Journal of Computational Physics最新文献

{"title":"Local randomized neural networks with finite difference methods for interface problems","authors":"Yunlong Li ,&nbsp;Fei Wang","doi":"10.1016/j.jcp.2025.113847","DOIUrl":"10.1016/j.jcp.2025.113847","url":null,"abstract":"<div><div>Accurate modeling of complex physical problems, such as fluid-structure interaction, requires multiphysics coupling across the interface, which often has intricate geometry and dynamic boundaries. Conventional numerical methods face challenges in handling interface conditions. Deep neural networks offer a mesh-free and flexible alternative, but they suffer from drawbacks such as time-consuming optimization and local optima. In this paper, we propose a mesh-free approach based on Randomized Neural Networks (RaNNs) and finite difference methods (FDM), which avoid optimization solvers during training, making them more efficient than traditional deep neural networks. Our approach, called Local Randomized Neural Networks with finite difference methods (LRaNN-FDM), uses different RaNNs to approximate solutions in different subdomains. We discretize the interface problem into a linear system at randomly sampled points across the domain, boundary, and interface using a finite difference scheme, and then solve it by a least-square method. Unlike automatic differentiation for partial derivative calculations, the finite difference approach offers significantly faster computation. For time-dependent interface problems, we use a space-time approach based on LRaNNs. We show the effectiveness and robustness of the LRaNN-FDM through numerical examples of elliptic and parabolic interface problems. We also demonstrate that our approach can handle high-dimension interface problems. Compared to conventional numerical methods, our approach achieves higher accuracy with fewer degrees of freedom, eliminates the need for complex interface meshing and fitting, and significantly reduces training time, outperforming deep neural networks.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"529 ","pages":"Article 113847"},"PeriodicalIF":3.8,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143429040","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":"On the preprocessing of physics-informed neural networks: How to better utilize data in fluid mechanics","authors":"Shengfeng Xu ,&nbsp;Yuanjun Dai ,&nbsp;Chang Yan ,&nbsp;Zhenxu Sun ,&nbsp;Renfang Huang ,&nbsp;Dilong Guo ,&nbsp;Guowei Yang","doi":"10.1016/j.jcp.2025.113837","DOIUrl":"10.1016/j.jcp.2025.113837","url":null,"abstract":"<div><div>Physics-Informed Neural Networks (PINNs) serve as a flexible alternative for tackling forward and inverse problems in differential equations, displaying impressive advancements in diverse areas of applied mathematics. Despite integrating both data and underlying physics to enrich the neural network's understanding, concerns regarding the effectiveness and practicality of PINNs persist. Over the past few years, extensive efforts in the current literature have been made to enhance this evolving method, by drawing inspiration from both machine learning algorithms and numerical methods. Despite notable progressions in PINNs algorithms, the important and fundamental field of data preprocessing remain unexplored, limiting the applications of PINNs especially in solving inverse problems. Therefore in this paper, a concise yet potent data preprocessing method focusing on data normalization was proposed. By applying a linear transformation to both the data and corresponding equations concurrently, the normalized PINNs approach was evaluated on the task of reconstructing flow fields in four turbulent cases. The results illustrate that by adhering to the data preprocessing procedure, PINNs can robustly achieve higher prediction accuracy for all flow quantities under different hyperparameter setups, without incurring extra computational cost, distinctly improving the utilization of limited training data. Though mainly verified in Navier-Stokes (NS) equations, this method holds potential for application to various other equations.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"528 ","pages":"Article 113837"},"PeriodicalIF":3.8,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143427521","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 new boundary condition for the nonlinear Poisson-Boltzmann equation in electrostatic analysis of proteins","authors":"Sylvia Amihere ,&nbsp;Yiming Ren ,&nbsp;Weihua Geng ,&nbsp;Shan Zhao","doi":"10.1016/j.jcp.2025.113844","DOIUrl":"10.1016/j.jcp.2025.113844","url":null,"abstract":"<div><div>As a well-established implicit solvent model, the Poisson-Boltzmann equation (PBE) models the electrostatic interactions between a solute biomolecule and its surrounding solvent environment over an unbounded domain. One numerical challenge in solving the nonlinear PBE lies in the boundary treatment. Physically, the boundary condition of this solute solvent system is defined at infinity where