Journal of Computational Physics最新文献

{"title":"Numerical simulations of the phase behaviors of rod-coil diblock copolymers confined on a spherical surface","authors":"Jiahui Luo ,&nbsp;Qin Liang ,&nbsp;Yunqing Huang","doi":"10.1016/j.jcp.2025.114339","DOIUrl":"10.1016/j.jcp.2025.114339","url":null,"abstract":"<div><div>The self-assembly of rod-coil diblock copolymers has garnered significant attention owing to their intricate phase behavior. One of the most successful theories to investigate these phase behaviors is the self-consistent field theory (SCFT). In this work, we employ SCFT to study the phase behavior of rod-coils when these polymers are confined on a spherical surface. While such confinement enriches the diversity of possible phases, it also increases the complexity of the numerical simulations with SCFT. To address this challenge, we develop a novel pseudo-spectral method that employs spherical harmonics, the Wigner D-matrix, and a time-splitting approach to efficiently solve the Fokker-Planck equations in SCFT. The interplay between the liquid crystalline nature of the rod-like units, microphase separation, and spherical confinement results in a remarkable diversity of morphologies. The choice of initial fields plays a crucial role in determining the final converged states. To facilitate the generation of initial states for various striped structures, we propose a cut-and-rotate method. Using this numerical framework, we systematically investigate the phase behavior of rod-coil diblock copolymers over a range of sphere radii. For rod-coils with symmetric composition, we observe a sequence of stable striped patterns, including lamellar, single-helical, and double-helical structures, which alternate as the sphere radius increases. For asymmetric compositions, spotted patterns emerge as stable configurations. These findings provide new insights into the self-assembly of rod-coil copolymers under spherical confinement and underscore the utility of advanced numerical techniques for exploring complex phase behaviors.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"541 ","pages":"Article 114339"},"PeriodicalIF":3.8,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145045130","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":"Structure-preserving and thermodynamically consistent finite element discretization for visco-resistive MHD with thermoelectric effect","authors":"Evan S. Gawlik ,&nbsp;François Gay-Balmaz ,&nbsp;Bastien Manach-Pérennou","doi":"10.1016/j.jcp.2025.114336","DOIUrl":"10.1016/j.jcp.2025.114336","url":null,"abstract":"<div><div>We present a structure-preserving and thermodynamically consistent numerical scheme for classical magnetohydrodynamics, incorporating viscosity, magnetic resistivity, heat transfer, and thermoelectric effect. The governing equations are shown to be derived from a generalized Hamilton’s principle, with the resulting weak formulation being mimicked at the discrete level. The resulting numerical method conserves mass and energy, satisfies Gauss’ magnetic law and magnetic helicity balance, and adheres to the Second Law of Thermodynamics, all at the fully discrete level. It is shown to perform well on magnetic Rayleigh–Bénard convection.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"542 ","pages":"Article 114336"},"PeriodicalIF":3.8,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145048012","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 dynamic domain semi-Lagrangian method for stochastic Vlasov equations","authors":"Jianbo Cui ,&nbsp;Derui Sheng ,&nbsp;Chenhui Zhang ,&nbsp;Tau Zhou","doi":"10.1016/j.jcp.2025.114335","DOIUrl":"10.1016/j.jcp.2025.114335","url":null,"abstract":"<div><div>We propose a dynamic domain semi-Lagrangian method for stochastic Vlasov equations driven by transport noise, which arise in plasma physics and astrophysics. This method combines the volume-preserving property of stochastic characteristics with a dynamic domain adaptation strategy and a reconstruction procedure. It offers a substantial reduction in computational costs compared to the traditional semi-Lagrangian techniques for stochastic problems. Furthermore, we present the first-order convergence analysis of the proposed method, partially addressing the conjecture in [1] on the convergence order of numerical methods for stochastic Vlasov equations. Several numerical tests are provided to show good performance of the proposed method.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"541 ","pages":"Article 114335"},"PeriodicalIF":3.8,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145026556","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":"Very high-order multi-layer compact schemes with shock-fitting method (MLC-SF) for compressible flow simulations","authors":"Yung-Tien Lin,&nbsp;Xiaolin Zhong","doi":"10.1016/j.jcp.2025.114332","DOIUrl":"10.1016/j.jcp.2025.114332","url":null,"abstract":"&lt;div&gt;&lt;div&gt;High-order numerical methods are commonly employed in direct numerical simulation (DNS) to achieve the required accuracy with fewer degrees of freedom, thereby improving computational efficiency. To further improve global spatial accuracy, Bai and Zhong proposed the multi-layer compact (MLC) schemes (JCP, 2019) to introduce spatial derivatives as new degrees of freedom and create a more compact stencil for the same spatial accuracy. Stability analysis showed MLC can achieve seventh-order global accuracy with closed boundaries, which surpasses most of the