Journal of Computational Physics最新文献

{"title":"RBF-FD discretization of the Oseen equations","authors":"Michael Koch,&nbsp;Sabine Le Borne","doi":"10.1016/j.jcp.2025.114375","DOIUrl":"10.1016/j.jcp.2025.114375","url":null,"abstract":"<div><div>The radial basis function - finite difference (RBF-FD) method is a (meshless) technique for the discretization of differential operators on scattered node sets. In recent years, it has been successfully applied mostly to scalar partial differential equations (PDEs). The extension to the application to the steady state Oseen equations on (several) scattered node sets is not straightforward but requires novel components which are the subject of this paper. We consider the steady-state Oseen equations in three spatial dimensions, and as a radial basis function, we restrict ourselves to the polyharmonic spline (PHS) with polynomial augmentation. However, the following contributions of our paper may also be applied to other model problems and RBFs. In particular, we will consider the selection of two node sets for the two types of unknowns, velocity and pressure, and subsequent (flexible order) RBF-FD discretization of the various differential operators in the coupled system. We discuss variants for the discretization of the pressure constraint as well as the influence of the viscosity parameter on the convergence of the RBF-FD discretization. Finally, we provide numerical tests for the Oseen equations in three dimensions on complex domains using several node arrangements, convection directions and parameters inherent to the PHS RBF-FD method. The tests demonstrate that the proposed method is stable for discretization step widths between <span><math><mrow><msub><mi>h</mi><mi>u</mi></msub><mo>=</mo><mn>0.01</mn></mrow></math></span> and <span><math><mrow><msub><mi>h</mi><mi>u</mi></msub><mo>=</mo><mn>0.5</mn></mrow></math></span> and viscosities in the range of <span><math><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></math></span> to 1 not just on the unit cube but also on a more complicated three-dimensional bunny-shaped domain. In particular, for even degrees of polynomial augmentation of the Laplacian (and lower degrees for involved first order differential operators), we can reach convergence of the same (even) order.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"542 ","pages":"Article 114375"},"PeriodicalIF":3.8,"publicationDate":"2025-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097982","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 finite element method for simulating surface plasmon polaritons on complex graphene sheets","authors":"Jichun Li ,&nbsp;Michael Neunteufel ,&nbsp;Li Zhu","doi":"10.1016/j.jcp.2025.114372","DOIUrl":"10.1016/j.jcp.2025.114372","url":null,"abstract":"<div><div>Surface plasmon polaritons (SPPs) are generated on the graphene surface, and provide a window into the nano-optical and electrodynamic response of their host material and its dielectric environment. An accurate simulation of SPPs presents several unique challenges, since SPPs often occur at complex interfaces between materials of different dielectric constants and appropriate boundary conditions at the graphene interfaces are crucial. Here we develop a simplified graphene model and propose a new finite element method accordingly. Stability for the continuous model is established, and extensive numerical results are presented to demonstrate that the new model can capture the SPPs very well for various complex graphene sheets.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"542 ","pages":"Article 114372"},"PeriodicalIF":3.8,"publicationDate":"2025-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097574","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":"Hybridizable discontinuous Galerkin methods for coupled poro-viscoelastic and thermo-viscoelastic systems","authors":"Salim Meddahi","doi":"10.1016/j.jcp.2025.114368","DOIUrl":"10.1016/j.jcp.2025.114368","url":null,"abstract":"<div><div>This article presents a unified mathematical framework for modeling coupled poro-viscoelastic and thermo-viscoelastic phenomena, formulated as a system of first-order in time partial differential equations. The model describes the evolution of solid velocity, elastic and viscous stress tensors, and additional fields related to either fluid pressure or temperature, depending on the physical context. We develop a hybridizable discontinuous Galerkin method for the numerical approximation of this coupled system, providing a high-order, stable discretization that efficiently handles the multiphysics nature of the problem. We establish stability analysis and derive optimal <span><math><mrow><mi>h</mi><mi>p</mi></mrow></math></span>-error estimates for the semi-discrete formulation. The theoretical convergence rates are validated through comprehensive numerical experiments, demonstrating the method’s accuracy and robustness across various test cases, including wave propagation in heterogeneous media with mixed viscoelastic properties.