the electrostatic potential decays to zero. Computationally, a finite domain has to be employed in grid-based numerical algorithms. However, the Dirichlet boundary conditions commonly used in protein simulations are known to produce unphysical solutions in some cases. This motivates the development of a few asymptotic conditions in the PBE literature, which are global boundary conditions and have to resort to iterative algorithms for calculating volume integrals from the previous step. To overcome these limitations, a modified Robin condition is proposed in this work as a local boundary condition for the nonlinear PBE, which can be implemented in any finite difference or finite element method. The derivation is based on the facts that away from the biomolecule, the asymptotic decaying pattern of the nonlinear PBE is essentially the same as that of the linearized PBE, and the monopole term will dominate other terms in the multipole expansion. Asymptotic analysis has been carried out to validate the application range and robustness of the proposed Robin condition. Moreover, a second order boundary implementation by means of a matched interface and boundary (MIB) scheme has been constructed for three-dimensional biomolecular simulations. Extensive numerical experiments have been conducted to examine the robustness, accuracy, and efficiency of the new boundary treatment for calculating electrostatic free energies of Kirkwood spheres and various protein systems.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"528 ","pages":"Article 113844"},"PeriodicalIF":3.8,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143419229","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":"High-order exponential time differencing multi-resolution alternative finite difference WENO methods for nonlinear degenerate parabolic equations","authors":"Ziyao Xu,&nbsp;Yong-Tao Zhang","doi":"10.1016/j.jcp.2025.113838","DOIUrl":"10.1016/j.jcp.2025.113838","url":null,"abstract":"<div><div>In this paper, we focus on the finite difference approximation of nonlinear degenerate parabolic equations, a special class of parabolic equations where the viscous term vanishes in certain regions. This vanishing gives rise to additional challenges in capturing sharp fronts, beyond the restrictive CFL conditions commonly encountered with explicit time discretization in parabolic equations. To resolve the sharp front, we adopt the high-order multi-resolution alternative finite difference WENO (A-WENO) methods for the spatial discretization, which is designed to effectively suppress oscillations in the presence of large gradients and achieve nonlinear stability. To alleviate the time step restriction from the nonlinear stiff diffusion terms, we employ the exponential time differencing Runge-Kutta (ETD-RK) methods, a class of efficient and accurate exponential integrators, for the time discretization. However, for highly nonlinear spatial discretizations such as high-order WENO schemes, it is a challenging problem how to efficiently form the linear stiff part in applying the exponential integrators, since direct computation of a Jacobian matrix for high-order WENO discretizations of the nonlinear diffusion terms is very complicated and expensive. Here we propose a novel and effective approach of replacing the exact Jacobian of high-order multi-resolution A-WENO scheme with that of the corresponding high-order linear scheme in the ETD-RK time marching, based on the fact that in smooth regions the nonlinear weights closely approximate the corresponding linear weights, while in non-smooth regions the stiff diffusion degenerates. The algorithm is described in detail, and numerous numerical experiments are conducted to demonstrate the effectiveness of such a treatment and the good performance of our method. The stiffness of the nonlinear parabolic partial differential equations (PDEs) is resolved well, and large time-step size computations of <span><math><mi>Δ</mi><mi>t</mi><mo>∼</mo><mi>O</mi><mo>(</mo><mi>Δ</mi><mi>x</mi><mo>)</mo></math></span> are achieved.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"529 ","pages":"Article 113838"},"PeriodicalIF":3.8,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143429044","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An asymptotic-preserving conservative semi-Lagrangian scheme for the Vlasov-Maxwell system in the quasi-neutral limit","authors":"Hongtao Liu ,&nbsp;Xiaofeng Cai ,&nbsp;Yong Cao ,&nbsp;Giovanni Lapenta","doi":"10.1016/j.jcp.2025.113840","DOIUrl":"10.1016/j.jcp.2025.113840","url":null,"abstract":"<div><div>In this paper, we present an asymptotic-preserving conservative Semi-Lagrangian (CSL) scheme for the Vlasov-Maxwell system in the quasi-neutral limit, where the Debye length is negligible compared to the macroscopic scales of interest. The proposed method relies on two key ingredients: the CSL scheme and a reformulated Maxwell equation (RME). The CSL scheme is employed for the phase space discretization of the Vlasov