Journal of Computational Physics最新文献

{"title":"P-adaptation of successive correction k-exact finite volume schemes for compressible flows","authors":"M. Salihoglu ,&nbsp;A. Liapi ,&nbsp;A. Belme ,&nbsp;P. Brenner ,&nbsp;G. Pont ,&nbsp;P. Cinnella","doi":"10.1016/j.jcp.2025.114330","DOIUrl":"10.1016/j.jcp.2025.114330","url":null,"abstract":"<div><div>A <span><math><mi>p</mi></math></span>-adaptation strategy is developed in the framework of successive correction <span><math><mi>k</mi></math></span>-exact finite volume schemes. A new adaptation indicator based on the decay of the successive correction terms used to reconstruct the solution within one cell is introduced to drive the adaptation process. The criterion relies on low-order derivatives, is efficiently estimated as part of the successive correction process, and identifies well flow regions characterized by steep gradients. Unlike other strategies in the literature, <span><math><mi>p</mi></math></span>-adaptation is only used to increase solution accuracy, while robust slope limiters are used to control the appearance of spurious oscillations. The performance of the proposed adaptive method is evaluated for a variety of 2D steady and unsteady, inviscid and viscous compressible flow configurations, as well as for a 3D transonic wing. The results show the effectiveness of <span><math><mi>p</mi></math></span>-adaptivity in achieving high-order solution quality while maintaining the computational effort close to that of a second-order (one-exact) scheme in terms of memory load and computation time.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"542 ","pages":"Article 114330"},"PeriodicalIF":3.8,"publicationDate":"2025-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097584","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":"Time-splitting methods for the cold-plasma model using Finite Element Exterior Calculus","authors":"Elena Moral Sánchez ,&nbsp;Martin Campos Pinto ,&nbsp;Yaman [Güşlü] ,&nbsp;Omar Maj","doi":"10.1016/j.jcp.2025.114305","DOIUrl":"10.1016/j.jcp.2025.114305","url":null,"abstract":"<div><div>In this work we propose a high-order structure-preserving discretization of the cold plasma model which describes the propagation of electromagnetic waves in magnetized plasmas. By utilizing B-Splines Finite Elements Exterior Calculus, we derive a space discretization that preserves the underlying Hamiltonian structure of the model, and we study two stable time-splitting geometrical integrators. We approximate an incoming wave boundary condition in such a way that the resulting schemes are compatible with a time-harmonic / transient decomposition of the solution, which allows us to establish their long-time stability. This approach readily applies to curvilinear and complex domains. We perform a numerical study of these schemes which compares their cost and accuracy against a standard Crank-Nicolson time integrator, and we run realistic simulations where the long-term behaviour is assessed using frequency-domain solutions. Our solvers are three-dimensional and parallel. They are implemented in the Python library PSYDAC, which makes them memory-efficient.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"541 ","pages":"Article 114305"},"PeriodicalIF":3.8,"publicationDate":"2025-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145010100","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":"Discontinuous Galerkin methods for the complete stochastic Euler equations","authors":"Dominic Breit ,&nbsp;Thamsanqa Castern Moyo ,&nbsp;Philipp Öffner","doi":"10.1016/j.jcp.2025.114324","DOIUrl":"10.1016/j.jcp.2025.114324","url":null,"abstract":"<div><div>In recent years, stochastic effects have become increasingly relevant for describing fluid behaviour, particularly in the context of turbulence. The most important model for inviscid fluids in computational fluid dynamics are the Euler equations of gas dynamics which we focus on in this paper. To take stochastic effects into account, we incorporate a stochastic forcing term in the momentum equation of the Euler system. To solve the extended system, we apply an entropy dissipative discontinuous Galerkin spectral element method including the Finite Volume setting, adjust it to the stochastic Euler equations and analyse its convergence properties. Our analysis is based on the concept of <em>dissipative martingale solutions</em>, as recently introduced by Moyo (J. Diff. Equ. 365, 408–464, 2023). Assuming no vacuum formation and bounded total energy, we prove that the scheme converges in law to a dissipative martingale solution. During the lifespan of a pathwise strong solution, we achieve convergence of at least order 1/2, measured by the expected <span><math><msup><mi>L</mi><mn>1</mn></msup></math></span> norm of the relative entropy. The results build a counterpart of those obtained in the deterministic case. In numerical simulations, we show the robustness of our scheme, visualise different stochastic realisations and support/extend the theoretical findings.