Journal of Computational Physics最新文献_第4页

Numerical solution of the unsteady Brinkman equations in the framework of H(div)-conforming finite element methods H（div）型有限元框架下非定常Brinkman方程的数值解

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2026-05-15 Epub Date: 2026-01-27 DOI: 10.1016/j.jcp.2026.114709

Costanza Aricò , Rainer Helmig , Ivan Yotov

{"title":"Numerical solution of the unsteady Brinkman equations in the framework of H(div)-conforming finite element methods","authors":"Costanza Aricò , Rainer Helmig , Ivan Yotov","doi":"10.1016/j.jcp.2026.114709","DOIUrl":"10.1016/j.jcp.2026.114709","url":null,"abstract":"<div><div>We present projection-based mixed finite element methods for the solution of the unsteady Brinkman equations for incompressible single-phase flow with fixed in space porous solid inclusions. At each time step the method requires the solution of a predictor and a projection problem. The predictor problem, which uses a stress-velocity mixed formulation, accounts for the momentum balance, while the projection problem, which is based on a velocity-pressure mixed formulation, accounts for the incompressibility. The spatial discretization is <em>H</em>(div)-conforming and the velocity computed at the end of each time step is pointwise divergence-free. Unconditional stability of the fully-discrete scheme and first order in time accuracy are established. Due to the <em>H</em>(div)-conformity of the formulation, the methods are robust in both the Stokes and the Darcy regimes. In the specific code implementation, we discretize the computational domain using the Raviart–Thomas space <em>RT</em><sub>1</sub> in two and three dimensions, applying a second-order accurate multipoint flux mixed finite element scheme with a quadrature rule that samples the flux degrees of freedom. In the predictor problem this allows for a local elimination of the viscous stress and results in element-based symmetric and positive definite systems for each velocity component with <span><math><mrow><mo>(</mo><mi>d</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></math></span> degrees of freedom per simplex (where <em>d</em> is the dimension of the problem). In a similar way, we locally eliminate the corrected velocity in the projection problem and solve an element-based system for the pressure. Numerical experiments are presented to verify the convergence of the proposed scheme and illustrate its performance for several challenging applications, including one-domain modeling of coupled free fluid and porous media flows and heterogeneous porous media with strong discontinuity of the porosity and permeability values.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"553 ","pages":"Article 114709"},"PeriodicalIF":3.8,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146186549","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}

引用次数: 0

Asymptotic-preserving PINNs for relaxation systems of conservation laws: Applications to the Euler equations 守恒律松弛系统的渐近保持pinn：在欧拉方程中的应用

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2026-05-15 Epub Date: 2026-01-28 DOI: 10.1016/j.jcp.2026.114712

Ming Kang, Xin Lei, Junfang Zhao

{"title":"Asymptotic-preserving PINNs for relaxation systems of conservation laws: Applications to the Euler equations","authors":"Ming Kang, Xin Lei, Junfang Zhao","doi":"10.1016/j.jcp.2026.114712","DOIUrl":"10.1016/j.jcp.2026.114712","url":null,"abstract":"<div><div>This paper presents an innovative Asymptotic-Preserving Physics-Informed Neural Networks (AP-PINNs) framework for solving conservation law systems with enhanced numerical stability. The proposed methodology introduces relaxation terms to transform the original conservation laws into relaxation systems, effectively mitigating numerical oscillations when solving discontinuous solutions, particularly shock waves. A key aspect of solving relaxation systems involves maintaining rigorous attention to the long-term convergence and stability of the system state, ensuring strict adherence to the AP property. Through the incorporation of AP physics constraints, the proposed AP-PINNs demonstrate superior performance over traditional PINNs in solving complex wave phenomena. We provide rigorous theoretical proofs establishing the AP property of our network architecture. The methodology’s effectiveness is validated through comprehensive testing across multiple one- and two-dimensional cases, demonstrating exceptional capability in capturing various wave phenomena including shocks, rarefaction waves, contact discontinuities, and their complex interactions. Furthermore, we also analyze the impact of varying relaxation rates ϵ on AP-PINN performance, accompanied by detailed error quantification. The results indicate that AP-PINNs not only significantly enhance predictive performance but also enable robust and efficient simulations in compressible fluid dynamics applications.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"553 ","pages":"Article 114712"},"PeriodicalIF":3.8,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146186546","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}

引用次数: 0

A rule of thumb for choosing points-per-wavelength for finite difference approximations of Helmholtz problems 亥姆霍兹问题有限差分近似中选择每波长点的经验法则

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2026-05-15 Epub Date: 2026-01-23 DOI: 10.1016/j.jcp.2026.114703

