Pub Date : 2024-10-30DOI: 10.1016/j.cma.2024.117483
Steffen W.R. Werner , Benjamin Peherstorfer
Stability is a basic requirement when studying the behavior of dynamical systems. However, stabilizing dynamical systems via reinforcement learning is challenging because only little data can be collected over short time horizons before instabilities are triggered and data become meaningless. This work introduces a reinforcement learning approach that is formulated over latent manifolds of unstable dynamics so that stabilizing policies can be trained from few data samples. The unstable manifolds are minimal in the sense that they contain the lowest dimensional dynamics that are necessary for learning policies that guarantee stabilization. This is in stark contrast to generic latent manifolds that aim to approximate all—stable and unstable—system dynamics and thus are higher dimensional and often require higher amounts of data. Experiments demonstrate that the proposed approach stabilizes even complex physical systems from few data samples for which other methods that operate either directly in the system state space or on generic latent manifolds fail.
{"title":"System stabilization with policy optimization on unstable latent manifolds","authors":"Steffen W.R. Werner , Benjamin Peherstorfer","doi":"10.1016/j.cma.2024.117483","DOIUrl":"10.1016/j.cma.2024.117483","url":null,"abstract":"<div><div>Stability is a basic requirement when studying the behavior of dynamical systems. However, stabilizing dynamical systems via reinforcement learning is challenging because only little data can be collected over short time horizons before instabilities are triggered and data become meaningless. This work introduces a reinforcement learning approach that is formulated over latent manifolds of unstable dynamics so that stabilizing policies can be trained from few data samples. The unstable manifolds are minimal in the sense that they contain the lowest dimensional dynamics that are necessary for learning policies that guarantee stabilization. This is in stark contrast to generic latent manifolds that aim to approximate all—stable and unstable—system dynamics and thus are higher dimensional and often require higher amounts of data. Experiments demonstrate that the proposed approach stabilizes even complex physical systems from few data samples for which other methods that operate either directly in the system state space or on generic latent manifolds fail.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"433 ","pages":"Article 117483"},"PeriodicalIF":6.9,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142552280","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-30DOI: 10.1016/j.cma.2024.117470
P. Gómez-Molina , L. Sanz-Lorenzo , J. Carpio
In this paper we present an efficient numerical algorithm to solve stationary problems of hydrodynamic lubrication with cavitation in bearings using the method of characteristics in a finite element framework. The problem is based on the Elrod–Adams mathematical model for the lubricant fluid behavior. To achieve realistic pressure solutions, cavitation must be considered. This leads to a non-linear system of equations including a multivalued operator. In order to solve this problem, we propose a modified Newton algorithm that presents a high convergence speed, allowing one to use small tolerances to solve the problem with high accuracy and efficiency using a low number of iterations, in comparison with alternative numerical algorithms in the literature to solve the same problem. Numerical results are presented and analyzed in the work.
{"title":"An efficient numerical algorithm to solve hydrodynamic lubrication problems with cavitation","authors":"P. Gómez-Molina , L. Sanz-Lorenzo , J. Carpio","doi":"10.1016/j.cma.2024.117470","DOIUrl":"10.1016/j.cma.2024.117470","url":null,"abstract":"<div><div>In this paper we present an efficient numerical algorithm to solve stationary problems of hydrodynamic lubrication with cavitation in bearings using the method of characteristics in a finite element framework. The problem is based on the Elrod–Adams mathematical model for the lubricant fluid behavior. To achieve realistic pressure solutions, cavitation must be considered. This leads to a non-linear system of equations including a multivalued operator. In order to solve this problem, we propose a modified Newton algorithm that presents a high convergence speed, allowing one to use small tolerances to solve the problem with high accuracy and efficiency using a low number of iterations, in comparison with alternative numerical algorithms in the literature to solve the same problem. Numerical results are presented and analyzed in the work.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"433 ","pages":"Article 117470"},"PeriodicalIF":6.9,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142550564","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-30DOI: 10.1016/j.cma.2024.117481
J.L.M. Thiesen , B. Klahr , T.A. Carniel , G.A. Holzapfel , P.J. Blanco , E.A. Fancello
We introduce a second-order computational homogenization procedure designed to address heterogeneous poromechanical media. Our approach relies on the method of multiscale virtual power, a variational multiscale method that extends the Hill–Mandel principle of macro-homogeneity. Constraints on displacement and pore pressure fields are managed using periodic and second-order minimally constrained fluctuating spaces. Numerical comparisons reveal that first-order models fail to accurately represent nonzero net fluid flow and volume changes at the micro-scale. In contrast, our second-order approach effectively captures nonuniform fluid flow across representative volume element boundaries, in agreement with results from direct numerical simulations. Our findings indicate that the classical first-order expansion of the pressure field is inadequate for poromechanical homogenization in cases involving micro-scale volume changes, such as swelling or contraction. The proposed second-order approach not only overcomes these limitations but also proves effective in cases where the principle of separation of scales is not strictly upheld.