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"542 ","pages":"Article 114368"},"PeriodicalIF":3.8,"publicationDate":"2025-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097573","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":"Large-scale semi-discrete optimal transport with distributed Voronoi diagrams","authors":"Bruno Lévy ,&nbsp;Nicolas Ray ,&nbsp;Quentin Mérigot ,&nbsp;Hugo Leclerc","doi":"10.1016/j.jcp.2025.114374","DOIUrl":"10.1016/j.jcp.2025.114374","url":null,"abstract":"<div><div>In this article, we propose a numerical method to solve semi-discrete optimal transport problems for gigantic pointsets (<span><math><msup><mn>10</mn><mn>8</mn></msup></math></span> points and more). By pushing the limits by several orders of magnitude, it opens the path to new applications in cosmology, fluid simulation and data science to name but a few. The method is based on a new algorithm that computes (generalized) Voronoi diagrams in parallel and in a distributed way. First we make the simple observation that the cells defined by a subgraph of the Delaunay graph contain the Voronoi cells, and that one can deduce the missing edges from the intersections between those cells. Based on this observation, we introduce the Distributed Voronoi Diagram algorithm (DVD) that can be used on a cluster and that exchanges vertices between the nodes as need be. We also report early experimental results, demonstrating that the DVD algorithm has the potential to solve some giga-scale semi-discrete optimal transport problems encountered in computational cosmology.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"542 ","pages":"Article 114374"},"PeriodicalIF":3.8,"publicationDate":"2025-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097585","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":"Recovery of initial displacement and velocity in anisotropic elastic systems by the time dimensional reduction method","authors":"Trong D. Dang ,&nbsp;Chanh V. Le ,&nbsp;Khoa D. Luu ,&nbsp;Loc H. Nguyen","doi":"10.1016/j.jcp.2025.114371","DOIUrl":"10.1016/j.jcp.2025.114371","url":null,"abstract":"<div><div>We introduce a time-dimensional reduction method for the inverse source problem in linear elasticity, where the goal is to reconstruct the initial displacement and velocity fields from partial boundary measurements of elastic wave propagation. The key idea is to employ a novel spectral representation in time, using an orthonormal basis composed of Legendre polynomials weighted by exponential functions. This Legendre polynomial-exponential basis enables a stable and accurate decomposition in the time variable, effectively reducing the original space-time inverse problem to a sequence of coupled spatial elasticity systems that no longer depend on time. These resulting systems are solved using the quasi-reversibility method. On the theoretical side, we establish a convergence theorem ensuring the stability and consistency of the regularized solution obtained by the quasi-reversibility method as the noise level tends to zero. On the computational side, two-dimensional numerical experiments confirm the theory and demonstrate the method’s ability to accurately reconstruct both the geometry and amplitude of the initial data, even under substantial measurement noise. The results highlight the effectiveness of the proposed framework as a robust and computationally efficient strategy for inverse elastic source problems.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"542 ","pages":"Article 114371"},"PeriodicalIF":3.8,"publicationDate":"2025-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097570","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":"Multi-material ALE remap with interface sharpening using high-order matrix-free finite element methods","authors":"Arturo Vargas ,&nbsp;Vladimir Z. Tomov ,&nbsp;M. Aaron Skinner ,&nbsp;Veselin Dobrev ,&nbsp;Jan Nikl ,&nbsp;Tzanio Kolev ,&nbsp;Robert N. Rieben","doi":"10.1016/j.jcp.2025.114367","DOIUrl":"10.1016/j.jcp.2025.114367","url":null,"abstract":"<div><div>The arbitrary Lagrangian-Eulerian (ALE) technique involves remapping field quantities from a Lagrangian mesh to an optimized mesh in a conservative, accurate and bounds-preserving manner. For methods based on arbitrary order finite elements, as described in [5], material volume fractions are advected in pseudo-time using flux-corrected transport (FCT) without any form of interface reconstruction. In practice, this can lead to excessive propagation of small volume fractions throughout the domain. In addition, this method requires assembly of a global advection matrix to compute the bounds-preserving low-order FCT solution. In this work, we introduce a new approach for ALE remap using a high-order matrix-free technique which incorporates a flux modification to sharpen material interfaces in a conservative manner.