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"541 ","pages":"Article 114324"},"PeriodicalIF":3.8,"publicationDate":"2025-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144933157","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 robust structure-preserving surface reconstruction scheme for two-layer shallow water equations based on a relaxation model and an extension on adaptive moving triangles","authors":"Jian Dong,&nbsp;Xu Qian,&nbsp;Zige Wei","doi":"10.1016/j.jcp.2025.114328","DOIUrl":"10.1016/j.jcp.2025.114328","url":null,"abstract":"<div><div>We present a structure-preserving surface reconstruction scheme for the relaxation two-layer shallow water equation, inspired by the approach in [Computers &amp; Fluids 272 (2024) 106193], along with its two-dimensional extension on adaptive moving triangular meshes. The original two-layer shallow water equation is conditionally hyperbolic, which presents challenges in designing shock-capturing numerical schemes. To address this, we propose a relaxation two-layer shallow water equation that is hyperbolic. However, this relaxation equation still contains nonconservative products associated with layer heights and bottom topography, which cannot be defined in the distributional sense. Utilizing the surface reconstruction method, we define Riemann states linked to the layer heights and bottom topography. This approach smooths the solution, facilitating the discretization of the nonconservative product across cell boundaries. We introduce a structure-preserving parameter crucial for demonstrating convergence, maintaining stationary steady states, and ensuring the positivity-preserving property. We establish a Lax-Wendroff type convergence theorem for the structure-preserving surface reconstruction scheme applied to the relaxation two-layer shallow water equation. To validate our approach, we conduct several classical numerical experiments for both one-dimensional and two-dimensional cases. Notably, we numerically confirm that the structure-preserving surface reconstruction scheme for the one-dimensional relaxation two-layer shallow water equation exhibits <span><math><mi>K</mi></math></span>-convergence based on the Cesàro average, particularly in the context of the well-known Kelvin-Helmholtz instabilities. Finally, we show several numerical results of the two-dimensional two-layer shallow water equations on adaptive moving triangles to verify the theoretical results.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"541 ","pages":"Article 114328"},"PeriodicalIF":3.8,"publicationDate":"2025-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144917543","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":"Energy-dissipative evolutionary Kolmogorov-Arnold networks for complex PDE systems","authors":"Guang Lin ,&nbsp;Changhong Mou ,&nbsp;Jiahao Zhang","doi":"10.1016/j.jcp.2025.114326","DOIUrl":"10.1016/j.jcp.2025.114326","url":null,"abstract":"<div><div>In this work, we introduce an evolutionary Kolmogorov-Arnold Network (EvoKAN), a novel framework for solving complex partial differential equations (PDEs). EvoKAN builds on Kolmogorov-Arnold Networks (KANs), where activation functions are spline-based and trainable on each edge, offering localized flexibility across multiple scales. Rather than retraining the network repeatedly, EvoKAN encodes only the initial state of the PDE during an initial learning phase. EvoKAN models Kolmogorov-Arnold network weights as time-dependent functions and updates them through the evolution of the governing PDEs. By treating EvoKAN weights as continuous functions in the relevant coordinates and updating them over time, EvoKAN can predict system trajectories over arbitrarily long horizons, a notable challenge for many conventional neural network-based methods. In addition, EvoKAN employs the scalar auxiliary variable (SAV) method to guarantee unconditional energy stability and computational efficiency. At individual time step, SAV only needs to solve the decoupled linear systems with constant coefficients, the implementation is significantly simplified. We test the proposed framework in several complex PDEs, including one-dimensional and two-dimensional Allen–Cahn equations and two-dimensional Navier-Stokes equations. The numerical results show that the EvoKAN solutions closely match the analytical references and established numerical benchmarks, effectively capturing the sharp interfaces in predicting the solution of the Allen-Cahn equation and turbulent flow patterns in predicting the solution of the Navier-Stokes equations.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"541 ","pages":"Article 114326"},"PeriodicalIF":3.8,"publicationDate":"2025-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144917492","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 adaptive spectral element method for systems of conservation laws","authors":"Manuel Colera ,&nbsp;Vít Dolejší","doi":"10.1016/j.jcp.2025.114322","DOIUrl":"10.1016/j.jcp.2025.114322","url":null,"abstract":"<div><div>We present a novel method for the numerical solution of systems of conservation laws. For the space discretization, the scheme considers high-order continuous finite elements stabilized via subgrid modeling, as well as highly anisotropic adaptive meshes in order to capture efficiently any sharp features in the solution. Time integration is carried out via a time-step adaptive, linearly implicit Runge–Kutta method, which allows large time steps and requires only the solution of a linear system of equations at each internal stage. An important characteristic of the present method is that the mesh is adapted before solving for the next time interval, and not afterwards as in the common procedure. Furthermore, the error arising from the inexact solution of the linear systems is also estimated and controlled, in such a way that the numerical solution is sufficiently accurate and the linear systems are not oversolved. Numerical experiments, including a computationally difficult case of non-convex flux and the Euler equations for compressible flows, were performed with up to eight-degree elements and a third-order time marching formula to demonstrate the capabilities of the method.