Journal of Computational Physics最新文献

{"title":"The Hermite-Taylor correction function method for embedded boundary and Maxwell’s interface problems","authors":"Yann-Meing Law ,&nbsp;Daniel Appelö ,&nbsp;Thomas Hagstrom","doi":"10.1016/j.jcp.2025.114111","DOIUrl":"10.1016/j.jcp.2025.114111","url":null,"abstract":"<div><div>We propose a novel Hermite-Taylor correction function method to handle embedded boundary and interface conditions for Maxwell’s equations. The Hermite-Taylor method evolves the electromagnetic fields and their derivatives through order <span><math><mi>m</mi></math></span> in each Cartesian coordinate. This makes the development of a systematic approach to enforce boundary and interface conditions difficult. Here we use the correction function method to update the numerical solution where the Hermite-Taylor method cannot be applied directly. Time derivatives of boundary and interface conditions, converted into spatial derivatives, are enforced to obtain a stable method and relax the time-step size restriction of the Hermite-Taylor correction function method. The proposed high-order method offers a flexible systematic approach to handle embedded boundary and interface problems, including problems with discontinuous solutions at the interface. This method is also easily adaptable to other first order hyperbolic systems.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"537 ","pages":"Article 114111"},"PeriodicalIF":3.8,"publicationDate":"2025-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144167110","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":"Revisiting numerical artifacts in the generalized porous medium equation with continuous coefficients: Does averaging really matter ?","authors":"Vishnu Prakash K ,&nbsp;Ganesh Natarajan","doi":"10.1016/j.jcp.2025.114101","DOIUrl":"10.1016/j.jcp.2025.114101","url":null,"abstract":"<div><div>The Generalized Porous Medium Equation (GPME) with continuous coefficients is a degenerate parabolic equation and the finite volume solutions to this equation are known to exhibit numerical artifacts depending on how the non-linear diffusion coefficient <span><math><mrow><mi>k</mi><mo>(</mo><mi>p</mi><mo>)</mo></mrow></math></span> is computed at the faces. While arithmetic averaging is known to lead to reasonably accurate solutions for the degenerate diffusion equation, the use of harmonic averaging results in temporal oscillations and non-physical locking, neither of which can be eliminated by grid refinement. In this work, we propose an explicit finite volume discretisation of the GPME based on a novel approach to compute the diffusive fluxes referred to as the <span><math><mi>α</mi></math></span>-damping (AD) flux scheme. The <span><math><mi>α</mi></math></span>-damping flux scheme may be interpreted as a conservative “flux correction” approach which makes the averaging irrelevant to the numerical solution. Using theoretical analysis and numerical experiments in both one and two dimensions, we show that the new scheme is second-order accurate, applies to any temporal discretisation and that the solutions are independent of the choice of averaging while being free of numerical artifacts.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"537 ","pages":"Article 114101"},"PeriodicalIF":3.8,"publicationDate":"2025-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144147295","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 immersed interface method for incompressible flows and geometries with sharp features","authors":"Michael J. Facci ,&nbsp;Ebrahim M. Kolahdouz ,&nbsp;Boyce E. Griffith","doi":"10.1016/j.jcp.2025.114119","DOIUrl":"10.1016/j.jcp.2025.114119","url":null,"abstract":"<div><div>The immersed interface method (IIM) for models of fluid flow and fluid-structure interaction imposes jump conditions that capture stress discontinuities generated by forces that are concentrated along immersed boundaries. Most prior work using the IIM for fluid dynamics applications has focused on smooth interfaces, but boundaries with sharp features such as corners and edges can appear in practical analyses, particularly on engineered structures. The present study builds on our work to integrate finite element-type representations of interface geometries with the IIM. Initial realizations of this approach used a continuous Galerkin (CG) finite element discretization for the boundary, but as we show herein, these approaches generate large errors near sharp geometrical features. To overcome this difficulty, this study introduces an IIM approach using a discontinuous Galerkin (DG) representation of the jump conditions. Numerical examples explore the impacts of different interface representations on accuracy for both smooth and sharp boundaries, particularly flows interacting with fixed interface configurations. We demonstrate that using a DG approach provides accuracy that is comparable to the CG method for smooth cases. Further, we identify a time step size restriction for the CG representation that is directly related to the sharpness of the geometry. In contrast, time step size restrictions imposed by DG representations are demonstrated to be nearly insensitive to the presence of sharp features.