sixth-order conventional upwind finite difference schemes. Despite this high-order convergence rate, MLC faces challenges in supersonic flow simulations, primarily due to the Gibbs phenomenon across shock waves. The numerical oscillation can cause divergence in high-order numerical schemes if no additional treatment, such as shock-capturing or shock-fitting methods, is applied. Therefore, further studies are needed to enhance MLC’s applicability to realistic high-speed flow applications, particularly in the context of shock treatments and boundary condition implementation. This paper develops a novel MLC method to improve its applicability for supersonic flow simulations. The proposed method integrates MLC with the shock-fitting method (MLC-SF), treating the shock wave as a computational boundary that separates upstream and downstream solutions. The shock-fitting method mitigates spurious numerical oscillations across the discontinuous interface, preserving the high-order accuracy of MLC-SF. Additionally, this paper introduces a physically consistent boundary condition for the MLC-SF spatial derivative layers behind the shock. This boundary condition uses the inversion of the flux Jacobian matrix to estimate the correct spatial derivatives, ensuring consistency between MLC-SF value and derivative layers at the inflow boundary. In order to systematically benchmark the proposed method, MLC-SF is applied to five simulation cases involving linear advection, Euler, and Navier-Stokes equations on one- and two-dimensional domains. The studied cases aim to compare the results of shock-fitting and shock-capturing methods, evaluate the performance of MLC-SF within the arbitrary Lagrangian-Eulerian (ALE) framework for moving grid applications, and test the MLC-SF derivative layers on fluid mechanics problems involving non-Cartesian grids. In both one-dimensional and two-dimensional shock wave interaction cases, MLC-SF with the proposed physically consistent inflow condition achieves seventh-order spatial accuracy, which outperforms the other four tested methods. Notably, in the one-dimensional shock-interaction results, the fifth-order WENO methods exhibit only first-order accuracy behind the shock wave, highlighting the necessity of adopting the shock-fitting approach to maintain the high spatial accuracy property in MLC-SF. In terms of computational efficiency. MLC-SF can save at least 30 % of t","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"541 ","pages":"Article 114332"},"PeriodicalIF":3.8,"publicationDate":"2025-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145010101","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":"Bound-preserving and entropy stable enriched Galerkin methods for nonlinear hyperbolic equations","authors":"Dmitri Kuzmin ,&nbsp;Sanghyun Lee ,&nbsp;Yi-Yung Yang","doi":"10.1016/j.jcp.2025.114323","DOIUrl":"10.1016/j.jcp.2025.114323","url":null,"abstract":"<div><div>In this paper, we develop monolithic limiting techniques for enforcing nonlinear stability constraints in enriched Galerkin (EG) discretizations of nonlinear scalar hyperbolic equations. To achieve local mass conservation and gain control over the cell averages, the space of continuous (multi-)linear finite element approximations is enriched with piecewise-constant functions. The resulting spatial semi-discretization has the structure of a variational multiscale method. For linear advection equations, it is inherently stable but generally not bound preserving. To satisfy discrete maximum principles and ensure entropy stability in the nonlinear case, we use limiters adapted to the structure of our locally conservative EG method. The cell averages are constrained using a flux limiter, while the nodal values of the continuous component are constrained using a clip-and-scale limiting strategy for antidiffusive element contributions. The design and analysis of our new algorithms build on recent advances in the fields of convex limiting and algebraic entropy fixes for finite element methods. In addition to proving the claimed properties of the proposed approach, we conduct numerical studies for two-dimensional nonlinear hyperbolic problems. The numerical results demonstrate the ability of our limiters to prevent violations of the imposed constraints, while preserving the optimal order of accuracy in experiments with smooth solutions.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"541 ","pages":"Article 114323"},"PeriodicalIF":3.8,"publicationDate":"2025-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144997086","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":"Deep learning for high-dimensional PDEs with fat-tailed Lévy measure","authors":"Kamran Arif ,&nbsp;Guojiang Xi ,&nbsp;Heng Wang ,&nbsp;Weihua Deng","doi":"10.1016/j.jcp.2025.114327","DOIUrl":"10.1016/j.jcp.2025.114327","url":null,"abstract":"<div><div>The partial differential equations (PDEs) for jump process with Lévy measure have wide applications. When the measure has fat tails, it will bring big challenges for both computational cost and accuracy. In this work, we develop a deep learning method for high-dimensional PDEs related to fat-tailed Lévy measure, which can be naturally extended to the general case. Building on the theory of backward stochastic differential equations for Lévy processes, our deep learning method avoids the need for neural network differentiation and introduces a novel technique to address the singularity of fat-tailed Lévy measures. The developed