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"541 ","pages":"Article 114322"},"PeriodicalIF":3.8,"publicationDate":"2025-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144988010","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":"Total uncertainty quantification in inverse solutions with deep learning surrogate models","authors":"Yuanzhe Wang ,&nbsp;James L. McCreight ,&nbsp;Joseph D. Hughes ,&nbsp;Alexandre M. Tartakovsky","doi":"10.1016/j.jcp.2025.114315","DOIUrl":"10.1016/j.jcp.2025.114315","url":null,"abstract":"<div><div>We propose an approximate Bayesian method for quantifying the total uncertainty in inverse partial differential equation (PDE) solutions obtained with machine learning surrogate models, including operator learning models. The proposed method accounts for uncertainty in the observations, PDE, and surrogate models. First, we use the surrogate model to formulate a minimization problem in the reduced space for the maximum a posteriori (MAP) inverse solution. Then, we randomize the MAP objective function and obtain samples of the posterior distribution by minimizing different realizations of the objective function. We test the proposed framework by comparing it with the iterative ensemble smoother and deep ensembling methods for a nonlinear diffusion equation with an unknown space-dependent diffusion coefficient. Among other applications, this equation describes the flow of groundwater in an unconfined aquifer. Depending on the training dataset and ensemble sizes, the proposed method provides similar or more descriptive posteriors of the parameters and states than the iterative ensemble smoother method. Deep ensembling underestimates uncertainty and provides less-informative posteriors than the other two methods. Our results show that, despite inherent uncertainty, surrogate models can be used for parameter and state estimation as an alternative to the inverse methods relying on (more accurate) numerical PDE solvers.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"541 ","pages":"Article 114315"},"PeriodicalIF":3.8,"publicationDate":"2025-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145019863","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":"FC-PINNs: Physics-informed neural networks for solving neutron diffusion eigenvalue problem with interface considerations","authors":"Hongtao Bi,&nbsp;Meiqi Song,&nbsp;Tengfei Zhang,&nbsp;Xiaojing Liu","doi":"10.1016/j.jcp.2025.114311","DOIUrl":"10.1016/j.jcp.2025.114311","url":null,"abstract":"<div><div>In this study, a refined methodology for Physics-informed Neural Networks (PINNs), referred to as fixed-point constraint PINNs (FC-PINNs), is introduced, which leverages fixed-point transformation and computational domain concatenation method to address eigenvalue problems and contact boundary conditions in differential eigenvalue equations, with application to solving the neutron diffusion equation, a classic eigenvalue problem in neutron transport theory. Conventional PINNs may face challenges in computing differential eigenvalue equations and handling contact boundaries, which sometimes leads to difficulties in converging to non-trivial solutions during the training process. For the eigenvalue, known as the effective multiplication factor <span><math><msub><mi>k</mi><mtext>eff</mtext></msub></math></span>, two methods are proposed applying hard or soft-constraint fixed-point transformation, ensuring accurate predictions of eigenvalue and eigenfunction distribution. For the contact boundary, a computational domain concatenation technique is employed, combining fixed-point constraints with extrapolated boundary constraints, which effectively stitches together multiple outputs to handle calculations at contact boundaries. FC-PINNs enable high-precision computation of differential eigenvalue equations through solving the inverse problem of PDEs, significantly enhancing the efficiency of eigenvalue computation. FC-PINNs are tested across one-dimensional, two-dimensional, and specific engineering problems, comparing the results with analytical and numerical solutions obtained from the outer-inner iteration method, with all test cases showing errors below 0.3 %.