Journal of Computational Physics最新文献

英文中文

Assessment of an explicit wall function implementation for the high-order discontinuous Galerkin solution of the RANS and k−ω turbulence model equations RANS和k−ω湍流模型方程的高阶不连续Galerkin解的显式壁函数实现的评估

IF 3.8 2区物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Physics

Pub Date : 2026-04-01 Epub Date: 2025-12-31 DOI: 10.1016/j.jcp.2025.114637

Antonio Ghidoni , Edoardo Mantecca , Gianmaria Noventa , David Pasquale

The aim of this paper is to describe, validate and assess an explicit wall function implementation for the high-order spatial discretization of the Reynolds-Averaged Navier-Stokes and

k - ω

turbulence model equations. Wall functions are used to increase the computational efficiency of the solvers for numerical simulations, reducing the need for high quality computational meshes with fine near-wall spatial resolution. An explicit power-law to model the velocity profile of the flow in the boundary layer allows the proposed formulation to avoid iterative computations and ensures enhanced computational efficiency and robustness. These are demonstrated on different test cases with turbulent flows and adiabatic wall modelled boundaries. The accuracy of the numerical solutions is preserved up to a non dimensional height of the first element adjacent to the wall of 320 with a drastic computing time reduction. The high-order spatial discretization and the proposed formulation of wall function pave the way for numerical simulation of complex industrial applications with very coarse near-wall spatial resolution.

本文的目的是描述，验证和评估一个显式壁函数实现的高阶空间离散的雷诺平均Navier-Stokes和k−ω湍流模型方程。利用壁面函数提高了数值模拟求解器的计算效率，减少了对具有良好近壁面空间分辨率的高质量计算网格的需求。一个明确的幂律来模拟边界层中流动的速度分布，使所提出的公式避免了迭代计算，并确保了提高的计算效率和鲁棒性。在紊流和绝热壁模拟边界的不同测试用例上进行了验证。数值解的精度一直保持到与墙相邻的第一个元素的无因次高度320，计算时间大大减少。高阶空间离散化和提出的壁面函数公式为具有非常粗的近壁面空间分辨率的复杂工业应用的数值模拟铺平了道路。

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引用次数: 0

Angular-momentum enhanced non-hourglass formulation for SPH solid dynamics SPH固体动力学的角动量增强非沙漏公式

IF 3.8 2区物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Physics

Pub Date : 2026-04-01 Epub Date: 2025-12-31 DOI: 10.1016/j.jcp.2025.114646

Shuaihao Zhang , Jidong Zhao , Honghu Zhu , Xiangyu Hu

Updated Lagrangian smoothed particle hydrodynamics (SPH) for solid dynamics is often plagued by numerical instabilities, particularly hourglass modes that produce unphysical zigzag patterns. While recent essentially non-hourglass (SPH-ENOG) and generalized non-hourglass (SPH-GNOG) formulations have improved stability, they suffer from poor angular momentum conservation, limiting their accuracy in rotational problems. To overcome this, this paper presents two angular-momentum enhanced non-hourglass formulations. First, we enhance the SPH-ENOG method with rotation matrices derived from Rodrigues’ formula, creating SPH-ENOG-A for elastic materials, which explicitly accounts for rigid rotations during time integration, thereby significantly enhancing angular momentum conservation. To strictly enforce linear momentum conservation, the average of the rotation matrices is computed and applied to each particle. We then extend this approach to reformulate the corrective term in SPH-GNOG, yielding SPH-GNOG-A—a unified method for both elastic and plastic materials that not only improves angular momentum conservation but also eliminates prior dependencies on material-specific coefficients. Validated against elastic (oscillating plates, spinning solids) and plastic (Taylor bars, high-velocity impacts) benchmarks, our methods retain the hourglass-free stability, convergence, and accuracy of their predecessors while achieving a significant leap in angular momentum conservation.

