Journal of Computational Physics最新文献

{"title":"A direct forcing, immersed boundary method for conjugate heat transport","authors":"Kimmo Koponen ,&nbsp;Amneet Pal Singh Bhalla ,&nbsp;Brennan Sprinkle ,&nbsp;Ning Wu ,&nbsp;Nils Tilton","doi":"10.1016/j.jcp.2025.114135","DOIUrl":"10.1016/j.jcp.2025.114135","url":null,"abstract":"<div><div>Motivated by applications to fluid flows with conjugate heat transfer and electrokinetic effects, we propose a direct forcing immersed boundary method for simulating general, discontinuous, Dirichlet and Robin conditions at the interface between two materials. In comparison to existing methods, our approach uses smaller stencils and accommodates complex geometries with sharp corners. The method is built on the concept of a “forcing pair,” defined as two grid points that are adjacent to each other, but on opposite sides of an interface. For 2D problems this approach can simultaneously enforce discontinuous Dirichlet and Robin conditions using a six-point stencil at one of the forcing points, and a 12-point stencil at the other. In comparison, prior work requires up to 14-point stencils at both points. We also propose two methods of accommodating surfaces with sharp corners. The first locally reduces stencils in sharp corners. The second uses the signed distance function to globally smooth all corners on a surface. The smoothing is defined to recover the actual corners as the grid is refined. We verify second-order spatial accuracy of our proposed methods by comparing to manufactured solutions to the Poisson equation with challenging discontinuous fields across immersed surfaces. Next, to explore the performance of our method for simulating fluid flows with conjugate heat transport, we couple our method to the incompressible Navier–Stokes and continuity equations using a finite-volume projection method. We verify the spatial-temporal accuracy of the solver using manufactured solutions and an analytical solution for circular Couette flow with conjugate heat transfer. Finally, to demonstrate that our method can model moving surfaces, we simulate fluid flow and conjugate heat transport between a stationary cylinder and a rotating ellipse or square.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"538 ","pages":"Article 114135"},"PeriodicalIF":3.8,"publicationDate":"2025-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144280107","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An incompressibility, divB=0 preserving, current density, helicity, energy-conserving finite element method for incompressible MHD systems","authors":"Shipeng Mao ,&nbsp;Ruijie Xi","doi":"10.1016/j.jcp.2025.114130","DOIUrl":"10.1016/j.jcp.2025.114130","url":null,"abstract":"<div><div>In this paper, we propose a novel structure-preserving finite element scheme for the three-dimensional incompressible magnetohydrodynamic (MHD) equations. The contribution of our research is three-fold. Firstly, the proposed scheme exactly preserves critical physical properties, including the incompressibility condition, the solenoidal condition of magnetic field, current density conservation, energy conservation and magnetic/fluid helicity conservation in their respective physical limits. To the best of our knowledge, this is the first numerical method that preserves all these properties simultaneously. Secondly, it introduces the first linear scheme that upholds the helicity-preserving property for MHD, thus eliminating the necessity for fixed-point iterations as seen in existing literature. Last but not least, for the resulting large linear systems, we develop efficient block preconditioners that remain robust at high fluid and magnetic Reynolds numbers by incorporating techniques such as the augmented Lagrangian method and mass augmentation. Finally, a series of numerical experiments demonstrate that our method is accurate, stable, robust under extreme physical parameters and capable of preserving all the stated physical properties, including benchmark problems of Orszag Tang vortex and driven magnetic reconnection with fluid and magnetic Reynolds numbers up to <span><math><msup><mn>10</mn><mn>5</mn></msup></math></span>–<span><math><msup><mn>10</mn><mn>6</mn></msup></math></span>.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"538 ","pages":"Article 114130"},"PeriodicalIF":3.8,"publicationDate":"2025-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144243524","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A natural deep Ritz method for essential boundary value problems","authors":"Haijun Yu ,&nbsp;Shuo Zhang","doi":"10.1016/j.jcp.2025.114133","DOIUrl":"10.1016/j.jcp.2025.114133","url":null,"abstract":"<div><div>Deep neural network approaches show promise in solving partial differential equations. However, unlike traditional numerical methods, they face challenges in enforcing essential boundary conditions. The widely adopted penalty-type methods, for example, offer a straightforward implementation but introduces additional complexity due to the need for hyper-parameter tuning; moreover, the use of a large penalty parameter can lead to artificial extra stiffness, complicating the optimization process. In this paper, we propose a novel, intrinsic approach to impose essential boundary conditions through a framework inspired by intrinsic structures. We demonstrate the effectiveness of this approach using the deep Ritz method applied to Poisson problems, with the potential for extension to more general equations and other deep learning techniques. Numerical results are provided to substantiate the efficiency and robustness of the proposed method.