International Journal for Numerical Methods in Engineering最新文献

{"title":"Parameter Identification for a Reduced Transport Model in Fusion Plasma","authors":"Louis Lamérand,&nbsp;Didier Auroux,&nbsp;Francesca Rapetti","doi":"10.1002/nme.70115","DOIUrl":"https://doi.org/10.1002/nme.70115","url":null,"abstract":"<div>\u0000 \u0000 <p>Two-dimensional transport codes for the simulation of tokamak plasmas are simplified versions of full 3D fluid models, where plasma turbulence is averaged out. One of the main challenges in such reduced models is to accurately reconstruct transverse transport fluxes that arise from the averaging of stresses due to fluctuations. These transverse fluxes are typically approximated by ad-hoc diffusion coefficients (turbulent eddy viscosity), manually adjusted to align numerical solutions with experimental observations. They can vary significantly depending on the type of tokamak, the experimental conditions, and even the location within the device, severely limiting the predictive capability of these codes for new configurations. To address this issue, we recently proposed an innovative approach to fusion plasma simulations by introducing two additional transport equations for turbulence-related variables (specifically, the turbulent kinetic energy <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>κ</mi>\u0000 </mrow>\u0000 <annotation>$$ kappa $$</annotation>\u0000 </semantics></math> and its dissipation rate <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>ε</mi>\u0000 </mrow>\u0000 <annotation>$$ varepsilon $$</annotation>\u0000 </semantics></math>) into the mean-flow system to estimate the turbulent eddy viscosity. This approach also introduces new free parameters, but they are primarily governed by the underlying transport physics and thus exhibit considerably less variation across devices and plasma regions. In this article, we continue an ongoing study of data assimilation techniques to determine the free parameters of the <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>κ</mi>\u0000 <mo>−</mo>\u0000 <mi>ε</mi>\u0000 </mrow>\u0000 <annotation>$$ kappa -varepsilon $$</annotation>\u0000 </semantics></math> model for transverse turbulent plasma transport. Based on digital twin experiments within the framework of equations averaged over the magnetic surfaces of the tokamak, we provide an in-depth study of optimization strategies to improve the performance of the calibration algorithm in a complex configuration with considerable scale variation of the parameters.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 17","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144934844","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":"A Stabilized Finite Element Framework for Incompressible Hyperelastic Materials at Finite Strains: Analysis, Implementation, and Applications","authors":"Ujwal Warbhe","doi":"10.1002/nme.70121","DOIUrl":"https://doi.org/10.1002/nme.70121","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;This paper presents a stabilized finite element method (FEM) for incompressible hyperelastic materials at finite strains, addressing the computational and implementational challenges of traditional inf-sup-stable mixed FEMs. By augmenting the weak formulation with Galerkin/Least-Squares (GLS) stabilization terms, the method enables equal-order Lagrange elements (&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ℙ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;/&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ℙ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {mathbb{P}}_k/{mathbb{P}}_k $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;), eliminating the need for complex element pairings like Taylor–Hood (&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ℙ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;/&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ℙ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {mathbb{P}}_2/{mathbb{P}}_1 $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;). The stabilization parameter is defined as &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;τ&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;mo&gt;.&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mspace&gt;&lt;/mspace&gt;\u0000 &lt;mfrac&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;h&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;μ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mfrac&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ tau =0.1kern0.3em frac{h^2}{mu } $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; where &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;h&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ h $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; denotes the finite-element mesh siz","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 17","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144934845","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":"Fourth- and Higher-Order Finite Element Methods for the Incompressible Navier–Stokes Equations With Dirichlet Boundary Conditions","authors":"Yang Li,&nbsp;Heyu Wang,&nbsp;Qinghai Zhang","doi":"10.1002/nme.70102","DOIUrl":"https://doi.org/10.1002/nme.70102","url":null,"abstract":"<div>\u0000 \u0000 <p>Inspired by the unconstrained pressure Poisson equation (PPE) formulation [Liu, Liu, &amp; Pego, Comm. Pure Appl. Math. 60 (2007): 1443–1487], we previously proposed the generic projection and unconstrained PPE (GePUP) formulation [Zhang, J. Sci. Comput. 