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"537 ","pages":"Article 114119"},"PeriodicalIF":3.8,"publicationDate":"2025-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144167108","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":"Scaled-cPIKANs: Spatial variable and residual scaling in chebyshev-based physics-informed kolmogorov-Arnold networks","authors":"Farinaz Mostajeran,&nbsp;Salah A. Faroughi","doi":"10.1016/j.jcp.2025.114116","DOIUrl":"10.1016/j.jcp.2025.114116","url":null,"abstract":"<div><div>Partial Differential Equations (PDEs) are integral to modeling many scientific and engineering problems. Physics-informed Neural Networks (PINNs) have emerged as promising tools for solving PDEs by embedding governing equations into the neural network loss function. However, when dealing with PDEs characterized by strong oscillatory dynamics over large computational domains, PINNs based on Multilayer Perceptrons (MLPs) often exhibit poor convergence and reduced accuracy. To address these challenges, this paper introduces Scaled-cPIKAN, a physics-informed architecture rooted in Kolmogorov-Arnold Networks (KANs). Scaled-cPIKAN integrates Chebyshev polynomial representations with a domain scaling approach that transforms spatial variables in residual PDEs into the standardized domain <span><math><msup><mrow><mo>[</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow><mi>d</mi></msup></math></span>, as intrinsically required by Chebyshev polynomials. By combining the flexibility of Chebyshev-based KANs (cKANs) with the physics-driven principles of PINNs, and the spatial domain transformation, Scaled-cPIKAN enables efficient representation of oscillatory dynamics across extended spatial domains while improving computational performance. The importance of scaling variables across extended spatial regions is further examined by analyzing the convergence rate determined by the Neural Tangent Kernel (NTK) matrix associated with the cKAN framework. We demonstrate Scaled-cPIKAN efficacy using four benchmark problems: the diffusion equation, the Helmholtz equation, the Allen-Cahn equation, as well as both forward and inverse formulations of the reaction-diffusion equation (with and without noisy data). Our results show that Scaled-cPIKAN significantly outperforms existing methods in all test cases. In particular, it achieves several orders of magnitude higher accuracy and faster convergence rate, making it a highly efficient tool for approximating PDE solutions that feature oscillatory behavior over large spatial domains.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"537 ","pages":"Article 114116"},"PeriodicalIF":3.8,"publicationDate":"2025-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144167111","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 denoising multiscale particle method for nonequilibrium flow simulations","authors":"Hao Yang,&nbsp;Kaikai Feng,&nbsp;Ziqi Cui,&nbsp;Jun Zhang","doi":"10.1016/j.jcp.2025.114096","DOIUrl":"10.1016/j.jcp.2025.114096","url":null,"abstract":"<div><div>The direct simulation Monte Carlo (DSMC) method is promising for simulating rarefied nonequilibrium flows, but its inherent limitations on spatiotemporal resolution and statistical noise hinder applications in near-continuum and low-signal regimes. This work proposes a denoising multiscale particle (DMP) method for efficient particle-based simulations. The DMP method employs a Bhatnagar–Gross–Krook (BGK) relaxation process to simplify binary collisions. Its denoising strategy, inspired by the information preservation method, incorporates low-noise collective information into each simulation particle. This collective information evolves anchored on the information-augmented Shakhov BGK equation, which provides a theoretical foundation for analyzing transport and denoising properties. Macroscopic flow quantities are obtained by statistically averaging this collective information, resulting in a signal-to-noise ratio independent of signal magnitude in low- to moderate-signal regimes, while proportional to the local rarefaction level. An operator splitting scheme is utilized to decouple particle movement and relaxation, enabling a simple and efficient implementation but introducing numerical dissipation in the Navier–Stokes limit. In DMP, this numerical dissipation error is quantified and mitigated through incorporating anti-dissipation target distribution and information compensation terms, endowing the method with multiscale simulation capability. Consequently, the DMP method allows for coarser spatiotemporal resolutions and requires fewer sampling particles than DSMC. Various numerical experiments validate the accuracy and demonstrate the efficiency of the DMP method in low- to moderate-rarefaction and signal regimes.