Daniel Appelö , Jeffrey W. Banks , William D. Henshaw , Donald W. Schwendeman

引用次数: 0

An explicit fully one-sided diffuse-interface immersed boundary method for compressible flows 可压缩流动的显式全单边扩散界面浸入边界法

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2026-05-15 Epub Date: 2026-01-29 DOI: 10.1016/j.jcp.2026.114721

Qian Mao, Jian Eduardo Cardenas Cabezas, Song Zhao, Pierre Boivin, Julien Favier

{"title":"An explicit fully one-sided diffuse-interface immersed boundary method for compressible flows","authors":"Qian Mao, Jian Eduardo Cardenas Cabezas, Song Zhao, Pierre Boivin, Julien Favier","doi":"10.1016/j.jcp.2026.114721","DOIUrl":"10.1016/j.jcp.2026.114721","url":null,"abstract":"<div><div>We present a novel fully one-sided diffuse-interface immersed boundary method (IBM) for simulating compressible flows involving shock waves. Interpolation and spreading are only performed on the interior of the immersed boundary. This strategy avoids interpolating external flow variables with discontinuities, and suppresses the diffusion effect of the conventional diffuse-interface IBM, thereby improving predictive accuracy and numerical stability in cases involving attached shocks and strong shock-obstacle interactions. A scaling factor is defined to restore the zero-moment condition of the delta function and ensure equality between the Eulerian and Lagrangian variables during interpolation and spreading. An improved expression of the Lagrangian weight is introduced to explicitly correct the forcing terms and ensure the reciprocity condition of the interpolation/spreading process, which greatly reduces boundary errors. Moreover, the Lagrangian weight enables the use of a relatively coarse Lagrangian mesh without compromising boundary accuracy. The fully one-sided IBM coupled with a hybrid lattice Boltzmann method (LBM) solver is second-order accurate in space. A series of validation cases are conducted to assess the performance of the proposed method in compressible flows, including supersonic flows over both simple and complex geometries, as well as configurations involving detached/attached shocks and strong shock-obstacle interactions. The results are compared against body-fitted methods, theoretical models, and experiments, demonstrating good agreement.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"553 ","pages":"Article 114721"},"PeriodicalIF":3.8,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146186542","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}

引用次数: 0

Improved finite difference method for phase-field modelling of dendritic solidification 枝晶凝固相场模拟的改进有限差分法

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2026-05-15 Epub Date: 2026-01-30 DOI: 10.1016/j.jcp.2026.114716

Tadej Dobravec , Boštjan Mavrič , Božidar Šarler

{"title":"Improved finite difference method for phase-field modelling of dendritic solidification","authors":"Tadej Dobravec , Boštjan Mavrič , Božidar Šarler","doi":"10.1016/j.jcp.2026.114716","DOIUrl":"10.1016/j.jcp.2026.114716","url":null,"abstract":"<div><div>This paper introduces a novel numerical approach for solving phase-field models of dendritic solidification in 3-D. Traditional approaches utilising finite difference or finite element methods often introduce discretisation-induced anisotropy in the phase-field modelling of dendrite growth, particularly noticeable at low surface energy anisotropy strengths, necessitating adjustments to phase-field model parameters. Our study demonstrates an effective reduction of discretisation-induced anisotropy without altering phase-field model parameters, achieved by employing the generalised finite difference method (GFDM) with sufficiently large local support domains (stencils). We show that the GFDM can employ larger node spacings than the finite difference method and, therefore, larger time steps in the explicit time marching schemes, mitigating the increased computational cost due to the requirement for larger stencils. The GFDM is based on the polynomial weighted least squares approximation in the local support domains. Although the GFDM is usually applied to scattered node distributions, we apply the standard uniform regular distribution of nodes; hence, the insights of the current study can be straightforwardly applied to any phase-field modelling utilising the finite difference method by simply increasing the stencil size and updating the finite difference coefficients. The efficacy of the novel numerical procedure is assessed through simulations of dendrite growth in a supercooled pure melt, varying the strength of surface energy anisotropy. Additionally, we test how the nonlinear preconditioning of the phase-field model enhances computational efficiency. We mitigate the high computational cost of phase-field simulations by employing an octree-based space-time adaptive algorithm.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"553 ","pages":"Article 114716"},"PeriodicalIF":3.8,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146186469","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}

引用次数: 0

Neural entropy-stable conservative flux form neural networks for learning hyperbolic conservation laws 神经熵稳定的保守通量形成学习双曲守恒定律的神经网络

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2026-05-15 Epub Date: 2026-01-30 DOI: 10.1016/j.jcp.2026.114719