{"title":"Second-order computational homogenization for bridging poromechanical scales under large deformations","authors":"J.L.M. Thiesen , B. Klahr , T.A. Carniel , G.A. Holzapfel , P.J. Blanco , E.A. Fancello","doi":"10.1016/j.cma.2024.117481","DOIUrl":"10.1016/j.cma.2024.117481","url":null,"abstract":"<div><div>We introduce a second-order computational homogenization procedure designed to address heterogeneous poromechanical media. Our approach relies on the method of multiscale virtual power, a variational multiscale method that extends the Hill–Mandel principle of macro-homogeneity. Constraints on displacement and pore pressure fields are managed using periodic and second-order minimally constrained fluctuating spaces. Numerical comparisons reveal that first-order models fail to accurately represent nonzero net fluid flow and volume changes at the micro-scale. In contrast, our second-order approach effectively captures nonuniform fluid flow across representative volume element boundaries, in agreement with results from direct numerical simulations. Our findings indicate that the classical first-order expansion of the pressure field is inadequate for poromechanical homogenization in cases involving micro-scale volume changes, such as swelling or contraction. The proposed second-order approach not only overcomes these limitations but also proves effective in cases where the principle of separation of scales is not strictly upheld.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"433 ","pages":"Article 117481"},"PeriodicalIF":6.9,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142550566","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-30DOI: 10.1016/j.cma.2024.117500
Todd Arbogast , Chuning Wang
We construct direct serendipity finite elements on general cuboidal hexahedra, which are -conforming and optimally approximate to any order. The new finite elements are direct in that the shape functions are directly defined on the physical element. Moreover, they are serendipity by possessing a minimal number of degrees of freedom satisfying the conformity requirement. Their shape function spaces consist of polynomials plus (generally nonpolynomial) supplemental functions, where the polynomials are included for the approximation property and supplements are added to achieve -conformity. The finite elements are fully constructive. The shape function spaces of higher order are developed first, and then the lower order spaces are constructed as subspaces of the third order space. Under a shape regularity assumption, and a mild restriction on the choice of supplemental functions, we develop the convergence properties of the new direct serendipity finite elements. Numerical results with different choices of supplements are compared on two mesh sequences, one regularly distorted and the other one randomly distorted. They all possess a convergence rate that aligns with the theory, while a slight difference lies in their performance.