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"537 ","pages":"Article 114096"},"PeriodicalIF":3.8,"publicationDate":"2025-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144147296","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 efficient multidomain RBF mesh deformation method based on MPI/OpenMP hybrid parallel interpolation","authors":"Zhenyu Hu,&nbsp;Yu Yuan,&nbsp;Dapeng Xiong,&nbsp;Chenglong Wang,&nbsp;Mingbo Sun,&nbsp;Yongchao Sun","doi":"10.1016/j.jcp.2025.114113","DOIUrl":"10.1016/j.jcp.2025.114113","url":null,"abstract":"<div><div>Radial basis function (RBF) interpolation has been prevalent in mesh deformation schemes due to its great quality-preserving ability and generality. However, the cost time scales as <span><math><mrow><mi>O</mi><mo>(</mo><msup><mrow><msub><mi>N</mi><mi>s</mi></msub></mrow><mn>3</mn></msup><mo>)</mo></mrow></math></span>, where <span><math><msub><mi>N</mi><mi>s</mi></msub></math></span> is the number of surface nodes, which makes full RBF interpolation prohibitively expensive to implement for large mesh. The key improvement is the application of efficient reduced-data methods. But the greedy-type reduced-data method remains expensive when applied to large-scale meshes, requiring iterative linear system solutions and interpolation error calculations to generate the reduced dataset. Furthermore, a supplementary surface correction procedure must be implemented to ensure exact surface shape. In this paper, a novel multidomain method is proposed that stochastically splits the surface nodes into <span><math><mi>n</mi></math></span> small subsets and a small sub-RBF interpolant is constructed on each subset. The mesh deformation is computed by the weight of sub-RBF interpolations. Since the above processes are independent, this method is perfectly parallel. The computational complexity analysis reveals that this method reduces the solution cost to <span><math><mrow><mi>O</mi><mo>(</mo><msup><mrow><msub><mi>N</mi><mi>s</mi></msub></mrow><mn>3</mn></msup><mo>/</mo><msup><mi>n</mi><mn>2</mn></msup><mo>)</mo></mrow></math></span> for a serial algorithm, and this method can be faster than the multiscale method Kedward et al.(2017) in all stages. By appropriately selecting the weighting coefficients, the exact surface shape is naturally preserved and the surface correction issue is eliminated. Further enhancements are achieved by dividing the volume into near-surface, intermediate, far-surface and stationary domains based on their distances from the surface. These domains can adopt distinct weighting schemes and utilize varying numbers of radial centers. The efficiency and accuracy of this method are analyzed in detail using two-dimensional (2D) airfoils, a three-dimensional (3D) scramjet combustor and a 3D hypersonic vehicle examples. In comparison with the conventional greedy method and the contemporary multiscale method, this method gains higher efficiency and comparable mesh quality.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"537 ","pages":"Article 114113"},"PeriodicalIF":3.8,"publicationDate":"2025-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144147297","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":"Minimizing information loss reduces spiking neuronal networks to differential equations","authors":"Jie Chang ,&nbsp;Zhuoran Li ,&nbsp;Zhongyi Wang ,&nbsp;Louis Tao ,&nbsp;Zhuo-Cheng Xiao","doi":"10.1016/j.jcp.2025.114117","DOIUrl":"10.1016/j.jcp.2025.114117","url":null,"abstract":"<div><div>Spiking neuronal networks (SNNs) are widely used in computational neuroscience, from biologically realistic modeling of local cortical networks to phenomenological modeling of the whole brain. Despite their prevalence, a systematic mathematical theory for finite-sized SNNs remains elusive, even for idealized homogeneous networks. The primary challenges are twofold: 1) the rich, parameter-sensitive SNN dynamics, and 2) the singularity and irreversibility of spikes. These challenges pose significant difficulties when relating SNNs to systems of differential equations, leading previous studies to impose additional assumptions or to focus on individual dynamic regimes. In this study, we introduce a Markov approximation of homogeneous SNN dynamics to minimize information loss when translating SNNs into ordinary differential equations. Our only assumption for the Markov approximation is the fast self-decorrelation of synaptic conductances. The system of ordinary differential equations derived from the Markov model effectively captures high-frequency partial synchrony and the metastability of finite-neuron networks produced by interacting excitatory and inhibitory populations. Besides accurately predicting dynamical statistics, such as firing rates, our theory also quantitatively captures the geometry of attractors and bifurcation structures of SNNs. Thus, our work provides a comprehensive mathematical framework that can systematically map parameters of single-neuron physiology, network coupling, and external stimuli to homogeneous SNN dynamics.