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"541 ","pages":"Article 114311"},"PeriodicalIF":3.8,"publicationDate":"2025-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144919832","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 overset grid assembly strategy based on immersed boundary method for fluid-structure interaction","authors":"Qiang Wang ,&nbsp;Kangping Liao ,&nbsp;Qingwei Ma ,&nbsp;Abbas Khayyer","doi":"10.1016/j.jcp.2025.114321","DOIUrl":"10.1016/j.jcp.2025.114321","url":null,"abstract":"<div><div>The overset grid method and the immersed boundary (IB) method, which have significant advantages in dealing with moving boundaries involving large amplitude motion, are widely used for fluid-structure interaction (FSI) problems in engineering applications. However, these methods still have some limitations. In the overset grid method, the hole-cutting operator and iterative procedure, which are complex and time-consuming, are necessary for flow field information exchange between the sub-domains and the background domain. In the IB method, non-physical pressure oscillations, which can result in numerical instability, often exist in simulating FSI problems with moving boundaries. In order to integrate the advantages of these two methods and overcome their limitations, a novel overset grid assembly strategy based on the IB method is proposed. In the present method, two additional body force terms, obtained by the diffuse-interface IB method, are considered in the momentum equations for solving the flow field in the background domain. The first body force term implicitly imposes a no-slip boundary condition of the body surface in the background domain. The second body force term is used to further correct the background flow field, and to ensure the continuity of the flow field between the background domain and the sub-domains. In this way, the explicit flow field information interpolation process from the sub-domains to the background domain is not necessary. Therefore, the complicated hole-cutting operator can be avoided. In addition, a third-order polynomial time extrapolation technique is adopted to estimate the pressure at the sub-domain boundaries. The velocity at the sub-domain boundaries can be determined with the estimated pressure. Therefore, the velocity and pressure boundary conditions at the sub-domain boundaries can be ensured without an iterative process between the sub-domains and the background domain. It significantly enhances the computational efficiency since the iterative process is avoided. Several benchmark cases are carried out to verify and validate the novel overset grid assembly strategy. In all cases, the results are in good agreement with the published experimental or numerical results. Furthermore, the results demonstrate that the present method can effectively suppress non-physical pressure oscillations, which often exist in the IB method when considering moving boundaries.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"541 ","pages":"Article 114321"},"PeriodicalIF":3.8,"publicationDate":"2025-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144997087","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 study of PINN incorporating action principle to predict Landau phase transition","authors":"Semin Lee,&nbsp;Youngtaek Oh,&nbsp;Byeonghyeon Goh,&nbsp;Hayoung Chung","doi":"10.1016/j.jcp.2025.114325","DOIUrl":"10.1016/j.jcp.2025.114325","url":null,"abstract":"<div><div>The Landau phase transition materials, making significant configurational changes from subtle perturbation given to the system, have garnered considerable interest because they underpin many engineering applications such as display and semiconductor devices. However, understanding and predicting the transition behavior requires accurate simulation of the complex energetics and finding the energetic minimum, which can only be handled by advanced numerical methods. The recent development of Physics-informed Neural Networks (PINNs), capitalizing on the recent development of deep learning methods and ever-increasing computing power, are deemed promising for revolutionizing numerical simulations as they do not require sophisticated numerical methods but the governing equations describing the system. Nevertheless, the capabilities are significantly limited in predicting phase transition and the dissipative characteristics of the system, which is reported for the first time in the present work. In this study, we present a method predicting relaxed states of the system having phase transitions using a PINN that directly minimizes free energy (Action-PINN) based on the action principle instead of a PINN that searches the equilibrium point of free energy (PDE-PINN). Focusing on the Landau modeling, a general free energy model accounting for the first-, and the second-order phase transition, we first demonstrate that the standard PINN is unable to predict the phase transition and leads only to degenerated solutions. We also demonstrate that the proposed variant of PINN can predict more complex phase transition behavior exhibited by liquid crystals in both 2D and 3D. Moreover, we underscore the model’s efficiency and potential for broader applicability through representative numerical examples. Specifically, we demonstrate enhancing solution fidelity through transfer learning, accurate predictions in heterogeneous systems, and end-to-end optimization.This work offers a significant advancement in extending the utility of PINNs for materials having complex behavior, paving the way for future research and applications for Landau phase transition materials.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"541 ","pages":"Article 114325"},"PeriodicalIF":3.8,"publicationDate":"2025-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144911745","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}