turkel Smooth Particle Hydrodynamics algorithm for large strain explicit fast dynamics
Computer Methods in Applied Mechanics and Engineering, 2016Co-Authors: Chun Hean Lee, Giorgio Greto, Sivakumar Kulasegaram, Antonio J Gil, Javier BonetAbstract:This paper presents a new Smooth Particle Hydrodynamics (SPH) computational framework for large strain explicit solid dynamics. A mixed-based set of Total Lagrangian conservation laws (Bonet et al., 2015; Gil et al., 2016) is presented in terms of the linear momentum and an extended set of geometric strain measures, comprised of the deformation gradient, its co-factor and the Jacobian. Taking advantage of this representation, the main aim of this paper is the adaptation of the very efficient Jameson–Schmidt–Turkel (JST) algorithm (Jameson et al., 1981) extensively used in computational fluid dynamics, to a SPH based discretisation of the mixed-based set of conservation laws, with three key distinct novelties. First, a conservative JST-based SPH computational framework is presented with emphasis in nearly incompressible materials. Second, the suppression of numerical instabilities associated with the non-physical zero-energy modes is addressed through a well-established stabilisation procedure. Third, the use of a discrete angular momentum projection algorithm is presented in conjunction with a monolithic Total Variation Diminishing Runge–Kutta time integrator in order to guarantee the global conservation of angular momentum. For completeness, exact enforcement of essential boundary conditions is incorporated through the use of a Lagrange multiplier projection technique. A series of challenging numerical examples (e.g. in the near incompressibility regime) are examined in order to assess the robustness and accuracy of the proposed algorithm. The obtained results are benchmarked against a wide spectrum of alternative numerical strategies.
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a stabilised total lagrangian corrected Smooth Particle Hydrodynamics technique in large strain explicit fast solid dynamics
VII European Congress on Computational Methods in Applied Sciences and Engineering, 2016Co-Authors: Giorgio Greto, Sivakumar Kulasegaram, Chun Hean Lee, Antonio J Gil, Javier BonetAbstract:An explicit Total Lagrangian mixed momentum/strains formulation [1-5], in the form of a system of first order conservation laws, has been recently proposed to overcome the shortcomings posed by the traditional second order displacement-based formulation, namely: (1) bending and volumetric locking difficulties; (2) hydrostatic pressure fluctuations; and (3) reduced order of convergence for derived variables. Following the work of Bonet and Kulasegaram [6, 7], the main objective of this paper is the adaptation of Corrected Smooth Particle Hydrodynamics (CSPH) in the context of Total Lagrangian mixed formulation. Appropriate nodally conservative Jameson-Schmidt-Turkel (JST) stabilisation is introduced by taking advantage of the conservation laws. This mixed linear momentum-deformation gradient technique performs extremely well in nearly incompressible bending dominated scenarios [1, 2] without the appearance of spurious pressure oscillations. Additionally, as both linear momentum and deformation gradient are used as primary variables of the system, equal order of approximation should be achieved in both fields. A series of numerical examples are carried out to assess the applicability and robustness of the proposed algorithm.
Stephan Rosswog - One of the best experts on this subject based on the ideXlab platform.
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Relativistic Smooth Particle Hydrodynamics on a given background spacetime
Classical and Quantum Gravity, 2010Co-Authors: Stephan RosswogAbstract:We review the derivation of fixed-metric, relativistic Smooth Particle Hydrodynamics (SPH) from the Lagrangian of an ideal fluid. Combining the Euler-Lagrange equations with the first law of thermodynamics, we explicitely derive evolution equations for the canonical momentum and energy. This new set of SPH equations also accounts for corrective terms that result from derivatives of the SPH Smoothing kernel and that are called " grad-h " terms in non-relativistic SPH. The new equations differ from earlier formulations with respect to these corrective terms and the symmetries in the SPH Particle indices while being identical in the gravitational terms.
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relativistic Smooth Particle Hydrodynamics on a given background spacetime
Classical and Quantum Gravity, 2010Co-Authors: Stephan RosswogAbstract:We review the derivation of fixed-metric, relativistic Smooth Particle Hydrodynamics (SPH) from the Lagrangian of an ideal fluid. Combining the Euler‐Lagrange equations with the first law of thermodynamics, we explicitly derive evolution equations for the canonical momentum and energy. This new set of SPH equations also accounts for corrective terms that result from derivatives of the SPH Smoothing kernel and that are called ‘grad-h’ terms in non-relativistic SPH. The new equations differ from earlier formulations with respect to these corrective terms and the symmetries in the SPH Particle indices while being identical in gravitational terms.