equation, ensuring mass conservation and removing the Courant-Friedrichs-Lewy restriction, thereby enhancing computational efficiency. To efficiently calculate the electromagnetic field in both non-neutral and quasi-neutral regimes, the RME is derived by semi-implicitly coupling the Maxwell equation and the moments of the Vlasov equation. Furthermore, we apply Gauss's law correction to the electric field derived from the RME to prevent unphysical charge separation. The synergy of the CSL and RME enables the proposed method to provide reliable solutions, even when the spatial and temporal resolution might not fully resolve the Debye length and plasma period. As a result, the proposed method offers a unified and accurate numerical simulation approach for complex electromagnetic plasma physics while maintaining efficiency in both quasi-neutral and non-quasi-neutral regimes. Several numerical experiments, ranging from 3D to 5D simulations, are presented to demonstrate the accuracy, stability, and efficiency of the proposed method.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"528 ","pages":"Article 113840"},"PeriodicalIF":3.8,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143419232","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":"Adaptive time-stepping Hermite spectral scheme for nonlinear Schrödinger equation with wave operator: Conservation of mass, energy, and momentum","authors":"Shimin Guo ,&nbsp;Zhengqiang Zhang ,&nbsp;Liquan Mei","doi":"10.1016/j.jcp.2025.113842","DOIUrl":"10.1016/j.jcp.2025.113842","url":null,"abstract":"<div><div>The aim of this paper is to establish an efficient numerical scheme for nonlinear Schrödinger equation with wave operator (NLSW) on unbounded domains to simultaneously conserve the first three kinds of invariants, namely the mass, the energy, and the momentum conservation laws. Regarding the mass and momentum conservation laws as the globally physical constraints, we elaborately combine the exponential scalar auxiliary variable (ESAV) method with Lagrange multiplier approach to build up the algorithm-friendly reformulation which links between the invariants and existing numerical methods. We employ the Crank-Nicolson and Hermite-Galerkin spectral methods for temporal discretization and spatial approximation, respectively. Additionally, we design a new adaptive time-stepping strategy based on the variation of the solution to improve the efficiency of our scheme. At each time level, we only need to solve a linear system plus a set of quadratic algebraic equations which can be efficiently solved by Newton's method. To enhance the applicability of the proposed scheme, we extend our methodology to <em>N</em>-coupled NLSW system where the mass, the energy, and the momentum are simultaneously conserved at the fully-discrete level. Numerical experiments are provided to show the convergence rates, the efficiency, and the conservation properties of the proposed scheme. In addition, the nonlinear dynamics of 2D/3D solitons are simulated to deepen the understanding of NLSW model.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"528 ","pages":"Article 113842"},"PeriodicalIF":3.8,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143419227","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":"Local time-stepping for discrete exterior calculus on spacetime mesh with refinements","authors":"Joona Räty,&nbsp;Sanna Mönkölä","doi":"10.1016/j.jcp.2025.113839","DOIUrl":"10.1016/j.jcp.2025.113839","url":null,"abstract":"<div><div>A geometrical method for solving wave equations on a spacetime mesh is studied. The construction can be used for local mesh refinement both in space and time or efficient and simple simulation of moving domains. The construction uses a pair of mesh and dual mesh that is orthogonal with respect to the Minkowski metric. Orthogonality is the key factor in defining a diagonal discrete Hodge operator, which can then be efficiently used for explicit time-stepping. The approach considered is well suited for wave problems defined on Minkowski spacetimes where geometric accuracy, topological correctness, and the preservation of physical laws are crucial for obtaining reliable and accurate results.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"529 ","pages":"Article 113839"},"PeriodicalIF":3.8,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143429043","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The KAN-MHA model: A novel physical knowledge based multi-source data-driven adaptive method for airfoil flow field prediction","authors":"Siyao Yang ,&nbsp;Kun Lin ,&nbsp;Annan Zhou","doi":"10.1016/j.jcp.2025.113846","DOIUrl":"10.1016/j.jcp.2025.113846","url":null,"abstract":"<div><div>The power generation efficiency and operational safety of wind turbines depend heavily on the aerodynamic performance of their airfoils, which is primarily controlled by the flow field. Traditional methods for predicting this flow field rely on solving the Navier-Stokes (NS) equations, which are computationally