用于固体动力学的更新拉格朗日光滑粒子流体动力学（SPH）经常受到数值不稳定性的困扰，特别是产生非物理之字形的沙漏模式。虽然最近的基本非沙漏（SPH-ENOG）和广义非沙漏（SPH-GNOG）配方提高了稳定性，但它们的角动量守恒性差，限制了它们在旋转问题中的精度。为了克服这个问题，本文提出了两种角动量增强的非沙漏公式。首先，我们利用Rodrigues公式导出的旋转矩阵对SPH-ENOG方法进行了改进，创建了弹性材料的SPH-ENOG- a，该方法在时间积分过程中明确考虑了刚性旋转，从而显著提高了角动量守恒。为了严格执行线性动量守恒，计算旋转矩阵的平均值并将其应用于每个粒子。然后，我们将该方法扩展到SPH-GNOG中重新制定校正项，从而得到SPH-GNOG- a -一种适用于弹性和塑性材料的统一方法，该方法不仅改善了角动量守恒，而且消除了对材料特定系数的先前依赖。经过弹性（振荡板，旋转固体）和塑料（泰勒杆，高速撞击）基准的验证，我们的方法保留了其前辈的无沙漏稳定性，收敛性和准确性，同时实现了角动量守恒的重大飞跃。

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引用次数: 0

Genuinely multi-dimensional stationarity preserving Finite Volume formulation for nonlinear hyperbolic PDEs 非线性双曲偏微分方程的真正多维保持平稳的有限体积公式

IF 3.8 2区物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Physics

Pub Date : 2026-04-01 Epub Date: 2026-01-06 DOI: 10.1016/j.jcp.2025.114633

Wasilij Barsukow , Mirco Ciallella , Mario Ricchiuto , Davide Torlo

Classical Finite Volume methods for multi-dimensional problems include stabilization (e.g. via a Riemann solver), that is derived by considering several one-dimensional problems in different directions. Such methods therefore ignore a possibly existing balance of contributions coming from different directions, such as the one characterizing multi-dimensional stationary states. Instead of being preserved, they are usually diffused away by such methods. Stationarity preserving methods use a better suited stabilization term that vanishes at the stationary state, allowing the method to preserve it. This work presents a general approach to stationarity preserving Finite Volume methods for nonlinear conservation/balance laws. It is based on a multi-dimensional stationarity preserving quadrature strategy that allows to naturally introduce genuinely multi-dimensional numerical fluxes. The new methods are shown to significantly outperform existing ones even if the latter are of higher order of accuracy and even on non-stationary solutions.

多维问题的经典有限体积方法包括稳定化（例如通过黎曼解算器），它是通过考虑几个一维问题在不同方向上得到的。因此，这种方法忽略了可能存在的来自不同方向的贡献平衡，例如表征多维平稳状态的平衡。它们通常不是保存下来，而是通过这种方法扩散出去。平稳性保持方法使用更合适的稳定项，该稳定项在平稳状态下消失，使方法能够保持它。本文提出了一种非线性守恒/平衡律的保平稳有限体积法的一般方法。它基于一个多维平稳性保持正交策略，允许自然地引入真正的多维数值通量。新方法被证明明显优于现有的方法，即使后者具有更高的精度阶，甚至在非平稳解上。

引用次数: 0

Linear and nonlinear boundary conditions: What’s the difference? 线性和非线性边界条件：有什么区别？

IF 3.8 2区物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Physics

Pub Date : 2026-04-01 Epub Date: 2025-12-31 DOI: 10.1016/j.jcp.2025.114649

Jan Nordström

In previous work, we derived new energy and entropy stable open boundary conditions and implementation techniques for linear and nonlinear initial boundary value problems. These boundary procedures result in estimates bounded by external data only. Interestingly, these new boundary conditions generalize the well-known classical characteristic boundary conditions for linear problems to the nonlinear setting. We discuss the similarities and differences between these two boundary procedures and point out the advantages with the new procedures. In particular we show that the new boundary conditions bound solutions to both linear and nonlinear initial boundary value problems and can be implemented both strongly and weakly.

在以前的工作中，我们推导了新的能量和熵稳定开放边界条件和实现技术，用于线性和非线性初始边值问题。这些边界程序产生的估计仅受外部数据的限制。有趣的是，这些新的边界条件将众所周知的经典线性问题特征边界条件推广到非线性问题。讨论了这两种边界程序的异同，并指出了新程序的优点。特别地，我们证明了新的边界条件约束了线性和非线性初始边值问题的解，并且可以强实现和弱实现。

引用次数: 0

Smoothed particle-mesh hydrodynamics (SPMH) for fluid-structure interactions involving thin structures 涉及薄结构的流固相互作用的光滑颗粒网格流体动力学