{"title":"Direct serendipity finite elements on cuboidal hexahedra","authors":"Todd Arbogast , Chuning Wang","doi":"10.1016/j.cma.2024.117500","DOIUrl":"10.1016/j.cma.2024.117500","url":null,"abstract":"<div><div>We construct direct serendipity finite elements on general cuboidal hexahedra, which are <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-conforming and optimally approximate to any order. The new finite elements are <em>direct</em> in that the shape functions are directly defined on the physical element. Moreover, they are <em>serendipity</em> by possessing a minimal number of degrees of freedom satisfying the conformity requirement. Their shape function spaces consist of polynomials plus (generally nonpolynomial) supplemental functions, where the polynomials are included for the approximation property and supplements are added to achieve <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-conformity. The finite elements are fully constructive. The shape function spaces of higher order <span><math><mrow><mi>r</mi><mo>≥</mo><mn>3</mn></mrow></math></span> are developed first, and then the lower order spaces are constructed as subspaces of the third order space. Under a shape regularity assumption, and a mild restriction on the choice of supplemental functions, we develop the convergence properties of the new direct serendipity finite elements. Numerical results with different choices of supplements are compared on two mesh sequences, one regularly distorted and the other one randomly distorted. They all possess a convergence rate that aligns with the theory, while a slight difference lies in their performance.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"433 ","pages":"Article 117500"},"PeriodicalIF":6.9,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142551904","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-30DOI: 10.1016/j.cma.2024.117475
Yukun Feng , Takayuki Yamada
Multi-material topology optimization has become a promising method in structural design due to its excellent structural performance. However, existing research assumes that the multi-material structures are joined by welding, adhesive, or other methods that do not support reassembly and disassembly and are unsuitable for manufacturing, limiting the practical application of topology optimization. An interlocking joint is a type of connection between two parts where the shapes of the parts are designed to fit together precisely, the multi-material structure joined by interlocking joints can be easily reassembled repeatedly. To solve the joint problem of multi-material structure, this study proposes an assemblable interlocking joint generation method for multi-material topology optimization, the connection between material components is achieved through compression at the joint areas. To generate the interlocking joints, a novel interfacial partial stress constraint is proposed by converting a part of the interface bearing tensile stress into the interface bearing compressive stress. A novel filtering process is used to control the shape of the interlocking joints and the filtered tensile stresses are integrated by a P-norm function. To constrain the distribution area of material components and ensure structural manufacturability, dimensional constraints are applied. The sensitivity is based on the topological derivative and adjoint variable method. The proposed method was applied to several numerical examples including one manufactured prototype to demonstrate its effectiveness and contribution to the practical application of topology optimization.
{"title":"An assemblable interlocking joint generation method for multi-material topology optimization using interfacial partial stress constraints and dimensional constraints","authors":"Yukun Feng , Takayuki Yamada","doi":"10.1016/j.cma.2024.117475","DOIUrl":"10.1016/j.cma.2024.117475","url":null,"abstract":"<div><div>Multi-material topology optimization has become a promising method in structural design due to its excellent structural performance. However, existing research assumes that the multi-material structures are joined by welding, adhesive, or other methods that do not support reassembly and disassembly and are unsuitable for manufacturing, limiting the practical application of topology optimization. An interlocking joint is a type of connection between two parts where the shapes of the parts are designed to fit together precisely, the multi-material structure joined by interlocking joints can be easily reassembled repeatedly. To solve the joint problem of multi-material structure, this study proposes an assemblable interlocking joint generation method for multi-material topology optimization, the connection between material components is achieved through compression at the joint areas. To generate the interlocking joints, a novel interfacial partial stress constraint is proposed by converting a part of the interface bearing tensile stress into the interface bearing compressive stress. A novel filtering process is used to control the shape of the interlocking joints and the filtered tensile stresses are integrated by a P-norm function. To constrain the distribution area of material components and ensure structural manufacturability, dimensional constraints are applied. The sensitivity is based on the topological derivative and adjoint variable method. The proposed method was applied to several numerical examples including one manufactured prototype to demonstrate its effectiveness and contribution to the practical application of topology optimization.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"433 ","pages":"Article 117475"},"PeriodicalIF":6.9,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142550563","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-30DOI: 10.1016/j.cma.2024.117482
E.S. Kocaman , B.Y. Chen , S.T. Pinho
When simulating pressure-driven fracture with the Finite Element Method (FEM), significant difficulties can arise upon representing newly formed complex damage surfaces and their concurrent crack face loading. Application of this loading can also be required when additional physics is involved as in the case of hydraulic fracture where fluid physics inside a damage need to be considered. This paper presents a new Finite Element based practical numerical framework which can model pressure-driven fractures as they form on-the-fly without remeshing. The exact location of physical discontinuities passing through the element domain can be represented in the numerical model. The numerical framework can be implemented as a user-defined element and can be integrated into any FE package. A new element (called pressure element) is formulated with the capability to apply pressure and associated forces onto the crack surfaces in an adaptive manner. This element is verified using relevant examples from literature. The framework can also be configured for multi-physics problems where crack face loading is dictated by an additional physics. The element formulation is then extended for multi-physics problems involving fluid–solid interaction. The formulation provides the capability for multi-physics coupling adaptively as the crack propagates. The element is used to successfully simulate a test case from literature using different solution procedures (iterative and simultaneous). This element is also used to model failure in different pressure vessel problems to demonstrate its potential use in structural applications. A new higher-scale vessel element is developed which can represent different size, partitioning and failure states of composite vessel systems at element level. Composite vessel failure involving high number of pressurized cracks and delaminations as well as their interaction is modelled, and burst pressures are predicted for different vessel systems. The proposed numerical framework can be used towards designing more damage-tolerant vessels critical for the sustainable propulsion technologies.