expensive and inefficient. To address these challenges, this paper proposes a novel neural network model, the KAN-MHA, which integrates a Kolmogorov-Arnold Network (KAN) with a Multi-Head Attention (MHA) mechanism, leveraging multi-source datasets that include wind tunnel experiments, XFoil results, and CFD simulations. By incorporating physical constraints, the KAN-MHA model achieves precise predictions of flow fields with a simpler architecture and reduced computational cost. Experimental results indicate that, compared to traditional multilayer perceptron (MLP) networks, the KAN-MHA model achieves a substantial reduction in testing loss, while maintaining a significantly simpler architecture with fewer neurons. Through an analysis of the attention weights in the MHA mechanism, we found that MHA effectively guides the network to focus on regions with more intricate flow variations, thereby enhancing the model's ability to capture subtle flow field features with higher accuracy. As a result, the model demonstrates excellent prediction performance for aerodynamic coefficients and effectively identifies stall behavior in airfoils at high angles of attack. This work provides a novel approach for the design and optimization of wind turbine airfoils, offering valuable insights for enhancing aerodynamic performance under complex flow conditions.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"528 ","pages":"Article 113846"},"PeriodicalIF":3.8,"publicationDate":"2025-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143419230","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Entropy conservative discretization of compressible Euler equations with an arbitrary equation of state","authors":"Alessandro Aiello ,&nbsp;Carlo De Michele ,&nbsp;Gennaro Coppola","doi":"10.1016/j.jcp.2025.113836","DOIUrl":"10.1016/j.jcp.2025.113836","url":null,"abstract":"<div><div>This study proposes a novel spatial discretization procedure for the compressible Euler equations which guarantees entropy conservation at a discrete level when an arbitrary equation of state is assumed. The proposed method, based on a locally-conservative discretization, guarantees also the spatial conservation of mass, momentum, and total energy and is kinetic-energy-preserving. In order to achieve the entropy-conservation property for an arbitrary non-ideal gas, a general strategy is adopted based on the manipulation of discrete balance equations through the imposition of global entropy conservation and the use of a summation-by-parts rule. The procedure, which is extended to an arbitrary order of accuracy, conducts to a general form of the internal-energy numerical flux which results in a nonlinear function of thermodynamic and dynamic variables and still admits the mass flux as a residual degree of freedom. The effectiveness of the novel entropy-conservative formulation is demonstrated through numerical tests making use of some of the most popular cubic equations of state.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"528 ","pages":"Article 113836"},"PeriodicalIF":3.8,"publicationDate":"2025-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143395847","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Entropy-stable model reduction of one-dimensional hyperbolic systems using rational quadratic manifolds","authors":"R.B. Klein ,&nbsp;B. Sanderse ,&nbsp;P. Costa ,&nbsp;R. Pecnik ,&nbsp;R.A.W.M. Henkes","doi":"10.1016/j.jcp.2025.113817","DOIUrl":"10.1016/j.jcp.2025.113817","url":null,"abstract":"<div><div>In this work we propose a novel method to ensure important entropy inequalities are satisfied semi-discretely when constructing reduced order models (ROMs) on nonlinear reduced manifolds. We are in particular interested in ROMs of systems of nonlinear hyperbolic conservation laws. The so-called entropy stability property endows the semi-discrete ROMs with physically admissible behaviour. The method generalizes earlier results on entropy-stable ROMs constructed on linear spaces. The ROM works by evaluating the projected system on a well-chosen approximation of the state that ensures entropy stability. To ensure accuracy of the ROM after this approximation we locally enrich the tangent space of the reduced manifold with important quantities. Using numerical experiments on some well-known equations (the inviscid Burgers equation, shallow water equations and compressible Euler equations) we show the improved structure-preserving properties of our ROM compared to standard approaches and that our approximations have minimal impact on the accuracy of the ROM. We additionally generalize the recently proposed polynomial reduced manifolds to rational polynomial manifolds and show that this leads to an increase in accuracy for our experiments.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"528 ","pages":"Article 113817"},"PeriodicalIF":3.8,"publicationDate":"2025-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143419228","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}