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"537 ","pages":"Article 114133"},"PeriodicalIF":3.8,"publicationDate":"2025-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144205467","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Multilevel matrix-free method for high-performance isogeometric analysis of lattice structures","authors":"C. Guillet ,&nbsp;T. Hirschler ,&nbsp;P. Jolivet ,&nbsp;R. Bouclier","doi":"10.1016/j.jcp.2025.114136","DOIUrl":"10.1016/j.jcp.2025.114136","url":null,"abstract":"<div><div>This paper presents a novel high-performance solver for the isogeometric analysis of lattice structures, designed to jointly exploit distributed-memory computing architectures and the specific nature of the problem. This work breaks with conventional approaches that primarily focus on multiscale homogenization or structural elements like beams and shells. Instead, it introduces a solver capable of meeting the overwhelming computational demands of full high-fidelity, fine-scale simulations of lattice structures. The solver features a two-level geometric preconditioner with a fine-level smoother based on overlapping domain decomposition, and a coarse-level correction utilizing an algebraic multigrid method. By leveraging the multiscale nature of the lattice structures, a matrix-free approach is employed at the fine level to perform matrix-vector products and apply transfer operators based on spline <span><math><mi>k</mi></math></span>-refinement. The structural similarities of the cells are also exploited through a reduced-order modeling procedure applied within each subdomain, which is used to efficiently compute the corresponding local solves within the fine-level smoother. A series of numerical experiments in both 2D and 3D, spanning various micro- and macro-geometries, are conducted to evaluate the efficiency of the solver in terms of memory usage, computational time, and robustness with respect to mesh refinement, spline degree, and problem size. Notably, an industrially representative spiral channel regenerative cooling thrust chamber lattice structure, consisting of over 66,000 cells, is simulated in minutes using thousands of processes.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"537 ","pages":"Article 114136"},"PeriodicalIF":3.8,"publicationDate":"2025-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144205744","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A novel deep convolutional surrogate model with incomplete solve loss for parameterized steady-state diffusion problems","authors":"Junqing Jia ,&nbsp;Xiaoping Zhang ,&nbsp;Shuting Wang ,&nbsp;Lili Ju ,&nbsp;Hui Feng","doi":"10.1016/j.jcp.2025.114132","DOIUrl":"10.1016/j.jcp.2025.114132","url":null,"abstract":"<div><div>In this paper, we propose a deep convolutional surrogate model for learning parameterized steady-state diffusion problems in the end-to-end fashion, which integrates the convolutional neural networks with traditional numerical discretization schemes. The parameters are embedded into images as the input and a slightly modified U-Net is adopted as the backbone of the proposed model. A novel loss function is specially designed for the training process, which incorporates iterative solvers of linear systems and incomplete solves into generation of pseudo data. In addition to linear diffusion problems, our method also can effectively handle nonlinear ones by further utilizing the Picard’s iteration with linearization technique. Extensive numerical experiments including ablation studies and applications to engineering problems are presented to verify the effectiveness of the proposed deep convolutional surrogate model and demonstrate its excellent performance in solving parameterized diffusion problems in various scenarios.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"537 ","pages":"Article 114132"},"PeriodicalIF":3.8,"publicationDate":"2025-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144229904","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Network scaling and scale-driven loss balancing for intelligent characterization of poroelastic systems","authors":"Yang Xu ,&nbsp;Fatemeh Pourahmadian","doi":"10.1016/j.jcp.2025.114129","DOIUrl":"10.1016/j.jcp.2025.114129","url":null,"abstract":"<div><div>A deep learning framework is developed for multiscale characterization of poroelastic media from full waveform data which is known as poroelastography. Special attention is paid to heterogeneous environments whose multiphase properties may drastically change across several scales. Described in space-frequency, the data takes the form of focal