IF 3.8 2区物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Physics

Pub Date : 2026-04-01 Epub Date: 2026-01-06 DOI: 10.1016/j.jcp.2025.114650

Tianrun Gao , Mingduo Yuan , Lin Fu

In this study, a general smoothed particle-mesh hydrodynamics (SPMH) method is developed for fluid-structure interaction (FSI), particularly for those involving thin structures. The proposed SPMH method obtains improved accuracy in the user-defined mesh domain, which is typically defined near the thin structures. Meanwhile, SPMH can also preserve the free-surface tracking ability of smoothed particle hydrodynamics (SPH). The SPMH integrates SPH and finite-volume method (FVM), for which the weakly compressible SPH and unstructured arbitrary Lagrangian-Eulerian (ALE) FVM are adopted, respectively. The mesh update of the ALE framework is achieved by combining the finite-element method (FEM) with the spring analogy method. For thin structures, a new beam solver degenerated from the three-dimensional shell is developed based on FVM. In SPMH, the data communication between particle and mesh domains is achieved through activated, non-activated particles of SPH particles and interface points on mesh domain edges. To handle the free-surface flow in the mesh domain, the fluid-phase and void cells are identified according to the non-activated SPH particles, and flux calculation at the free-surface region is designed accordingly. A set of challenging FSI cases involving thin structures is simulated using the proposed SPMH method, and SPMH shows higher accuracy than the previous SPH method, particularly for FSI problems in the specified mesh domain.

在本研究中，发展了一种通用的光滑颗粒网格流体动力学（SPMH）方法，用于流固耦合（FSI），特别是涉及薄结构的流固耦合（FSI）。所提出的SPMH方法在用户自定义网格域中（通常定义在薄结构附近）获得了更高的精度。同时，SPMH还能保持光滑粒子流体力学（SPH）的自由表面跟踪能力。SPMH将SPH法与有限体积法（FVM）相结合，分别采用弱可压缩SPH法和非结构化任意拉格朗日-欧拉（ALE） FVM法。将有限元法与弹簧类比法相结合，实现了ALE框架的网格更新。针对薄型结构，提出了一种基于FVM的三维壳简并梁解算器。在SPMH中，粒子和网格域之间的数据通信是通过SPH粒子的激活粒子、非激活粒子和网格域边缘上的界面点来实现的。为了处理网格域内的自由表面流动，根据非活化SPH颗粒识别出液相和空隙单元，并相应地设计了自由表面区域的通量计算。利用SPMH方法模拟了一组涉及薄结构的具有挑战性的FSI案例，SPMH方法比以前的SPH方法具有更高的精度，特别是对于特定网格域的FSI问题。

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引用次数: 0

A stable iterative direct sampling method for elliptic inverse problems with partial Cauchy data 具有部分柯西数据的椭圆型反问题的稳定迭代直接抽样方法

IF 3.8 2区物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Physics

Pub Date : 2026-04-01 Epub Date: 2025-12-31 DOI: 10.1016/j.jcp.2025.114642

Bangti Jin, Fengru Wang, Jun Zou

We develop a novel iterative direct sampling method (IDSM) for solving linear or nonlinear elliptic inverse problems with partial Cauchy data. It integrates three innovations: a data completion scheme to reconstruct missing boundary information, a heterogeneously regularized Dirichlet-to-Neumann map to enhance the near-orthogonality of probing functions, and a stabilization-correction strategy to ensure the numerical stability. The resulting method is remarkably robust with respect to measurement noise, is flexible with the measurement configuration, enjoys provable stability guarantee, and achieves enhanced resolution for recovering inhomogeneities. Numerical experiments in electrical impedance tomography, diffuse optical tomography, and cardiac electrophysiology show its effectiveness in accurately reconstructing the locations and geometries of inhomogeneities.

提出了一种求解具有部分柯西数据的线性或非线性椭圆型反问题的迭代直接抽样方法。它集成了三个创新：一个数据补全方案来重建缺失的边界信息，一个异构正则化的Dirichlet-to-Neumann映射来增强探测函数的近正交性，以及一个稳定校正策略来确保数值稳定性。所得到的方法对测量噪声具有显著的鲁棒性，对测量配置具有灵活性，具有可证明的稳定性保证，并且提高了恢复非均匀性的分辨率。电阻抗层析成像、漫射光学层析成像和心脏电生理学的数值实验表明，该方法在精确重建非均匀性的位置和几何形状方面是有效的。

引用次数: 0

The Fourier Spectral Transformer for efficient and generalizable nonlinear PDEs 高效、可推广的非线性偏微分方程的傅立叶谱变换器