67 (2016): 1134–1180] for numerically solving the incompressible Navier–Stokes equations (INSE) with no-slip boundary conditions. In GePUP, the main evolutionary variable does not have to be solenoidal, with its divergence controlled by a heat equation. This work presents GePUP–FEM, high-order finite-element solvers for the INSE under the framework of the method-of-lines. Continuous Lagrange finite elements of equal order are utilized for the velocity and pressure finite element spaces to discretize the weak form of GePUP in space, while high-order implicit–explicit Runge–Kutta methods are then employed to treat the stiff diffusion term implicitly and the other terms explicitly. Due to the implicit treatment of the diffusion term, the time step size is only restricted by convection. The solver is efficient in that advancing the solution at each time step only involves solving a sequence of linear systems either on the velocity or on the pressure, with geometric multigrid methods. Furthermore, the solver is enhanced with adaptive mesh refinement (AMR) so that the multiple length scales and time scales in flows at moderate or high Reynolds numbers can be efficiently resolved. Numerical tests with various Reynolds numbers are performed for the single-vortex test, the lid-driven cavity, and the flow past a cylinder/sphere, demonstrating the high-order accuracy of GePUP–FEM both in time and in space and its capability of accurately and efficiently resolving the right physics. Moreover, GePUP–FEM offers the flexibility in choosing velocity and pressure finite element spaces and is free of the standard inf-sup condition.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 17","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144934931","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":"A New Contact Algorithm for the Total-Lagrangian Material Point Method","authors":"Quang Hieu Bui,&nbsp;Vinh Phu Nguyen,&nbsp;Alban de Vaucorbeil","doi":"10.1002/nme.70105","DOIUrl":"https://doi.org/10.1002/nme.70105","url":null,"abstract":"<p>The Total Lagrangian Material Point Method (TLMPM) is a relatively new variant of the now popular MPM, a method to solve partial differential equations appearing in solid and fluid mechanics problems. In TLMPM, each solid has its own grid, and all calculations are carried out in a configuration of reference, often the original configuration. Because of this, TLMPM is free of numerical fracture, cell crossing instability and is efficient. An unfortunate result of having individual grids is that TLMPM does not have a built-in contact algorithm. Recently, a contact algorithm based on particle-to-particle contact was published for TLMPM. However, it scales quadratically with the number of particles and is therefore slow for a large number of particles. This paper introduces a new contact algorithm for TLMPM using a flexible contact grid. The advantages of this algorithm are: (1) all the advantages of TLMPM are kept, such as the absence of numerical fracture and good convergence rates; (2) the core principle of using a background grid in the material point method for contacts is preserved; (3) different basis functions can be used for each grid, and (4) boundary conditions can be enforced with more flexibility. The performance of the new algorithm is demonstrated through several two and three-dimensional numerical examples exhibiting large elastic and plastic deformation.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 17","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70105","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144934927","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":"Learning the Solution Operator Family in Elastic Mechanics for Response Prediction Under Various Load Scenarios","authors":"Xuliang Liu,&nbsp;Yuequan Bao","doi":"10.1002/nme.70085","DOIUrl":"https://doi.org/10.1002/nme.70085","url":null,"abstract":"<div>\u0000 \u0000 <p>Analyzing the responses of solid materials under diverse loading scenarios with different types and forms is a fundamental engineering necessity. However, a load-adaptable machine learning model that can predict such responses still needs to be explored. This study formulates the load-adaptable response prediction problem as a solution operator family regression task and develops a Load-Adaptable Physics-Informed DeepONet (LA-PIDON) to learn the solution operator family of mechanics. The proposed method utilizes the product space