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astrophysical Smooth Particle Hydrodynamics
New Astronomy Reviews, 2009Co-Authors: Stephan RosswogAbstract:Abstract The paper presents a detailed review of the Smooth Particle Hydrodynamics (SPH) method with particular focus on its astrophysical applications. We start by introducing the basic ideas and concepts and thereby outline all ingredients that are necessary for a practical implementation of the method in a working SPH code. Much of SPH’s success relies on its excellent conservation properties and therefore the numerical conservation of physical invariants receives much attention throughout this review. The self-consistent derivation of the SPH equations from the Lagrangian of an ideal fluid is the common theme of the remainder of the text. We derive a modern, Newtonian SPH formulation from the Lagrangian of an ideal fluid. It accounts for changes of the local resolution lengths which result in corrective, so-called “grad-h-terms”. We extend this strategy to special relativity for which we derive the corresponding grad-h equation set. The variational approach is further applied to a general-relativistic fluid evolving in a fixed, curved background space-time. Particular care is taken to explicitly derive all relevant equations in a coherent way.
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astrophysical Smooth Particle Hydrodynamics
arXiv: Instrumentation and Methods for Astrophysics, 2009Co-Authors: Stephan RosswogAbstract:The paper presents a detailed review of the Smooth Particle Hydrodynamics (SPH) method with particular focus on its astrophysical applications. We start by introducing the basic ideas and concepts and thereby outline all ingredients that are necessary for a practical implementation of the method in a working SPH code. Much of SPH's success relies on its excellent conservation properties and therefore the numerical conservation of physical invariants receives much attention throughout this review. The self-consistent derivation of the SPH equations from the Lagrangian of an ideal fluid is the common theme of the remainder of the text. We derive a modern, Newtonian SPH formulation from the Lagrangian of an ideal fluid. It accounts for changes of the local resolution lengths which result in corrective, so-called "grad-h-terms". We extend this strategy to special relativity for which we derive the corresponding grad-h equation set. The variational approach is further applied to a general-relativistic fluid evolving in a fixed, curved background space-time. Particular care is taken to explicitely derive all relevant equations in a coherent way.
M X Rodriguezpaz - One of the best experts on this subject based on the ideXlab platform.
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a corrected Smooth Particle Hydrodynamics formulation of the shallow water equations
Computers & Structures, 2005Co-Authors: M X Rodriguezpaz, Javier BonetAbstract:A shallow-waters formulation based on a variable Smoothing length SPH method is presented. This new formulation of the SPH equations treats the continuum as a Hamiltonian system of Particles where the constitutive relationships for the materials are introduced via an internal energy term. Some of the advantages of the new SPH formulation are evident in the solution of the shallow-water equations for expanding flows. The shallow-waters approach incorporates the terrain into the equation of motion through terrain properties evaluated using SPH methodology. Several examples are presented on the simulation of breaking dams on different geometries. A comparison with the analytical solutions is also included.
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variational formulation for the Smooth Particle Hydrodynamics sph simulation of fluid and solid problems
Computer Methods in Applied Mechanics and Engineering, 2004Co-Authors: Javier Bonet, Sivakumar Kulasegaram, M X Rodriguezpaz, M ProfitAbstract:The paper describes the variational formulation of Smooth Particle Hydrodynamics for both fluids and solids applications. The resulting equations treat the continuum as a Hamiltonian system of Particles where the constitutive equation of the continuum is represented via an internal energy term. For solids this internal energy is derived from the deformation gradient of the mapping in terms of a hyperelastic strain energy function. In the case of fluids, the internal energy term is a function of the density. Once the internal energy terms are established the equations of motion are developed as equations of Lagrange, where the Lagrangian coordinates are the current positions of the Particles. Since the energy terms are independent of rigid body rotations and translations, this formulation ensures the preservation of physical constants of the motion such as linear and angular momentum.
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a corrected Smooth Particle Hydrodynamics method for the simulation of debris flows
Numerical Methods for Partial Differential Equations, 2004Co-Authors: M X Rodriguezpaz, Javier BonetAbstract:This article presents the development and application of a corrected Smooth Particle Hydrodynamics (CSPH) code to the simulation of debris flow and avalanches. The advantages of a mesh-free method over other traditional numerical methods such as the finite element method are discussed. A new frictional approach for the boundary conditions and modified constitutive equations are introduced in the SPH method. The resulting technique is then applied for the simulation of debris flows, comparing the results with those obtained from experiments reported by other researchers. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 20: 140–163, 2004.
Chun Hean Lee - One of the best experts on this subject based on the ideXlab platform.