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"537 ","pages":"Article 114117"},"PeriodicalIF":3.8,"publicationDate":"2025-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144167107","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":"Finite difference alternative WENO schemes with Riemann invariant-based local characteristic decompositions for compressible Euler equations","authors":"Yue Wu,&nbsp;Chi-Wang Shu","doi":"10.1016/j.jcp.2025.114104","DOIUrl":"10.1016/j.jcp.2025.114104","url":null,"abstract":"<div><div>The weighted essentially non-oscillatory (WENO) schemes are widely used for hyperbolic conservation laws due to the ability to resolve discontinuities and maintain high-order accuracy in smooth regions at the same time. For hyperbolic systems, the WENO procedure is usually performed on local characteristic variables that are obtained by local characteristic decompositions to avoid oscillation near shocks. However, such decompositions are often computationally expensive. In this paper, we study a Riemann invariant-based local characteristic decomposition for the compressible Euler equations that reduces the cost. We apply the WENO procedure to the local characteristic fields of the Riemann invariants, where the eigenmatrix is sparse and thus the computational cost can be reduced. It is difficult to obtain the cell averages of Riemann invariants from those of the conserved variables due to the nonlinear relation between them, so we only focus on the finite difference alternative WENO versions. The efficiency and non-oscillatory property of the proposed schemes are well demonstrated by our numerical results.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"537 ","pages":"Article 114104"},"PeriodicalIF":3.8,"publicationDate":"2025-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144147293","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 coupled PFEM-DEM model for fluid-granular flows with free surface dynamics applied to landslides","authors":"Thomas Leyssens,&nbsp;Michel Henry,&nbsp;Jonathan Lambrechts,&nbsp;Vincent Legat,&nbsp;Jean-François Remacle","doi":"10.1016/j.jcp.2025.114082","DOIUrl":"10.1016/j.jcp.2025.114082","url":null,"abstract":"<div><div>Free surface and granular fluid mechanics problems combine the challenges of fluid dynamics with aspects of granular behaviour. This type of problem is particularly relevant in contexts such as the flow of sediments in rivers, the movement of granular soils in reservoirs, or the interactions between a fluid and granular materials in industrial processes such as silos. The numerical simulation of these phenomena is challenging because the solution depends not only on the multiple phases that strongly interact with each other, but also on the need to describe the geometric evolution of the different interfaces. This paper presents an approach to the simulation of fluid-granular phenomena involving strongly deforming free surfaces. The Discrete Element Method (DEM) is combined with the Particle Finite Element Method (PFEM) and the fluid–grain interface is treated by a two-way coupling between the two phases. The fluid-air interface is solved by a free surface model. The geometric and topological variations are therefore naturally provided by the full Lagrangian description of all phases. The approach is validated on benchmark test cases such as two-phase dam failures and then applied to a historical landslide event.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"537 ","pages":"Article 114082"},"PeriodicalIF":3.8,"publicationDate":"2025-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144106293","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 micro-macro decomposition-based asymptotic-preserving random feature method for multiscale radiative transfer equations","authors":"Jingrun Chen ,&nbsp;Zheng Ma ,&nbsp;Keke Wu","doi":"10.1016/j.jcp.2025.114103","DOIUrl":"10.1016/j.jcp.2025.114103","url":null,"abstract":"<div><div>This paper introduces the Asymptotic-Preserving Random Feature Method (APRFM) for the efficient resolution of multiscale radiative transfer equations. The APRFM effectively addresses the challenges posed by stiffness and multiscale characteristics inherent in radiative transfer equations through the application of a micro-macro decomposition strategy. This approach decomposes the distribution function into equilibrium and non-equilibrium components, allowing for the approximation of both parts through the random feature method (RFM) within a least squares minimization framework. The proposed method exhibits remarkable robustness across different scales and achieves high accuracy with fewer degrees of freedom and collocation points than the vanilla RFM. Additionally, compared to the deep neural network-based method, our approach offers significant advantages in terms of parameter efficiency and computational speed. These benefits have been substantiated through numerous numerical experiments conducted on both one- and two-dimensional problems.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"537 ","pages":"Article 114103"},"PeriodicalIF":3.8,"publicationDate":"2025-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144131178","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}