International Journal for Numerical Methods in Engineering最新文献

{"title":"A Numerical Framework for Fast Transient Compressible Flows Using Lattice Boltzmann and Immersed Boundary Methods","authors":"Hippolyte Lerogeron,&nbsp;Pierre Boivin,&nbsp;Vincent Faucher,&nbsp;Julien Favier","doi":"10.1002/nme.7647","DOIUrl":"https://doi.org/10.1002/nme.7647","url":null,"abstract":"<p>This article is dedicated to the development of a model to simulate fast transient compressible flows on solid structures using immersed boundary method (IBM) and a lattice Boltzmann solver. Ultimately, the proposed model aims at providing an efficient algorithm to simulate strongly-coupled fluid-structure interactions (FSI). Within this goal, it is necessary to propose a precise and robust numerical framework and validate it on stationary solid cases first, which is the scope of the present study. Classical FSI methods, such as body-fitted approaches, are facing challenges with moving or complex geometries in realistic conditions, requiring computationally expensive re-meshing operations. IBM offers an alternative by treating the solid structure geometry independently from the fluid mesh. This study focuses on the extension of the IBM to compressible flows, and a particular attention is given to the enforcement of various thermal boundary conditions. A hybrid approach, combining diffuse forcing for Dirichlet-type boundary conditions and ghost-nodes forcing for Neumann-type boundary conditions is introduced. Finally, a simplified model, relying only on diffuse IBM forcing, is investigated to treat specific cases where the fluid solid interface is considered as adiabatic. The accuracy of the method is validated through various test cases of increasing complexity.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.7647","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143362633","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Stability and Accuracy of a Meshless Finite Difference Method for the Stokes Equations","authors":"Alexander Westermann,&nbsp;Oleg Davydov,&nbsp;Andriy Sokolov,&nbsp;Stefan Turek","doi":"10.1002/nme.70000","DOIUrl":"https://doi.org/10.1002/nme.70000","url":null,"abstract":"<p>We study the behavior of the meshless finite difference method based on radial basis functions applied to the stationary incompressible Stokes equations in two spatial dimensions, with the velocity and the pressure discretized on their own node sets. We demonstrate that the main condition for the stability of the numerical solution is that the distribution of the pressure nodes has to be coarser than that of the velocity both globally and locally in the domain, and there is no need for any more complex assumptions similar to the Ladyzhenskaya-Babuška-Brezzi condition in the finite element method. Optimal stability is achieved when the relative local density of the velocity to pressure nodes is about 4:1. The convergence rates of the method correspond to the convergence rates of numerical differentiation for both low and higher order discretizations. The method works well on both mesh-based and irregular nodes, such as those generated by random or quasi-random numbers and on nodes with varying density. There is no need for special staggered arrangements, which suggests that node generation algorithms may produce just one node set and obtain the other by either refinement or coarsening. Numerical results for the benchmark Driven Cavity Problem confirm the robustness and high accuracy of the method, in particular resolving a cascade of multiple Moffatt Eddies at the tip of the wedge by using nodes obtained from the quasi-random Halton sequence.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70000","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143362929","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Hybrid Collocation Method for Long-Time Simulation of Heat Conduction in Anisotropic Functionally Graded Materials","authors":"Lin Qiu,&nbsp;Fajie Wang,&nbsp;Wenzhen Qu,&nbsp;Ji Lin,&nbsp;Yan Gu,&nbsp;Qing-Hua Qin","doi":"10.1002/nme.70002","DOIUrl":"https://doi.org/10.1002/nme.70002","url":null,"abstract":"<div>\u0000 \u0000 <p>This study proposes a hybrid collocation approach for simulating heat conduction problems in anisotropic functionally graded materials over extended time intervals. In this approach, the Krylov deferred correction (KDC) scheme is employed for the temporal discretization of dynamic problems, featuring a novel numerical implementation designed to ensure the precise satisfaction of boundary conditions. The localized radial basis function (LRBF) collocation method is modified and utilized to solve the resulting boundary value problems. A new radial basis function is developed and combined with an optimization strategy for the distribution of source points to enhance the performance of the LRBF scheme. This method synergizes the KDC technique, which supports large time step sizes, with the LRBF collocation method, characterized by its truly meshless nature, to address dynamic problems over long durations. Additionally, the coefficient matrix produced by the LRBF method is sparse and depends solely on the spatial distances between collocation points and source points, which is advantageous for long-term simulations. Numerical simulations spanning thousands of time steps demonstrate the accuracy, stability, and convergence of the hybrid approach. The developed numerical framework shows significant improvements over existing methods, particularly in handling dynamic problems with substantial temperature variations.