IF 3.8 2区物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Physics

Pub Date : 2026-04-01 Epub Date: 2026-01-01 DOI: 10.1016/j.jcp.2025.114648

Beibei Li

In this work we propose a unified Fourier Spectral Transformer network that integrates the strengths of classical spectral methods and attention based neural architectures. By transforming the original PDEs into spectral ordinary differential equations, we use high precision numerical solvers to generate training data and use a Transformer network to model the evolution of the spectral coefficients. We design two complementary sequence models for the evolution of spectral coefficients, a Fourier Spectral Transformer and an exponential time difference Transformer. The latter embeds the analytic linear propagator of the PDE through an exponential time differencing update, while a Transformer is used to learn the nonlinear contribution. We evaluate the proposed Transformer with Burgers’ equation, two-dimensional and three-dimensional incompressible Navier-Stokes equations. The numerical experiments show that the models achieve highly accurate long-term predictions from relatively limited training data, and that the exponential time difference Transformer exhibits improved stability and convergence. The proposed Transformer generalizes well to unseen data, bringing a promising paradigm for real time prediction and control of complex dynamical systems.

在这项工作中，我们提出了一个统一的傅立叶频谱变压器网络，它集成了经典频谱方法和基于注意力的神经结构的优势。通过将原始偏微分方程转化为频谱常微分方程，我们使用高精度数值求解器生成训练数据，并使用Transformer网络对频谱系数的演变进行建模。我们设计了两个互补序列模型用于谱系数的演化，一个傅立叶谱变换和一个指数时差变换。后者通过指数时差更新嵌入PDE的解析线性传播算子，而使用变压器来学习非线性贡献。我们用Burgers方程、二维和三维不可压缩的Navier-Stokes方程来评估所提出的变压器。数值实验表明，该模型在相对有限的训练数据基础上实现了高精度的长期预测，并且指数时差变压器具有较好的稳定性和收敛性。提出的变压器可以很好地推广到未知数据，为复杂动态系统的实时预测和控制提供了一个有前途的范例。

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引用次数: 0

A Central Differential flux with high-Order dissipation for robust simulations of transcritical flows 跨临界流动鲁棒模拟的高阶耗散中心微分通量

IF 3.8 2区物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Physics

Pub Date : 2026-04-01 Epub Date: 2026-01-07 DOI: 10.1016/j.jcp.2026.114653

Bonan Xu , Chang Sun , Peixu Guo

The simulation of transcritical flows remains challenging due to strong thermodynamic nonlinearities that induce spurious pressure oscillations in conventional schemes.While primitive-variable formulations offer improved robustness under such conditions, they are always limited by energy conservation errors and the absence of systematic high-order treatments for numerical fluxes. In this paper, we introduce the Central Differential flux with High-Order Dissipation (CDHD), a novel numerical flux solver designed for primitive-variable discretization. This method combines a central flux for advection with a minimal, upwind-biased dissipation term to stabilize the simulation while maintaining formal accuracy. The dissipation term effectively suppresses oscillations and improves stability in transcritical flows. Compared to traditional primitive-variable approaches, CDHD reduces the energy conservation error in two order of magnitude. When incorporated into a hybrid framework with a conservative shock-capturing scheme, the method robustly handles both smooth transcritical phenomena and shock waves. Numerical tests validate the accuracy, stability, and energy-preserving capabilities of CDHD, demonstrating its potential as a reliable tool for complex real-gas flow simulations.

跨临界流动的模拟仍然具有挑战性，因为在传统的方案中，强烈的热力学非线性会导致虚假的压力振荡。虽然原始变量公式在这种情况下提供了更好的鲁棒性，但它们总是受到能量守恒误差和缺乏系统的高阶数值通量处理的限制。本文介绍了一种新颖的高阶耗散中心微分通量求解器（CDHD），它是一种用于原始变量离散化的数值通量求解器。该方法将平流的中心通量与最小的逆风偏置耗散项结合起来，在保持形式精度的同时稳定模拟。在跨临界流动中，耗散项有效地抑制了振荡，提高了稳定性。与传统的原始变量方法相比，CDHD将节能误差降低了两个数量级。当将该方法与保守激波捕获方案结合到混合框架中时，该方法对光滑跨临界现象和激波都具有鲁棒性。数值测试验证了CDHD的准确性、稳定性和节能能力，证明了它作为复杂真实气体流动模拟的可靠工具的潜力。

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引用次数: 0

An improved lattice Boltzmann method with a novel conservative boundary scheme for viscoelastic fluid flows 粘弹性流体流动的一种新的保守边界格式改进晶格玻尔兹曼方法

