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 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

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

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 H(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 H(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 RT₁ 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

(d + 1)

degrees of freedom per simplex (where d 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.

本文提出了一种基于投影的混合有限元方法，用于求解具有固定空间多孔固体包裹体的不可压缩单相流的非定常Brinkman方程。在每个时间步，该方法需要解决一个预测问题和一个投影问题。使用应力-速度混合公式的预测问题解释了动量平衡，而基于速度-压力混合公式的投影问题解释了不可压缩性。空间离散符合H(div)，在每个时间步长结束时计算的速度是点向无散度的。建立了全离散格式的无条件稳定性和一阶时间精度。由于公式的H（div）符合性，该方法在Stokes和Darcy两种情况下都具有鲁棒性。在具体的代码实现中，我们使用二维和三维的Raviart-Thomas空间RT1离散计算域，采用二阶精确多点通量混合有限元格式，并采用正交规则对通量自由度进行采样。在预测问题中，这允许局部消除粘性应力，并导致每个速度分量的基于单元的对称和正定系统，每个单形具有（d+1）个自由度（d是问题的维度）。以类似的方式，我们局部消除了投影问题中的修正速度，并解决了基于单元的压力系统。数值实验验证了该方法的收敛性，并说明了其在一些具有挑战性的应用中的性能，包括自由流体和多孔介质耦合流动的单域建模以及孔隙度和渗透率值具有强不连续的非均质多孔介质。

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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 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

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

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.

本文提出了一种创新的渐近保持物理信息神经网络（ap - pinn）框架，用于求解具有增强数值稳定性的守恒律系统。提出的方法引入松弛项，将原来的守恒定律转化为松弛系统，有效地减轻了求解不连续解，特别是激波时的数值振荡。解决松弛系统的一个关键方面包括保持对系统状态的长期收敛和稳定性的严格关注，确保严格遵守AP属性。通过引入AP物理约束，所提出的AP- pin在求解复杂波现象方面表现出优于传统pin的性能。我们提供了严格的理论证明，建立了我们的网络架构的AP属性。通过在多个一维和二维情况下的综合测试，验证了该方法的有效性，展示了捕获各种波现象的卓越能力，包括冲击、稀疏波、接触不连续面及其复杂的相互作用。此外，我们还分析了不同弛豫率的λ对AP-PINN性能的影响，并进行了详细的误差量化。结果表明，ap - pinn不仅显著提高了预测性能，而且在可压缩流体动力学应用中实现了鲁棒和高效的模拟。

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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 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

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

It is well known that numerical solutions of Helmholtz boundary-value problems suffer from pollution (dispersion) errors that require much finer grids than expected for high frequencies. In this article a dispersion error analysis is presented that leads to an explicit rule-of-thumb formula to estimate the points-per-wavelength required for a p-th order accurate finite difference approximation for Helmholtz problems that accounts for pollution errors. The rule of thumb only depends on the wave-number (or frequency) of the periodic forcing, the size of the domain, and the desired relative error tolerance. Several numerical examples on simple and complex domains and with closed or open boundaries show that the rule of thumb is a useful predictor of the error. Having such a rule is important in practice to either avoid under-resolving the problem and obtaining the wrong answer, or over-resolving the problem resulting in a much more expensive computation.

众所周知，亥姆霍兹边值问题的数值解受到污染（色散）误差的影响，这需要比预期的高频更细的网格。在这篇文章中，色散误差分析导致一个明确的经验法则公式来估计每波长所需的点的p阶精确有限差分近似亥姆霍兹问题，考虑污染误差。经验法则仅取决于周期强迫的波数（或频率）、域的大小和期望的相对误差容限。在简单域和复杂域以及封闭边界和开放边界上的几个数值例子表明，经验法则是一个有用的误差预测器。拥有这样的规则在实践中非常重要，它可以避免问题解决不足而得到错误的答案，或者问题解决过度而导致更昂贵的计算。

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 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

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

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.