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143362931","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Multiscale Topology Optimization Based on Moving Iso-Surface Threshold Using Isogeometric Analysis","authors":"Xiaonan Su,&nbsp;Wenjiong Chen","doi":"10.1002/nme.70001","DOIUrl":"https://doi.org/10.1002/nme.70001","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper aims to optimize both the topology of microstructure and macrostructure, by using the Moving Iso- Surface Threshold (MIST) method under the framework of Isogeometric Analysis (IGA). To achieve this, the physical response and the equivalent properties of the microstructure are solved by IGA. The physical response functions are defined at the control points. The NURBS fitting method is used to fit the physical response function, generating a NURBS surface for describing the physical response function, that is, the explicitly described physical response function surface. An iso-surface cut the NURBS physical response surfaces to obtain the explicitly described structure topology. In addition, the standard IGS files of the NURBS physical response surface and iso-surface can be transferred to Computer-Aided-Design (CAD) software without post-processing. The multiscale structure can be easily assembled in CAD software using the proposed method. Finally, several numerical examples are performed to demonstrate the effectiveness and efficiency of the proposed method. Obtained results show good agreement with examples in literature in terms of both topology and final value of objective function.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143362930","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An Adjoint-Based Methodology for Sensitivity Analysis of Time-Periodic Flows With Reduced Time Integration","authors":"Tomás Sambiase Privato,&nbsp;João de Sá Brasil Lima,&nbsp;Daiane Iglesia Dolci,&nbsp;Bruno Souza Carmo,&nbsp;Marcelo Tanaka Hayashi,&nbsp;Ernani Vitillo Volpe","doi":"10.1002/nme.7663","DOIUrl":"https://doi.org/10.1002/nme.7663","url":null,"abstract":"<div>\u0000 \u0000 <p>Sensitivity analysis plays a vital role in understanding the impact of control parameter variations on system output, particularly in cases where an objective functional evaluates the output's merit. The adjoint method has gained popularity due to its efficient computation, especially when dealing with a large number of control parameters and a few functionals. While the discrete form of the adjoint method is prevalent, exploring its continuous counterpart can offer valuable insights into the underlying mathematical problem, particularly in characterizing the boundary conditions. This paper presents an investigation into the continuous form of the adjoint method applied to time-dependent viscous flows, where the time dependence is either imposed by boundary conditions or arises from the system dynamics itself. The proposed approach enables the computation of sensitivities with respect to both geometric and operational control parameters using the same adjoint solution. For time-periodic flows, a special formulation is developed to mitigate the computational costs associated with time integration. Results demonstrate that the methodology proposed in a previous work can be successfully extended to time-dependent flows with fixed time spans. In such applications, time-accurate simulations of physics and adjoint fields are sufficient. However, periodic flows necessitate the application of the Leibniz Rule because the period might depend on the control parameters, which introduces additional terms to the adjoint-based sensitivity gradient. In that case, time integration can be limited to a minimum common multiple of all appearing periods in the flow. Although the accurate estimation of such multiple poses a challenge, the approach promises significant benefits for sensitivity analysis of fully established periodic flows. It leads to substantial cuts in computational costs and avoids transient data contamination.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143362625","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An Extended B-Spline-Based Material Point Method for Contact Problems","authors":"Emmanouil G. Kakouris,&nbsp;Manolis N. Chatzis,&nbsp;Savvas Triantafyllou","doi":"10.1002/nme.70003","DOIUrl":"https://doi.org/10.1002/nme.70003","url":null,"abstract":"<p>A novel Material Point Method (MPM) is introduced for addressing contact problems. In contrast to the standard multi-velocity field approach, this method employs a penalty method to evaluate contact forces at the discretised boundaries of their respective physical domains. This enhances simulation fidelity by accurately considering the deformability of the contact surface and preventing fictitious gaps between bodies in contact. Additionally, the method utilises the Extended B-Splines (EBSs) domain approximation, providing two key advantages. First, EBSs robustly mitigate grid cell-crossing errors by offering continuous gradients of the basis functions on the interface between adjacent grid cells. Second, numerical integration errors are minimised, even with small physical domains in occupied grid cells. The proposed method's robustness and accuracy are evaluated through benchmarks, including comparisons with analytical solutions, other state-of-the-art MPM-based contact algorithms, and experimental observations from the literature. Notably, the method demonstrates effective mitigation of stress errors inherent in contact simulations.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143362635","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Penalty-Free SGFEM for Interface Problems With Nonhomogeneous Jump Conditions","authors":"Qinghui Zhang,&nbsp;Uday Banerjee","doi":"10.1002/nme.7667","DOIUrl":"https://doi.org/10.1002/nme.7667","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we present a stable generalized finite element method (SGFEM) to address the approximation of the discontinuous solutions of interface problems with nonhomogeneous interface conditions. We propose a set of enrichment functions based on the Heaviside and Distance functions on the patches that intersect the interface. The enrichment based on the Heaviside function is used to strongly enforce the given nonhomogeneous interface condition, that is, the jump in the solution, and only the enrichment based on the product of the Heaviside and Distance functions contributes to the degrees of freedom. Consequently, the number of degrees of freedom in this approach is the same as that is required for an interface problem with homogeneous interface conditions. The chief merit is that the proposed method totally confors and does not use conventional techniques for the nonhomogeneous interface condition in the literature, such as the penalty method or the Lagrange multiplier. Our experiments show that this method yields optimal order of convergence, its conditioning is not worse than that of the standard finite element method, and it is robust.