Lizuo Liu , Lu Zhang , Anne Gelb

{"title":"Neural entropy-stable conservative flux form neural networks for learning hyperbolic conservation laws","authors":"Lizuo Liu , Lu Zhang , Anne Gelb","doi":"10.1016/j.jcp.2026.114719","DOIUrl":"10.1016/j.jcp.2026.114719","url":null,"abstract":"<div><div>We propose a neural entropy-stable conservative flux form neural network (NESCFN) for learning hyperbolic conservation laws and their associated entropy functions directly from solution trajectories, without requiring any predefined numerical discretization. While recent neural network architectures have successfully integrated classical numerical principles into learned models, most rely on prior knowledge of the governing equations or assume a fixed discretization. Our approach removes this dependency by embedding entropy-stable design principles into the learning process itself, enabling the discovery of physically consistent dynamics in a fully data-driven setting. By jointly learning both the flux function and a corresponding entropy, NESCFN promotes conservation and entropy dissipation, which is critical for long-term stability and fidelity in the system of hyperbolic conservation laws. Numerical results demonstrate that the method achieves stability and conservation over extended time horizons and accurately captures shock propagation speeds, even without oracle access to future-time solution profiles in the training data.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"553 ","pages":"Article 114719"},"PeriodicalIF":3.8,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146186472","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}

引用次数: 0

A residual a posteriori error estimate for the stabilization-free virtual element method 无稳定虚元法的残差后验误差估计

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2026-05-15 Epub Date: 2026-01-29 DOI: 10.1016/j.jcp.2026.114704

Stefano Berrone, Andrea Borio, Davide Fassino, Francesca Marcon

引用次数: 0

Fast solution of a phase-field model of pitting corrosion 点蚀相场模型的快速求解

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2026-05-15 Epub Date: 2026-01-29 DOI: 10.1016/j.jcp.2026.114717

Gianluca Frasca-Caccia, Dajana Conte, Beatrice Paternoster

引用次数: 0

SFVnet: Finite-volume informed U-net for compressible flow prediction with sparse data under ill-conditions SFVnet：基于有限体积信息的U-net，用于病态条件下稀疏数据的可压缩流预测

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2026-05-01 Epub Date: 2026-01-16 DOI: 10.1016/j.jcp.2026.114696

Tong Zhu , Bingqian Si , Lin Fu , Yanglong Lu

{"title":"SFVnet: Finite-volume informed U-net for compressible flow prediction with sparse data under ill-conditions","authors":"Tong Zhu , Bingqian Si , Lin Fu , Yanglong Lu","doi":"10.1016/j.jcp.2026.114696","DOIUrl":"10.1016/j.jcp.2026.114696","url":null,"abstract":"<div><div>Physics-informed neural network (PINN) is a promising methodology in scientific computing. However, predicting compressible flows poses a challenge for PINNs, since they struggle to accurately capture discontinuities arising in flow evolutions. In this work, a novel physics-informed deep learning framework, called sparse finite-volume informed U-net (SFVnet), is developed to predict compressible flow fields with sparse data under ill-conditions. The major contributions are as follows: (1) a new physical loss function is designed by incorporating finite volume discretized residuals and fusing predictions from multiple points within each cell, effectively improving the discontinuity-capturing ability compared to original PINN; (2) the model leverages interior sparse samples to reconstruct the full flow field without the input of initial/boundary conditions, which is particularly challenging for traditional FVM; (3) the trained model can extrapolate basic flow patterns beyond the training time window, which original PINNs fail to achieve. Furthermore, the proposed framework is distinguished by reconstructing region-of-interest flow fields by sampling data only within this region. A series of one-dimensional (1D) and two-dimensional (2D) benchmark cases, including the 1D Sod’s tube, 1D Lax’s tube, 2D Riemann problems, and double Mach reflection problem, demonstrate the prediction accuracy and robustness of the framework. Notably, this is the first physics-informed deep learning framework successfully applied to the double Mach reflection simulation with Mach number of 10. These results also indicate the potential of present framework for flow field reconstruction, data compression, and restoration.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"552 ","pages":"Article 114696"},"PeriodicalIF":3.8,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146001718","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}

引用次数: 0

A modified Crank-Nicolson scheme for the Vlasov-Poisson system with a strong external magnetic field 强外磁场Vlasov-Poisson系统的改进Crank-Nicolson格式

IF 3.8 2区物理与天体物理

Journal of Computational Physics Pub Date : 2026-05-01 Epub Date: 2026-01-16 DOI: 10.1016/j.jcp.2026.114693

Francis Filbet , L. Miguel Rodrigues , Kim Han Trinh

引用次数: 0