{"title":"A new floating node-based element formulation for modelling pressure-driven fracture","authors":"E.S. Kocaman , B.Y. Chen , S.T. Pinho","doi":"10.1016/j.cma.2024.117482","DOIUrl":"10.1016/j.cma.2024.117482","url":null,"abstract":"<div><div>When simulating pressure-driven fracture with the Finite Element Method (FEM), significant difficulties can arise upon representing newly formed complex damage surfaces and their concurrent crack face loading. Application of this loading can also be required when additional physics is involved as in the case of hydraulic fracture where fluid physics inside a damage need to be considered. This paper presents a new Finite Element based practical numerical framework which can model pressure-driven fractures as they form on-the-fly without remeshing. The exact location of physical discontinuities passing through the element domain can be represented in the numerical model. The numerical framework can be implemented as a user-defined element and can be integrated into any FE package. A new element (called <em>pressure</em> element) is formulated with the capability to apply pressure and associated forces onto the crack surfaces in an adaptive manner. This element is verified using relevant examples from literature. The framework can also be configured for multi-physics problems where crack face loading is dictated by an additional physics. The element formulation is then extended for multi-physics problems involving fluid–solid interaction. The formulation provides the capability for multi-physics coupling adaptively as the crack propagates. The element is used to successfully simulate a test case from literature using different solution procedures (iterative and simultaneous). This element is also used to model failure in different pressure vessel problems to demonstrate its potential use in structural applications. A new higher-scale <em>vessel</em> element is developed which can represent different size, partitioning and failure states of composite vessel systems at element level. Composite vessel failure involving high number of pressurized cracks and delaminations as well as their interaction is modelled, and burst pressures are predicted for different vessel systems. The proposed numerical framework can be used towards designing more damage-tolerant vessels critical for the sustainable propulsion technologies.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"433 ","pages":"Article 117482"},"PeriodicalIF":6.9,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142550567","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-28DOI: 10.1016/j.cma.2024.117452
David E. Torres , Tianchen Hu , Andrew J. Stershic , Timothy R. Shelton , John E. Dolbow
A variational phase field model for dynamic ductile fracture is presented. The model is designed for elasto-viscoplastic materials subjected to rapid deformations in which the effects of heat generation and material softening are dominant. The variational framework allows for the consistent inclusion of plastic dissipation in the heat equation as well as thermal softening. It employs a coalescence function to degrade fracture energy during regimes of high plastic flow. A variationally consistent form of the Johnson–Cook model is developed for use with the framework. Results from various benchmark problems in dynamic ductile fracture are presented to demonstrate capabilities. In particular, the ability of the model to regularize shear band formation and subsequent damage evolution in two- and three-dimensional problems is demonstrated. Importantly, these phenomena are naturally captured through the underlying physics without the need for phenomenological criteria such as stability thresholds for the onset of shear band formation.