solid displacement and pore pressure fields in various neighborhoods furnished either by reconstruction from remote data or direct measurements depending on the application. The objective is to simultaneously recover the six hydromechanical properties germane to Biot equations and their spatial distribution in a robust and efficient manner. Two major challenges impede direct application of existing state-of-the-art techniques for this purpose: (i) the sought-for properties belong to vastly different and potentially uncertain scales, and (ii) the loss function is multi-objective and multi-scale (both in terms of its individual components and the total loss). To help bridge the gap, we propose the idea of <em>network scaling</em> where the neural property maps are constructed by unit shape functions composed into a scaling layer. In this model, the unknown network parameters (weights and biases) remain of O(1) during training. This forms the basis for explicit scaling of the loss components and their derivatives with respect to the network parameters. Thereby, we propose the physics-based <em>dynamic scaling</em> approach for adaptive loss balancing. The idea is first presented in a generic form for multi-physics and multi-scale PDE systems, and then applied through a set of numerical experiments to poroelastography. The results are presented along with reconstructions by way of gradient normalization (GradNorm) and Softmax adaptive weights (SoftAdapt) for loss balancing. A comparative analysis of the methods and corresponding results is provided. The case of multi-scale reconstructions from noisy data is also numerically investigated.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"537 ","pages":"Article 114129"},"PeriodicalIF":3.8,"publicationDate":"2025-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144205741","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"LESnets (large-eddy simulation nets): Physics-informed neural operator for large-eddy simulation of turbulence","authors":"Sunan Zhao ,&nbsp;Zhijie Li ,&nbsp;Boyu Fan ,&nbsp;Yunpeng Wang ,&nbsp;Huiyu Yang ,&nbsp;Jianchun Wang","doi":"10.1016/j.jcp.2025.114125","DOIUrl":"10.1016/j.jcp.2025.114125","url":null,"abstract":"<div><div>Acquisition of large datasets for three-dimensional (3D) partial differential equations (PDE) is usually very expensive. Physics-informed neural operator (PINO) eliminates the high costs associated with generation of training datasets, and shows great potential in a variety of partial differential equations. In this work, we employ physics-informed neural operator, encoding the large-eddy simulation (LES) equations directly into the neural operator for simulating three-dimensional incompressible turbulent flows. We develop the LESnets (Large-Eddy Simulation nets) by adding large-eddy simulation equations to two different data-driven models, including Fourier neural operator (FNO) and implicit Fourier neural operator (IFNO) without using label data. Notably, by leveraging only PDE constraints to learn the spatio-temporal dynamics, LESnets models retain the computational efficiency of data-driven approaches while obviating the necessity for data. Meanwhile, using LES equations as PDE constraints makes it possible to efficiently predict complex turbulence at coarse grids. We investigate the performance of the LESnets models with two standard three-dimensional turbulent flows: decaying homogeneous isotropic turbulence and temporally evolving turbulent mixing layer. In the numerical experiments, the LESnets models show similar accuracy as compared to traditional large-eddy simulation and data-driven models including FNO and IFNO, and exhibits a robust generalization ability to unseen regime of flow fields. By integrating a single set of flow data, the LESnets models can automatically learn the coefficient of the subgrid scale (SGS) model during the training of the neural operator. Moreover, the well-trained LESnets models are significantly faster than traditional LES, and exhibits comparable computational efficiency to the data-driven FNO and IFNO models. Thus, physics-informed neural operators have a strong potential for 3D nonlinear engineering applications.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"537 ","pages":"Article 114125"},"PeriodicalIF":3.8,"publicationDate":"2025-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144205740","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Efficient and accurate data-driven wall modelling strategy for Reynolds averaged Navier–Stokes simulations","authors":"Michele Romanelli ,&nbsp;Samir Beneddine ,&nbsp;Ivan Mary ,&nbsp;Héloïse Beaugendre ,&nbsp;Michel Bergmann ,&nbsp;Denis Sipp","doi":"10.1016/j.jcp.2025.114128","DOIUrl":"10.1016/j.jcp.2025.114128","url":null,"abstract":"<div><div>This article introduces a novel data-driven wall modeling strategy for Reynolds-Averaged Navier–Stokes (RANS) simulations. The method reformulates wall laws as a Dirichlet-to-Neumann map applied at a specific height within the boundary layer. This map is learned using neural networks trained on data from wall-resolved RANS