</div><div>Our approach begins with computing a bounds-preserving low-order solution to the ALE remap equations at the element level. We then compute a sharp interface solution (not guaranteed to be bounds-preserving) which comes from solving an augmented version of the ALE remap equations with a conservative flux modification which acts to sharpen material volume fractions based on their gradients and transport directions. Using the sharp interface solution, we make global corrections to the bounds-preserving solution while maintaining preservation of bounds. By blending with the sharpened solution at the global level we are able to globally conserve mass without hindering the remap pseudo-time step. This new interface-aware ALE remap method is based entirely on partial assembly techniques where globally assembled matrix operators are no longer needed, resulting in a globally matrix-free FCT method for multi-material, multi-field ALE remap with high performance on GPU architectures. We present results of our new remap method on 1D, 2D and 3D benchmarks and describe the algorithmic tailoring for GPU architectures that was developed.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"542 ","pages":"Article 114367"},"PeriodicalIF":3.8,"publicationDate":"2025-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097583","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 unsupervised PINN framework with dynamically self-adaptive strategy for solid mechanics","authors":"Feiyang Wang ,&nbsp;Wuzhou Zhai ,&nbsp;Shuai Zhao ,&nbsp;Jianhong Man","doi":"10.1016/j.jcp.2025.114373","DOIUrl":"10.1016/j.jcp.2025.114373","url":null,"abstract":"<div><div>Unbalance in multi-task training has always posed significant challenges in deep learning, particularly for Physics-Informed Neural Networks (PINN). A novel unsupervised PINN framework configured with two neural network architectures has been developed for solid mechanics problems with pure boundary data. This framework features an innovatively formulated loss function, where loss weights are dynamically updated through a self-adaptive strategy using either the gradient normalization algorithm or the augmented Lagrangian algorithm, effectively tackling training imbalances across different types of boundary data. The PINN model consistently approximates solutions for solid mechanics problems with improved convergence and accuracy, as validated through a uniaxial tensile test case. The novel framework is robust and adaptable to two neural network architectures with different numbers of layers and neurons. About 30000 training epochs can reduce the prediction error of deformation to below 10^-6, meeting the requirements of computational solid mechanics. An information entropy of 1.3 bits, calculated from 500 well-trained PINN models, indicates that the novel unsupervised PINN framework exhibits low uncertainty. The findings uncover the so-called “squared rule” for selecting a suitable threshold in the convergence criterion. This study successfully addresses the critical scientific problem inherent in multitask learning, positioning PINN as a potentially universal and user-friendly method, offering an alternative for numerical computations.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"542 ","pages":"Article 114373"},"PeriodicalIF":3.8,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097568","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 extension of the localized artificial diffusivity method for immiscible and high density ratio flows","authors":"Steven R. Brill,&nbsp;Britton J. Olson,&nbsp;Guillaume T. Bokman","doi":"10.1016/j.jcp.2025.114366","DOIUrl":"10.1016/j.jcp.2025.114366","url":null,"abstract":"<div><div>The localized artificial diffusivity (LAD) method is widely regarded as the preferred multi-material regularization scheme for the compact finite difference method, because it is conservative, easy to implement, and generally robust for a wide range of multi-material problems. However, traditional LAD methods face significant challenges when applied to flows with large density ratios and when maintaining thermodynamic equilibrium across material interfaces. These limitations arise from the formulation of the artificial diffusivity flux and the reliance on enthalpy diffusion for interface regularization. Additionally, traditional LAD methods struggle to ensure stability under large density ratio conditions, fail to maintain a finite interface thickness, and are therefore unsuitable for modeling immiscible interfaces. In this work, we discuss the origins of these issues in traditional LAD methods and propose modifications which enable the simulation of large density ratio and immiscible flows. The proposed method targets the artificial diffusion fluxes at gradients and ringing in the volume fraction, rather than the mass fraction in traditional methods, to consistently regularize large density ratio interfaces. Furthermore, the proposed method introduces an artificial bulk density diffusion term to enforce equilibrium conditions across interfaces. To address the challenge of modeling immiscible flows, a conservative diffuse interface term is incorporated into the formulation to ensure a finite interface thickness. Specific consideration is taken in the design of the method to ensure that these crucial properties are maintained for <span><math><mi>N</mi></math></span>-material flows. The effectiveness of the proposed method is demonstrated through a series of canonical test cases, and its accuracy is validated by comparison with experimental data on micro-bubble collapse in water. These results highlight the method’s robustness and its ability to overcome the limitations of traditional LAD approaches.