{"title":"A variational phase-field framework for thermal softening and dynamic ductile fracture","authors":"David E. Torres , Tianchen Hu , Andrew J. Stershic , Timothy R. Shelton , John E. Dolbow","doi":"10.1016/j.cma.2024.117452","DOIUrl":"10.1016/j.cma.2024.117452","url":null,"abstract":"<div><div>A variational phase field model for dynamic ductile fracture is presented. The model is designed for elasto-viscoplastic materials subjected to rapid deformations in which the effects of heat generation and material softening are dominant. The variational framework allows for the consistent inclusion of plastic dissipation in the heat equation as well as thermal softening. It employs a coalescence function to degrade fracture energy during regimes of high plastic flow. A variationally consistent form of the Johnson–Cook model is developed for use with the framework. Results from various benchmark problems in dynamic ductile fracture are presented to demonstrate capabilities. In particular, the ability of the model to regularize shear band formation and subsequent damage evolution in two- and three-dimensional problems is demonstrated. Importantly, these phenomena are naturally captured through the underlying physics without the need for phenomenological criteria such as stability thresholds for the onset of shear band formation.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"433 ","pages":"Article 117452"},"PeriodicalIF":6.9,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142529236","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-28DOI: 10.1016/j.cma.2024.117473
S. Marrone , M. Antuono , A. Agresta , A. Colagrossi
In the present work the evolution of viscous drops oscillating under the action of surface tension is tackled. Thanks to its structure, the SPH scheme allows for an analysis of the energy balance that is rarely addressed to in the general Computational Fluid Dynamics literature for this kind of flows. A procedure for checking the consistency between the energy of the surface-tension force and the free-surface evolution is proposed. Such a procedure relies on well-known analytical relations for the surface tension and on the evaluation of the free-surface area through a level-set function. Several test cases, in both two and three dimensional frameworks, are considered for validation. The study is performed by selecting a specific SPH scheme with a specific single-phase surface tension model. In any case, the procedure proposed is general and extendable to other SPH surface tension models and SPH schemes.
{"title":"A study on the energy consistency in SPH surface tension modelling","authors":"S. Marrone , M. Antuono , A. Agresta , A. Colagrossi","doi":"10.1016/j.cma.2024.117473","DOIUrl":"10.1016/j.cma.2024.117473","url":null,"abstract":"<div><div>In the present work the evolution of viscous drops oscillating under the action of surface tension is tackled. Thanks to its structure, the SPH scheme allows for an analysis of the energy balance that is rarely addressed to in the general Computational Fluid Dynamics literature for this kind of flows. A procedure for checking the consistency between the energy of the surface-tension force and the free-surface evolution is proposed. Such a procedure relies on well-known analytical relations for the surface tension and on the evaluation of the free-surface area through a level-set function. Several test cases, in both two and three dimensional frameworks, are considered for validation. The study is performed by selecting a specific SPH scheme with a specific single-phase surface tension model. In any case, the procedure proposed is general and extendable to other SPH surface tension models and SPH schemes.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"433 ","pages":"Article 117473"},"PeriodicalIF":6.9,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142529322","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-28DOI: 10.1016/j.cma.2024.117466
Wenhai Sheng , Qinglin Duan
The generalized finite element method (GFEM) without extra degrees of freedom (dof) is extended to solve incompressible Navier-Stokes (N-S) equations. Unlike the existing extra-dof-free GFEM, we propose a new approach to construct the nodal enrichments based on the weighted least-squares. As a result, the essential boundary conditions can be imposed more accurately. The Characteristic-Based Split (CBS) scheme is used to suppress oscillations due to the standard Galerkin discretization of the convective terms, and the pressure is further stabilized by the finite increment calculus (FIC) formulation. Hence, equal velocity-pressure interpolation and the incremental version of the split scheme can be used without inducing spurious oscillations. The developed extra-dof-free GFEM is very flexible and can achieve high-order spatial accuracy and convergence rates by adopting high-order polynomial enrichments. In particular, better accuracy could be obtained with special enrichments reflecting a-priori knowledge about the solution. This is demonstrated by numerical results. Benchmark examples such as the Lid-Driven Cavity flow and the flow past a circular cylinder are also presented to further verify the effectiveness of the proposed extra-dof-free GFEM for incompressible flow.