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A parameter-free total Lagrangian Smooth Particle Hydrodynamics algorithm applied to problems with free surfaces
Computational Particle Mechanics, 2021Co-Authors: Kenny W. Q. Low, Antonio J Gil, Chun Hean Lee, Jibran Haider, Javier BonetAbstract:This paper presents a new Smooth Particle Hydrodynamics computational framework for the solution of inviscid free surface flow problems. The formulation is based on the Total Lagrangian description of a system of first-order conservation laws written in terms of the linear momentum and the Jacobian of the deformation. One of the aims of this paper is to explore the use of Total Lagrangian description in the case of large deformations but without topological changes. In this case, the evaluation of spatial integrals is carried out with respect to the initial undeformed configuration, yielding an extremely efficient formulation where the need for continuous Particle neighbouring search is completely circumvented. To guarantee stability from the SPH discretisation point of view, consistently derived Riemann-based numerical dissipation is suitably introduced where global numerical entropy production is demonstrated via a novel technique in terms of the time rate of the Hamiltonian of the system. Since the kernel derivatives presented in this work are fixed in the reference configuration, the non-physical clumping mechanism is completely removed. To fulfil conservation of the global angular momentum, a posteriori (least-squares) projection procedure is introduced. Finally, a wide spectrum of dedicated prototype problems is thoroughly examined. Through these tests, the SPH methodology overcomes by construction a number of persistent numerical drawbacks (e.g. hour-glassing, pressure instability, global conservation and/or completeness issues) commonly found in SPH literature, without resorting to the use of any ad-hoc user-defined artificial stabilisation parameters. Crucially, the overall SPH algorithm yields equal second order of convergence for both velocities and pressure.
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a variationally consistent streamline upwind petrov galerkin Smooth Particle Hydrodynamics algorithm for large strain solid dynamics
Computer Methods in Applied Mechanics and Engineering, 2017Co-Authors: Chun Hean Lee, Javier Bonet, Antonio J Gil, Osama I Hassan, Sivakumar KulasegaramAbstract: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 et al. (2014), Gil et al. (2014,2016), 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.
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a new jameson schmidt turkel Smooth Particle Hydrodynamics algorithm for large strain explicit fast dynamics
Computer Methods in Applied Mechanics and Engineering, 2016Co-Authors: Chun Hean Lee, Giorgio Greto, Sivakumar Kulasegaram, Antonio J Gil, Javier BonetAbstract:This paper presents a new Smooth Particle Hydrodynamics (SPH) computational framework for large strain explicit solid dynamics. A mixed-based set of Total Lagrangian conservation laws (Bonet et al., 2015; Gil et al., 2016) is presented in terms of the linear momentum and an extended set of geometric strain measures, comprised of the deformation gradient, its co-factor and the Jacobian. Taking advantage of this representation, the main aim of this paper is the adaptation of the very efficient Jameson–Schmidt–Turkel (JST) algorithm (Jameson et al., 1981) extensively used in computational fluid dynamics, to a SPH based discretisation of the mixed-based set of conservation laws, with three key distinct novelties. First, a conservative JST-based SPH computational framework is presented with emphasis in nearly incompressible materials. Second, the suppression of numerical instabilities associated with the non-physical zero-energy modes is addressed through a well-established stabilisation procedure. Third, the use of a discrete angular momentum projection algorithm is presented in conjunction with a monolithic Total Variation Diminishing Runge–Kutta time integrator in order to guarantee the global conservation of angular momentum. For completeness, exact enforcement of essential boundary conditions is incorporated through the use of a Lagrange multiplier projection technique. A series of challenging numerical examples (e.g. in the near incompressibility regime) are examined in order to assess the robustness and accuracy of the proposed algorithm. The obtained results are benchmarked against a wide spectrum of alternative numerical strategies.
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a stabilised total lagrangian corrected Smooth Particle Hydrodynamics technique in large strain explicit fast solid dynamics
VII European Congress on Computational Methods in Applied Sciences and Engineering, 2016Co-Authors: Giorgio Greto, Sivakumar Kulasegaram, Chun Hean Lee, Antonio J Gil, Javier BonetAbstract:An explicit Total Lagrangian mixed momentum/strains formulation [1-5], in the form of a system of first order conservation laws, has been recently proposed to overcome the shortcomings posed by the traditional second order displacement-based formulation, namely: (1) bending and volumetric locking difficulties; (2) hydrostatic pressure fluctuations; and (3) reduced order of convergence for derived variables. Following the work of Bonet and Kulasegaram [6, 7], the main objective of this paper is the adaptation of Corrected Smooth Particle Hydrodynamics (CSPH) in the context of Total Lagrangian mixed formulation. Appropriate nodally conservative Jameson-Schmidt-Turkel (JST) stabilisation is introduced by taking advantage of the conservation laws. This mixed linear momentum-deformation gradient technique performs extremely well in nearly incompressible bending dominated scenarios [1, 2] without the appearance of spurious pressure oscillations. Additionally, as both linear momentum and deformation gradient are used as primary variables of the system, equal order of approximation should be achieved in both fields. A series of numerical examples are carried out to assess the applicability and robustness of the proposed algorithm.