as the input space, composed of function spaces for force boundaries, displacement boundaries, material properties, and other mechanical factors. Distinct branch networks are established for each mechanical factor and distinct trunk networks for each corresponding response. The solution family learning task is accomplished by using shared branch networks across multiple trunk networks. The load adaptability for both concentrated and distributed forces is achieved through the integration of Gaussian Random Fields(GRFs) and Fourier polynomials to generate function spaces for the force boundary; the load adaptability for force and imposed displacement excitation is achieved by incorporating the product space of force and displacement boundaries into the input space. The numerical cases of (1) elastic plates subjected to benchmark force and imposed displacement excitations, (2) benchmark beams under pure and tensile bending, and (3) 3D elastic cubes undergoing axial tension demonstrate the method's adaptability to various load scenarios and its capacity to handle complex stress states. The proposed method has potential applications in fields that require numerous simulations for diverse load scenarios, such as reliability analysis and digital twins.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 17","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144934930","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 Eulerian Framework for Modeling Visco-Plasticity and Isotropic and Directional Material Hardening Utilizing Neural Networks","authors":"Martin Kroon","doi":"10.1002/nme.70083","DOIUrl":"https://doi.org/10.1002/nme.70083","url":null,"abstract":"<p>A neural network is inserted into a theoretical framework for modeling the inelastic behavior of materials. The neural network replaces functional expressions for such phenomena as isotropic and directional hardening and viscoplasticity. The theoretical framework, into which the neural network is inserted, is Eulerian in the sense that all state variables are defined in the current state of the material, and the framework is independent of history variables, such as plastic strain, accumulated equivalent plastic strain, etc. The neural network-based model is compared to and trained to reproduce the uniaxial tension response of theoretical reference solutions as well as experimental results. The neural network-based model is able to reproduce the reference results with excellent precision. Also, the neural network-based model was implemented as a VUMAT in Abaqus together with one of the theoretical reference models. Deformation of a plate with a hole in it was simulated, and the outcome from the reference model and the trained neural network-based model was compared. The solutions, in terms of von Mises stress and accumulated equivalent plastic strain, were very similar. Hence, it seems like training the neural network model by use of uniaxial stress data is sufficient for being able to make accurate 3D predictions.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 17","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70083","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144935319","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 Novel Density Correction Method for Improved Prediction of Pressure Fields in SPH","authors":"Yoon Sung Jeong,&nbsp;Phill-Seung Lee","doi":"10.1002/nme.70116","DOIUrl":"https://doi.org/10.1002/nme.70116","url":null,"abstract":"<div>\u0000 \u0000 <p>Smoothed particle hydrodynamics (SPH) has been extensively studied for several decades, yet accurate calculation of pressure fields remains a significant challenge, hindering its widespread application in practical engineering. This paper focuses on developing a novel density correction method to enhance the accuracy of hydrostatic pressure distribution in SPH, both near solid boundaries and within the fluid domain. The method incorporates two innovative concepts: an interpolation grid and supplementary particles, both aimed at refining density distributions. The proposed method is straightforward to implement, making it accessible for a wide range of applications. It proves highly effective in calculating improved hydrostatic pressure fields in high-pressure regions close to solid boundaries. Moreover, the proposed method effectively suppresses unphysical oscillations and peaks in the hydrodynamic pressure fields while alleviating unintended numerical dissipation that often occurs in long-term simulations. Additionally, the method offers greater flexibility in determining the correction interval and demonstrates excellent compatibility with various solid boundary treatments. The performance of the proposed method is validated through several numerical tests, and comparisons with other related numerical schemes are presented.