我们提出了一种新的全单边扩散界面浸入边界法（IBM）来模拟激波可压缩流动。插值和扩展只在浸入边界的内部进行。该策略避免了对具有不连续的外部流动变量进行插值，抑制了传统扩散接口IBM的扩散效应，从而提高了附加冲击和强激波-障碍相互作用情况下的预测精度和数值稳定性。定义了一个比例因子，以恢复函数的零矩条件，并保证插值和扩展过程中欧拉变量和拉格朗日变量相等。引入改进的拉格朗日权表达式，明确修正了强迫项，保证了插补/扩展过程的互易条件，大大减小了边界误差。此外，拉格朗日权能在不影响边界精度的情况下使用相对粗糙的拉格朗日网格。与混合晶格玻尔兹曼方法（LBM）耦合的全单侧IBM解算器在空间上具有二阶精度。通过一系列验证案例来评估该方法在可压缩流动中的性能，包括简单和复杂几何形状的超音速流动，以及涉及分离/附加激波和强激波-障碍相互作用的配置。将计算结果与拟合方法、理论模型和实验结果进行了比较，结果吻合较好。

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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 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

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

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.

本文介绍了一种新的三维枝晶凝固相场模型的数值求解方法。利用有限差分或有限元方法的传统方法经常在枝晶生长的相场建模中引入离散诱导的各向异性，特别是在低表面能各向异性强度时，需要调整相场模型参数。我们的研究表明，在不改变相场模型参数的情况下，通过采用具有足够大的局部支持域（模板）的广义有限差分法（GFDM），可以有效地减少离散引起的各向异性。我们表明，GFDM可以使用比有限差分法更大的节点间距，因此，在显式时间推进方案中，更大的时间步长，减轻了由于需要更大的模板而增加的计算成本。该算法基于局部支持域的多项式加权最小二乘逼近。虽然GFDM通常应用于分散的节点分布，但我们采用节点的标准均匀规则分布；因此，通过简单地增加模板尺寸和更新有限差分系数，当前研究的见解可以直接应用于利用有限差分方法的任何相场建模。通过模拟过冷纯熔体中枝晶的生长，改变表面能各向异性的强度，评估了新数值程序的有效性。此外，我们还测试了相场模型的非线性预处理如何提高计算效率。我们采用基于八叉树的时空自适应算法来降低相场模拟的高计算成本。

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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 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

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

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.

我们提出了一种神经熵稳定的保守通量神经网络（NESCFN），用于直接从解轨迹中学习双曲守恒定律及其相关熵函数，而不需要任何预定义的数值离散化。虽然最近的神经网络架构已经成功地将经典数值原理集成到学习模型中，但大多数依赖于控制方程的先验知识或假设固定的离散化。我们的方法通过将熵稳定设计原则嵌入学习过程本身来消除这种依赖性，从而在完全数据驱动的环境中发现物理上一致的动态。NESCFN通过共同学习通量函数和相应的熵，促进守恒和熵耗散，这对于双曲守恒律系统的长期稳定性和保真性至关重要。数值结果表明，即使没有oracle访问训练数据中的未来解决方案配置文件，该方法也能在较长的时间范围内实现稳定性和守恒性，并准确捕获冲击传播速度。

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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 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

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

In this work, we present the a posteriori error analysis of Stabilization-Free Virtual Element Methods for the 2D Poisson equation. The absence of a stabilizing bilinear form in the scheme allows to prove the equivalence between a suitably defined error measure and standard residual error estimators, which is not obtained in general for stabilized virtual elements. Several numerical experiments are carried out, confirming the expected behaviour of the estimator in the presence of different mesh types, and robustness with respect to jumps of the diffusion term.