simulations. While the approach shares similarities with the work of Romanelli et al. (2023), it is significantly faster, as it eliminates the need for iterative resolution of the skin friction inherent in the implicit relation <span><math><mrow><msup><mi>u</mi><mo>+</mo></msup><mo>=</mo><mi>f</mi><mrow><mo>(</mo><msup><mi>y</mi><mo>+</mo></msup><mo>,</mo><msup><mi>p</mi><mo>+</mo></msup><mo>)</mo></mrow></mrow></math></span>. The model’s accuracy has also been improved through enhanced treatment of the turbulent variables and by incorporating additional input parameters that better describe the boundary layer state. The method is demonstrated on attached turbulent flows across various Reynolds numbers and wall pressure gradients. After training the neural networks on a subset of reference cases, their ability to generalize to both familiar and unseen conditions is evaluated. The model is further validated on a completely different setup (an airfoil), where it is compared to two existing analytical wall models, showing better accuracy and robustness with respect to pressure gradient conditions. The paper also introduces an efficient extrapolation-detection algorithm that could be used either to ensure that the model is always applied within its validity domain or to trigger an automated adaptive learning strategy of the wall-law or, in a zonal context, to select between wall-resolved/wall-modeled regions. Overall, our method provides a new practical intermediate-fidelity, cost-effective framework that displays an attractive balance between accuracy and computational efficiency, bridging the gap between the more computationally intensive approach of Romanelli et al. (2023) and the limited accuracy of conventional analytical wall models.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"538 ","pages":"Article 114128"},"PeriodicalIF":3.8,"publicationDate":"2025-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144229511","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"GD-VAEs: Geometric dynamic variational autoencoders for learning nonlinear dynamics and dimension reductions","authors":"Ryan Lopez ,&nbsp;Paul J. Atzberger","doi":"10.1016/j.jcp.2025.114127","DOIUrl":"10.1016/j.jcp.2025.114127","url":null,"abstract":"<div><div>We develop data-driven methods incorporating geometric and topological information to learn parsimonious representations of nonlinear dynamics from observations. The approaches learn nonlinear state-space models of the dynamics for general manifold latent spaces using training strategies related to Variational Autoencoders (VAEs). Our methods are referred to as Geometric Dynamic (GD) Variational Autoencoders (GD-VAEs). We learn encoders and decoders for the system states and evolution based on deep neural network architectures that include general Multilayer Perceptrons (MLPs), Convolutional Neural Networks (CNNs), and other architectures. Motivated by problems arising in parameterized PDEs and physics, we investigate the performance of our methods on tasks for learning reduced dimensional representations of the nonlinear Burgers Equations, Constrained Mechanical Systems, and spatial fields of Reaction-Diffusion Systems. GD-VAEs provide methods that can be used to obtain representations in manifold latent spaces for diverse learning tasks involving dynamics.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"537 ","pages":"Article 114127"},"PeriodicalIF":3.8,"publicationDate":"2025-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144194738","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Anti-symmetric barron functions and their approximation with sums of determinants","authors":"Nilin Abrahamsen ,&nbsp;Lin Lin","doi":"10.1016/j.jcp.2025.114118","DOIUrl":"10.1016/j.jcp.2025.114118","url":null,"abstract":"<div><div>A fundamental problem in quantum physics is to encode functions that are completely anti-symmetric under permutations of identical particles. The architecture of neural network models for the electron wave function typically comprises an equivariant component followed by a summation of determinants. The recently introduced Generic Antisymmetric (GA) block is designed to enhance the expressivity of such neural wave functions, and it was found that the 2-layer GA block achieved more accurate energies than the corresponding single-determinant FermiNet architecure, suggesting its promise as a way to improve the expressivity of neural wave functions. In this paper we show how the function expressed by the 2-layer GA block can be decomposed into a sum of determinants. We formalize this result by defining the antisymmetric Barron space as a generalized version of the 2-layer GA block and providing an appromation theorem for this function class. This result can be viewed as a negative result showing that the 2-layer GA block is not more expressive than using multiple determinants.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"537 ","pages":"Article 114118"},"PeriodicalIF":3.8,"publicationDate":"2025-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144205742","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}