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"542 ","pages":"Article 114366"},"PeriodicalIF":3.8,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145057317","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 rp-adaptive method for accurate resolution of shock-dominated viscous flow based on implicit shock tracking","authors":"Huijing Dong ,&nbsp;Masayuki Yano ,&nbsp;Tianci Huang ,&nbsp;Matthew J. Zahr","doi":"10.1016/j.jcp.2025.114337","DOIUrl":"10.1016/j.jcp.2025.114337","url":null,"abstract":"<div><div>This work introduces an optimization-based <span><math><mrow><mi>r</mi><mi>p</mi></mrow></math></span>-adaptive numerical method to approximate solutions of viscous, shock-dominated flows using implicit shock tracking and a high-order discontinuous Galerkin discretization on traditionally coarse grids without nonlinear stabilization (e.g., artificial viscosity or limiting). The proposed method adapts implicit shock tracking methods, originally developed to align mesh faces with solution discontinuities, to compress elements into viscous shocks and boundary layers, functioning as a novel approach to aggressive <span><math><mi>r</mi></math></span>-adaptation. This form of <span><math><mi>r</mi></math></span>-adaptation is achieved naturally as the minimizer of the enriched residual with respect to the discrete flow variables and coordinates of the nodes of the grid. Several innovations to the shock tracking optimization solver are proposed to ensure sufficient mesh compression at viscous features to render stabilization unnecessary, including residual weighting, step constraints and modifications, and viscosity-based continuation. Finally, <span><math><mi>p</mi></math></span>-adaptivity is used to locally increase the polynomial degree with three clear benefits: (1) lessens the mesh compression requirements near shock waves and boundary layers, (2) reduces the error in regions where <span><math><mi>r</mi></math></span>-adaptivity is not sufficient with the given grid topology, and (3) reduces computational cost by performing a majority of the <span><math><mi>r</mi></math></span>-adaptivity iterations on the coarsest discretization. A series of numerical experiments show the proposed method effectively resolves viscous, shock-dominated flows, including accurate prediction of heat flux profiles produced by hypersonic flow over a cylinder, and compares favorably in terms of accuracy per degree of freedom to <span><math><mi>h</mi></math></span>-adaptation with a high-order discretization.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"543 ","pages":"Article 114337"},"PeriodicalIF":3.8,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145218532","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":"Unconditionally energy stable high-order convex-splitting schemes for the square phase field crystal model with complex nonlinearity","authors":"Bingqing Hu ,&nbsp;Junping Yin ,&nbsp;Xuan Zhao","doi":"10.1016/j.jcp.2025.114365","DOIUrl":"10.1016/j.jcp.2025.114365","url":null,"abstract":"<div><div>This study presents the high-order schemes with unconditional energy stability for solving the square phase field crystal model. The proposed schemes couple BDF<span><math><mi>q</mi></math></span> (<span><math><mi>q</mi></math></span>=3,4,5) method with the convex-splitting strategy, incorporating the multi-time-level stabilization term, which is closely reformed by BDF<span><math><mi>q</mi></math></span> method. This newly introduced stabilization term acts as the additional diffusivity, while ensuring the unconditional energy dissipation and the optimal error analysis. Theoretical analysis confirms that the high-order convex-splitting schemes also preserve unique solvability and mass conservation. Notably, the unconditional energy stability guarantees the boundedness of the numerical solution in the discrete <span><math><msubsup><mi>H</mi><mi>h</mi><mn>2</mn></msubsup></math></span> and <span><math><msubsup><mi>W</mi><mi>h</mi><mrow><mn>1</mn><mo>,</mo><mn>6</mn></mrow></msubsup></math></span> norms, which allow precise estimation of nonlinear term via Young’s inequality, overcoming the analytical challenges brought by high-order nonlinear term. Consequently, the optimal error estimate is rigorously conducted using the global energy analysis technology based on the discrete orthogonal convolution kernels. Numerical examples are performed to validate the efficiency and accuracy of the proposed schemes, demonstrating that 5th-order scheme achieves enhanced accuracy especially with large time-step size. The distinct advantages of the proposed high-order schemes are particularly beneficial in long-term simulations. In addition, numerical tests confirm that the relatively large stabilization term <span><math><mrow><mi>S</mi><mo>=</mo><mn>5</mn></mrow></math></span> is essential for ensuring energy stability and reducing computational costs by <span><math><mrow><mn>75</mn><mspace></mspace><mo>%</mo></mrow></math></span> compared to <span><math><mrow><mi>S</mi><mo>=</mo><mn>1</mn></mrow></math></span>.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"542 ","pages":"Article 114365"},"PeriodicalIF":3.8,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097572","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}