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143362636","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Featured Cover","authors":"Zeng Meng,&nbsp;Qiaochu Qian,&nbsp;Peng Hao","doi":"10.1002/nme.7672","DOIUrl":"https://doi.org/10.1002/nme.7672","url":null,"abstract":"<p>The cover image is based on the article <i>On the Use of Fidelity Transformation Method for Stress-Constrained Reliability-Based Topology Optimization of Continuum Structure With High Accuracy</i> by Peng Hao et al., https://doi.org/10.1002/nme.7602.\u0000\u0000 <figure>\u0000 <div><picture>\u0000 <source></source></picture><p></p>\u0000 </div>\u0000 </figure></p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.7672","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143112378","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Thermo-Mechanical Localizing Gradient Damage Model With Modified Mazars Strain","authors":"HanWei Huang,&nbsp;Hao Yu,&nbsp;WenLong Xu,&nbsp;Quan Wang,&nbsp;HengAn Wu","doi":"10.1002/nme.7652","DOIUrl":"https://doi.org/10.1002/nme.7652","url":null,"abstract":"<div>\u0000 \u0000 <p>This work establishes a thermo-mechanical coupling model for thermally induced cracks in quasi-brittle materials within the framework of localizing gradient damage theory. The constitutive relation considering the thermal expansion effect, and the heat conduction equation integrating the volumetric strain and damage evolution, are formulated based on the Clausius–Duhem inequality to ensure thermodynamic consistency. In particular, to accommodate the tension-compression strength asymmetry across different quasi-brittle materials, a modified Mazars strain is proposed as the driving force for the micro equivalent strain, where the first invariant of strain tensor and an adjustable ratio of compressive strength to tensile strength (<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 <annotation>$$ k $$</annotation>\u0000 </semantics></math>) are introduced. The numerical implementation employs the generalized-α method for time domain discretization and the staggered scheme for decoupling. Numerical simulations demonstrate a nice feasibility of the modified Mazars strain in capturing both tensile and mixed-mode failures, and the proposed model proves capable of characterizing complex crack behaviors under thermal loading in both quasi-static and dynamic scenarios. The quenching test simulations of ceramic plates highlight the bidirectional coupling effects on crack patterns. Unidirectional coupling models that ignore the influence of volumetric strain and damage evolution on the temperature field would underestimate the temperature gradient, resulting in larger crack spacing and fewer cracks. In the thermal shock tests of cylindrical specimens, the transition in crack patterns from spiral shear bands to an annular damage zone with increasing compression-tension strength ratio (<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 <annotation>$$ k $$</annotation>\u0000 </semantics></math>) is precisely captured, demonstrating the generality of the proposed model for various quasi-brittle materials with tension-compression strength asymmetry.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 2","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143118863","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Interface-Filtering Structural Optimization","authors":"Tianye Wang,&nbsp;Xiaoping Qian","doi":"10.1002/nme.7669","DOIUrl":"https://doi.org/10.1002/nme.7669","url":null,"abstract":"<p>In this paper, we present an interface-filtering structural optimization method that optimizes structural shape and topology through successive interface movements. This interface filtering is achieved via the combination of the variable-radius-based partial-differential-equation (PDE) filtering and the Heaviside projection on a density representation. In the proposed method, designs are represented by a density field with sharp interface and no internal grey features, and a filter radius field is used as the design variable in the optimization process. With this method, any density distribution with sharp interfaces can be used as initial designs, and sharp density contrast in density distribution is preserved throughout the optimization process. An analytical relation between the maximum movements of interfaces and the maximum filter radius is given, so that the interface movement can be controlled during the optimization process. Sensitivities with respect to filter radius variables are derived. Two numerical treatments, involving the density update scheme and the radius re-initialization scheme, are developed to achieve smooth successive shape updates and avoid artificial local minima. Numerical examples, including geometric deformation problem, structural compliance minimization, thermal compliance minimization, and negative Poisson ratio problem, are presented to demonstrate the capabilities of the proposed method.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 2","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.7669","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143118416","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}