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 17","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144935318","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":"A h-Adaptivity Strategy for Hybridizable Discontinuous Galerkin (HDG) Simulations of Fluid Transport Models in Tokamak Plasma","authors":"Marcello Capasso,&nbsp;Ivan Kudashev,&nbsp;Frédéric Schwander,&nbsp;Éric Serre","doi":"10.1002/nme.70107","DOIUrl":"https://doi.org/10.1002/nme.70107","url":null,"abstract":"<p>The highly anisotropic, multi-scale nature of fusion plasma simulations in tokamaks, combined with the complexity in the geometries of plasma-facing components and magnetic equilibrium, challenges numerical schemes. They therefore require the development of advanced numerical techniques to enhance computational efficiency and enable codes to simulate realistic plasma configurations relevant to tokamak operation. This paper proposes an adaptive mesh refinement strategy (<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>h</mi>\u0000 </mrow>\u0000 <annotation>$$ h $$</annotation>\u0000 </semantics></math>-adaptivity) in the SolEdge-HDG code for the resolution of 2D fluid-drift Braginskii equations using the Hybrid Discontinuous Galerkin (HDG) method. The strategy is based on an oscillation indicator implemented to detect under-resolved regions and dynamically refine the mesh, associated with an a posteriori accuracy indicator built on the local difference between the solution at order <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 </mrow>\u0000 <annotation>$$ p $$</annotation>\u0000 </semantics></math> and the post-processed one at order <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>+</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$$ p+1 $$</annotation>\u0000 </semantics></math> considered as reference. The method thus enables both refinement, where necessary, as well as coarsening in regions where the solution is smooth. Numerical results obtained with this method in realistic tokamak geometry and plasma conditions show significant reductions in computational resources and an improvement in code robustness while maintaining high accuracy, particularly in regions with steep gradients or near the sharp angles of the tokamak walls. This work highlights the potential of such <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>h</mi>\u0000 </mrow>\u0000 <annotation>$$ h $$</annotation>\u0000 </semantics></math>-adaptivity technique to optimize transport simulations in realistic tokamak configurations, offering a fully automated, goal-oriented mesh refinement strategy. In addition to optimizing the numerical cost of simulation, this strategy offers all users a fully automated means of designing a mesh in any tokamak geometry.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 17","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70107","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144934846","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":"Featured Cover","authors":"Zhuo Deng,&nbsp;Shi-Xuan Liu,&nbsp;Song Cen,&nbsp;Ming Sun,&nbsp;Yan Shang","doi":"10.1002/nme.70122","DOIUrl":"https://doi.org/10.1002/nme.70122","url":null,"abstract":"<p>The cover image is based on the article <i>Corotational Unsymmetric Membrane Element Formulation for Geometric Nonlinear Analysis of Flexoelectric Solids Within the Consistent Couple Stress Theory</i> by Yan Shang et al., https://doi.org/10.1002/nme.70045.\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 11","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70122","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144915293","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":"Physics-Informed Neural Networks for Solving Parameterized Dual-Domain Darcy–Brinkman Flows in Gradient Porous Mediums","authors":"Haoyun Xing,&nbsp;Guice Yao,&nbsp;Hang Yuan,&nbsp;Jin Zhao,&nbsp;Dongsheng Wen","doi":"10.1002/nme.70110","DOIUrl":"https://doi.org/10.1002/nme.70110","url":null,"abstract":"<div>\u0000 \u0000 <p>The ability to solve parameterized partial differential equations is pivotal to improving engineering design efficiency, and with the advancement of machine learning technologies, physics-informed neural networks (PINNs) provide a promising avenue. In this work, a coupled dual-domain Darcy–Brinkman flow model for gradient porous media is established. Building upon this, the trunk-branch (TB)-net PINN framework, which is capable of dealing with multi-physical field issues, is utilized to conduct predictions for a specific porosity configuration scenario, and the performance of different data collocation strategies is examined. Following this, explorations for parameterized flows are implemented, demonstrating remarkable accuracy in two randomly chosen conditions. This is the first known application of PINNs-like methods to handle such complex parameterized dual-domain Darcy–Brinkman flows, yielding invaluable experience pertinent to engineering design and efficiency optimization.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 16","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144897584","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}