{"title":"An extra-dof-free generalized finite element method for incompressible Navier-Stokes equations","authors":"Wenhai Sheng , Qinglin Duan","doi":"10.1016/j.cma.2024.117466","DOIUrl":"10.1016/j.cma.2024.117466","url":null,"abstract":"<div><div>The generalized finite element method (GFEM) without extra degrees of freedom (dof) is extended to solve incompressible Navier-Stokes (N-S) equations. Unlike the existing extra-dof-free GFEM, we propose a new approach to construct the nodal enrichments based on the weighted least-squares. As a result, the essential boundary conditions can be imposed more accurately. The Characteristic-Based Split (CBS) scheme is used to suppress oscillations due to the standard Galerkin discretization of the convective terms, and the pressure is further stabilized by the finite increment calculus (FIC) formulation. Hence, equal velocity-pressure interpolation and the incremental version of the split scheme can be used without inducing spurious oscillations. The developed extra-dof-free GFEM is very flexible and can achieve high-order spatial accuracy and convergence rates by adopting high-order polynomial enrichments. In particular, better accuracy could be obtained with special enrichments reflecting a-priori knowledge about the solution. This is demonstrated by numerical results. Benchmark examples such as the Lid-Driven Cavity flow and the flow past a circular cylinder are also presented to further verify the effectiveness of the proposed extra-dof-free GFEM for incompressible flow.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"433 ","pages":"Article 117466"},"PeriodicalIF":6.9,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142529238","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-28DOI: 10.1016/j.cma.2024.117469
Oliver Boolakee , Martin Geier , Laura De Lorenzis
We propose a new second-order accurate lattice Boltzmann formulation for linear elastodynamics that is stable for arbitrary combinations of material parameters under a CFL-like condition. The construction of the numerical scheme uses an equivalent first-order hyperbolic system of equations as an intermediate step, for which a vectorial lattice Boltzmann formulation is introduced. The only difference to conventional lattice Boltzmann formulations is the usage of vector-valued populations, so that all computational benefits of the algorithm are preserved. Using the asymptotic expansion technique and the notion of pre-stability structures we further establish second-order consistency as well as analytical stability estimates. Lastly, we introduce a second-order consistent initialization of the populations as well as a boundary formulation for Dirichlet boundary conditions on 2D rectangular domains. All theoretical derivations are numerically verified by convergence studies using manufactured solutions and long-term stability tests.
{"title":"Lattice Boltzmann for linear elastodynamics: Periodic problems and Dirichlet boundary conditions","authors":"Oliver Boolakee , Martin Geier , Laura De Lorenzis","doi":"10.1016/j.cma.2024.117469","DOIUrl":"10.1016/j.cma.2024.117469","url":null,"abstract":"<div><div>We propose a new second-order accurate lattice Boltzmann formulation for linear elastodynamics that is stable for arbitrary combinations of material parameters under a CFL-like condition. The construction of the numerical scheme uses an equivalent first-order hyperbolic system of equations as an intermediate step, for which a vectorial lattice Boltzmann formulation is introduced. The only difference to conventional lattice Boltzmann formulations is the usage of vector-valued populations, so that all computational benefits of the algorithm are preserved. Using the asymptotic expansion technique and the notion of pre-stability structures we further establish second-order consistency as well as analytical stability estimates. Lastly, we introduce a second-order consistent initialization of the populations as well as a boundary formulation for Dirichlet boundary conditions on 2D rectangular domains. All theoretical derivations are numerically verified by convergence studies using manufactured solutions and long-term stability tests.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"433 ","pages":"Article 117469"},"PeriodicalIF":6.9,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142529237","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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