method is used to solve four kinds of high-dimensional PDEs: the diffusion equation with fractional Laplacian; the advective diffusion equation with fractional Laplacian; the advective diffusion reaction equation with fractional Laplacian; and the nonlinear reaction diffusion equation with fractional Laplacian. The parameter <span><math><mi>β</mi></math></span> in fractional Laplacian is an indicator of the strength of the singularity of Lévy measure. Specifically, for <span><math><mrow><mi>β</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></math></span>, the model describes super-ballistic diffusion; while for <span><math><mrow><mi>β</mi><mo>∈</mo><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow></math></span>, it characterizes super-diffusion. In addition, we experimentally verify that the developed algorithm can be easily extended to solve fractional PDEs with finite general Lévy measures. Our method achieves a relative error of <span><math><mrow><mi>O</mi><mo>(</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup><mo>)</mo></mrow></math></span> for low-dimensional problems and <span><math><mrow><mi>O</mi><mo>(</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>2</mn></mrow></msup><mo>)</mo></mrow></math></span> for high-dimensional ones. We also investigate three factors that influence the algorithm’s performance: the number of hidden layers; the number of Monte Carlo samples; and the choice of activation functions. Furthermore, we test the efficiency of the algorithm in solving problems in 3D, 10D, 20D, 50D, and 100D. Our numerical results demonstrate that the algorithm achieves excellent performance with deeper hidden layers, a larger number of Monte Carlo samples, and the Softsign activation function.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"541 ","pages":"Article 114327"},"PeriodicalIF":3.8,"publicationDate":"2025-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144997088","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 extreme learning machine for interface and free boundary problems","authors":"Anci Lin ,&nbsp;Zhiwen Zhang ,&nbsp;Weidong Zhao ,&nbsp;Wenju Zhao","doi":"10.1016/j.jcp.2025.114329","DOIUrl":"10.1016/j.jcp.2025.114329","url":null,"abstract":"<div><div>We present a machine-learning framework for interface and free-boundary problems, focusing on physics-informed neural networks (PINNs). Two major challenges are addressed: (i) interface-induced discontinuities and (ii) moving boundaries inherent to free-boundary problems. To meet these challenges, we introduce the discontinuous extreme learning machine (DELM), a mesh-free method that leverages an “artificial discontinuity” mechanism, and the local extreme learning machine (locELM) architecture. Our first innovation augments the input of a single-layer neural network with two additional variables: a piecewise-constant indicator that enforces discontinuities in the solution itself, and the absolute value of a signed-distance level-set function that produces the correct gradient jump across the interface. This design captures discontinuities without splitting the network into multiple pieces or inflating the parameter count. For problems with evolving interfaces (e.g., the Stefan problem), we devise a decoupled discrete-DELM strategy that integrates seamlessly with the classical front-tracking and time-discretization technique. At each time step, the front-tracking module updates the interface geometry, and DELM subsequently solves the governing PDE in the updated domain. To further reduce complexity while maintaining accuracy, the computational domain is partitioned, and an independent single-layer ELM is trained within each subdomain. Various numerical experiments validate the proposed framework, demonstrating high accuracy and fast computational speed across a wide range of benchmark problems.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"541 ","pages":"Article 114329"},"PeriodicalIF":3.8,"publicationDate":"2025-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144997085","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":"Solving cluster moment relaxation with hierarchical matrix","authors":"Yi Wang ,&nbsp;Rizheng Huang ,&nbsp;Yuehaw Khoo","doi":"10.1016/j.jcp.2025.114331","DOIUrl":"10.1016/j.jcp.2025.114331","url":null,"abstract":"<div><div>Convex relaxation methods are powerful tools for studying the lowest energy of many-body problems. By relaxing the representability conditions for marginals to a set of local constraints, along with a global semidefinite constraint, a polynomial-time solvable semidefinite program (SDP) that provides a lower bound for the energy can be derived. In this paper, we propose accelerating the solution of such an SDP relaxation by imposing a hierarchical structure on the positive semidefinite (PSD) primal and dual variables. Furthermore, these matrices can be updated efficiently using the algebra of the compressed representations within an augmented Lagrangian method. We achieve quadratic and even near-linear time per-iteration complexity. Through experimentation on the quantum transverse field Ising model, we showcase the capability of our approach to provide a sufficiently accurate lower bound for the exact ground-state energy.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"541 ","pages":"Article 114331"},"PeriodicalIF":3.8,"publicationDate":"2025-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144997089","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}