IF 3.8 2区物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Physics

Pub Date : 2026-04-01 Epub Date: 2026-01-09 DOI: 10.1016/j.jcp.2026.114667

Yuan Yu , Siwei Chen , Yuting Zhou , Lei Wang , Hai-Zhuan Yuan , Shi Shu

The high Weissenberg number problem has been a persistent challenge in the numerical simulation of viscoelastic fluid flows. This paper presents an improved lattice Boltzmann method for solving viscoelastic flow problems at high Weissenberg numbers. The proposed approach employs two independent two-relaxation-time regularized lattice Boltzmann models to solve the hydrodynamic field and conformation tensor field of viscoelastic fluid flows, respectively. The viscoelastic stress computed from the conformation tensor is directly embedded into the hydrodynamic field using a newly proposed local velocity discretization scheme, thereby avoiding spatial gradient calculations. The constitutive equations are treated as convection-diffusion equations and solved using an improved convection-diffusion model specifically designed for this purpose, incorporating a novel auxiliary source term that eliminates the need for spatial and temporal derivative computations. Additionally, a conservative non-equilibrium bounce-back (CNEBB) scheme is proposed for implementing solid wall boundary conditions in the constitutive equations. The robustness of the present algorithm is validated through a series of benchmark problems. The simplified four-roll mill problem demonstrates that the method effectively improves numerical accuracy and stability in bulk regions containing stress singularities. The Poiseuille flow problem validates the accuracy of the current algorithm with the CNEBB boundary scheme at extremely high Weissenberg numbers (tested up to

Wi = 10000

). The flow past a circular cylinder problem confirms the superior stability and applicability of the scheme for complex curved boundary problems compared to other existing common schemes.

高Weissenberg数问题一直是粘弹性流体流动数值模拟中的一个难题。本文提出了求解高维森伯格数粘弹性流动问题的改进晶格玻尔兹曼方法。该方法采用两个独立的双松弛时间正则化晶格玻尔兹曼模型分别求解粘弹性流体流动的水动力场和构象张量场。采用新提出的局部速度离散化方案，将构象张量计算得到的粘弹性应力直接嵌入到流体动力场中，从而避免了空间梯度计算。本构方程被视为对流-扩散方程，并使用专门为此目的设计的改进的对流-扩散模型进行求解，该模型包含了一个新的辅助源项，消除了对空间和时间导数计算的需要。此外，提出了一种保守的非平衡反弹（CNEBB）格式来实现本构方程中的实体壁边界条件。通过一系列的基准问题验证了该算法的鲁棒性。简化后的四辊轧机问题表明，该方法有效地提高了包含应力奇点的块体区域的数值精度和稳定性。泊泽维尔流问题验证了CNEBB边界格式在极高的Weissenberg数（测试Wi=10000）下的当前算法的准确性。经过圆柱的流动问题验证了该格式在复杂曲面边界问题上的稳定性和适用性。

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引用次数: 0

Higher order stray field computation on tensor product domains 张量积域上的高阶杂散场计算

IF 3.8 2区物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Physics

Pub Date : 2026-04-01 Epub Date: 2026-01-05 DOI: 10.1016/j.jcp.2026.114652

Lukas Exl , Sebastian Schaffer

We present an extension of the tensor grid method for stray field computation on rectangular domains that incorporates higher-order basis functions. Both the magnetization and the resulting magnetic field are represented using higher-order B-spline bases, which allow for increased accuracy and smoothness. The method employs a super-potential formulation, which circumvents the need to convolve with a singular kernel. The field is represented with high accuracy as a functional Tucker tensor, leveraging separable expansions on the tensor product domain and trained via a multilinear extension of the extreme learning machine methodology. Unlike conventional grid-based methods, the proposed mesh-free approach allows for continuous field evaluation. Numerical experiments confirm the accuracy and efficiency of the proposed method, demonstrating exponential convergence of the energy and linear computational scaling with respect to the multilinear expansion rank.

本文提出了一种包含高阶基函数的矩形域杂散场计算的张量网格方法的扩展。磁化强度和产生的磁场都使用高阶b样条基表示，这可以提高精度和平滑度。该方法采用了一个超势公式，避免了与奇异核进行卷积的需要。该领域被高精度地表示为函数Tucker张量，利用张量积域上的可分离展开，并通过极限学习机方法的多线性扩展进行训练。与传统的基于网格的方法不同，所提出的无网格方法允许连续的现场评估。数值实验验证了该方法的准确性和有效性，证明了能量的指数收敛性和对多线性展开阶的线性计算尺度。

引用次数: 0

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