在这项工作中，我们提出了二维泊松方程的无稳定虚元方法的后检误差分析。该方案中不存在稳定双线性形式，从而证明了适当定义的误差测度与标准残差估计之间的等价性，而这在稳定虚元中一般是得不到的。进行了几个数值实验，证实了估计器在不同网格类型存在时的预期行为，以及相对于扩散项跳跃的鲁棒性。

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 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

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

Excessive computational times represent a major challenge in the solution of corrosion models, limiting their practical applicability, e.g., as a support to predictive maintenance. In this paper, we propose an efficient strategy for solving a phase-field model for metal corrosion. Based on the Kronecker structure of the diffusion matrix in classical finite difference approximations on rectangular domains, time-stepping IMEX methods are efficiently solved in matrix form. However, when the domain is non-rectangular, the lack of the Kronecker structure prevents the direct use of the matrix-based approach. To address this issue, we reformulate the problem on an extended rectangular domain and introduce suitable iterative IMEX methods. The convergence of the iterations and the propagation of the numerical errors are analyzed. Test cases on two and three dimensional domains show that the proposed approach achieves accuracy comparable to existing methods, while significantly reducing the computational time, to the point of allowing actual predictions on standard workstations.

过多的计算时间是腐蚀模型解决方案的主要挑战，限制了它们的实际适用性，例如，作为预测性维护的支持。本文提出了一种求解金属腐蚀相场模型的有效策略。基于经典矩形域有限差分近似中扩散矩阵的Kronecker结构，采用矩阵形式有效地求解了时间步进IMEX方法。然而，当区域是非矩形时，缺乏Kronecker结构阻碍了直接使用基于矩阵的方法。为了解决这个问题，我们在一个扩展的矩形域上重新表述了这个问题，并引入了合适的迭代IMEX方法。分析了迭代的收敛性和数值误差的传播。二维和三维域上的测试用例表明，所提出的方法达到了与现有方法相当的准确性，同时显著减少了计算时间，达到允许在标准工作站上进行实际预测的程度。

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 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

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

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.

物理信息神经网络（PINN）是一种很有前途的科学计算方法。然而，预测可压缩流动对pinn来说是一个挑战，因为它们很难准确地捕捉流动演变过程中出现的不连续性。在这项工作中，开发了一种新的物理信息深度学习框架，称为稀疏有限体积信息U-net (SFVnet)，用于在病态条件下使用稀疏数据预测可压缩流场。主要贡献如下：(1)设计了一种新的物理损失函数，将有限体积离散残差和每个单元内多个点的预测融合在一起，与原始PINN相比，有效地提高了不连续性捕获能力；(2)该模型利用内部稀疏样本在没有初始/边界条件输入的情况下重建了整个流场，这对传统的FVM来说是一个特别的挑战；(3)训练后的模型可以外推超出训练时间窗的基本流态，这是原始pin无法做到的。此外，该框架的特点是仅通过采样该区域内的数据来重建感兴趣区域流场。一维Sod管、一维Lax管、二维Riemann问题和双马赫反射问题等一系列一维（1D）和二维（2D）基准案例验证了该框架的预测准确性和鲁棒性。值得注意的是，这是第一个基于物理的深度学习框架成功应用于马赫数为10的双马赫反射模拟。这些结果也表明了该框架在流场重建、数据压缩和恢复方面的潜力。

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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 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

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

We propose and study a Particle-In-Cell (PIC) method utilizing Crank-Nicolson time discretization for the Vlasov-Poisson system with a strong, inhomogeneous external magnetic field with fixed direction. Our focus is on particle dynamics in the plane orthogonal to the magnetic field. In this regime, traditional explicit schemes are constrained by stability conditions linked to the small Larmor radius and plasma frequency [1]. To avoid this limitation, our approach is based on numerical schemes [2, 3, 4], providing a consistent PIC discretization of the guiding-center system taking into account variations of the magnetic field. We carry out some theoretical proofs and perform several numerical experiments to validate the method demonstrating its robustness and accuracy.

针对具有固定方向的强非均匀外磁场的Vlasov-Poisson系统，提出并研究了一种基于Crank-Nicolson时间离散的细胞内粒子（PIC）方法。我们的重点是在与磁场正交的平面上的粒子动力学。在这种情况下，传统的显式方案受到与小拉莫尔半径和等离子体频率[1]相关的稳定性条件的限制。为了避免这一限制，我们的方法基于数值格式[2,3,4]，在考虑磁场变化的情况下，为导向中心系统提供一致的PIC离散化。通过理论证明和数值实验验证了该方法的鲁棒性和准确性。

引用次数: 0