Journal of Computational Physics最新文献

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Unconditional energy stable and mass-conserving Gauge–Uzawa MSAV methods for the Cahn–Hilliard–Navier–Stokes model Cahn-Hilliard-Navier-Stokes模型的无条件能量稳定和质量守恒的Gauge-Uzawa MSAV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 : 2025-12-23 DOI: 10.1016/j.jcp.2025.114614

Baolin Kuang , Hongfei Fu , Rihui Lan , Lili Ju

We develop linear, fully decoupled first- and second-order time-discretization schemes for the Cahn–Hilliard–Navier–Stokes system, by integrating the multiple scalar auxiliary variables (MSAV) approach with the Gauge–Uzawa (GU) method. The schemes are proved to ensure both mass conservation and unconditional energy stability. Moreover, by reformulating the system into matrix form, we present two linearly decoupled numerical solution algorithms through Gaussian elimination: a commonly adopted decoupled method with constant-coefficient matrices and an alternative approach involving solution-dependent coefficient matrices. Both schemes involve only solving a series of Poisson-type equations alongside a straightforward linear algebraic system at each time step. Notably, the proposed methods eliminate the need for artificial pressure boundary conditions. Besides, a rigorous error analysis of the first-order scheme is conducted, in which the idea of high-order consistency analysis is employed for the intermediate velocity by introducing an auxiliary momentum equation. It is shown that the scheme achieves optimal temporal convergence rates for the phase function and velocity across various norms. Finally, numerical experiments are performed to validate the theoretical findings and demonstrate the performance of the proposed schemes.

通过将多标量辅助变量（MSAV）方法与Gauge-Uzawa （GU）方法相结合，我们开发了Cahn-Hilliard-Navier-Stokes系统的线性、完全解耦的一阶和二阶时间离散化方案。证明了这些方案既能保证质量守恒，又能保证无条件能量稳定。此外，通过将系统重新表述为矩阵形式，我们通过高斯消去提出了两种线性解耦数值解算法：一种常用的常系数矩阵解耦方法和一种涉及解相关系数矩阵的替代方法。这两种方案都只涉及在每个时间步解一系列泊松型方程和一个直接的线性代数系统。值得注意的是，所提出的方法消除了人工压力边界条件的需要。此外，对一阶格式进行了严格的误差分析，其中通过引入辅助动量方程，对中间速度采用高阶一致性分析的思想。结果表明，该方案在不同范数的相函数和速度上均能达到最佳的时间收敛速率。最后，通过数值实验对理论结果进行了验证，并验证了所提方案的性能。

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引用次数: 0

Partition-of-unity flow-based solver for kinetic plasma simulations 基于单位分割流的动力学等离子体模拟求解器

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

Journal of Computational Physics

Pub Date : 2025-12-22 DOI: 10.1016/j.jcp.2025.114608

Bowen Zhu, Jian Wu, Yuanbo Lu, Xingwen Li, Aici Qiu

We introduce a novel flow-based solver for kinetic plasma simulations. Unlike Particle-in-Cell (PIC) methods that evolve particle weights (f_idz), our solver directly tracks the distribution function values (f_i) at specific phase-space points, or markers, providing an accurate point-wise representation. Unlike conventional semi-Lagrangian schemes, we maintain continuous marker trajectories along with the update of f_i and employ a Partition-of-Unity weighting to reconstruct macroscopic quantities without solving computationally expensive large linear systems. Validation shows our method achieves accuracy comparable to PIC while using 100 times fewer markers and reducing the computational wall time. The framework’s direct connection to Continuous Normalizing Flows opens promising avenues for developing hybrid physics-machine learning approaches.

我们介绍了一种新的基于流动的等离子体动力学模拟求解器。与进化粒子权重（fidz）的PIC方法不同，我们的求解器直接跟踪特定相空间点或标记处的分布函数值（fi），提供准确的逐点表示。与传统的半拉格朗日格式不同，我们在fi更新的同时保持连续的标记轨迹，并采用统一分割加权来重建宏观数量，而无需求解计算成本高昂的大型线性系统。验证表明，我们的方法在使用100倍的标记和减少计算时间的同时，达到了与PIC相当的精度。该框架与连续规范化流的直接连接为开发混合物理-机器学习方法开辟了有希望的途径。

引用次数: 0

A semi-implicit weakly compressible solver for gas-liquid two-phase flows 气液两相流半隐式弱可压缩求解器

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

Journal of Computational Physics

Pub Date : 2025-12-22 DOI: 10.1016/j.jcp.2025.114534

Kenta Sugihara , Naoyuki Onodera , Yasuhiro Idomura , Yos Panagaman Sitompul , Susumu Yamashita

We propose a new gas-liquid two-phase fluid calculation method that improves computational efficiency compared with the conventional incompressible method (Incompressible). The methods are called the semi-implicit compressible method (SI-C) and the semi-implicit weakly compressible method (SI-WC). SI-C improves the convergence of the iterative solver by computing the pressure Poisson-type equation derived from the compressible fluid equation. In SI-WC, the number of iterations can be further reduced by computing a weakly compressible Poisson-type equation that uses an artificial sound speed controlled by the Mach number. The validity of the proposed method was verified by dam breaking problems and bubbly flow analysis, and comparative verification showed that compared to Incompressible, SI-C and SI-WC accelerate the pressure Poisson-type equation solver by a factor of two and four, respectively, while achieving almost the same solutions.

本文提出了一种新的气液两相流体计算方法，与传统的不可压缩方法（incompressible）相比，提高了计算效率。这些方法被称为半隐式可压缩方法（SI-C）和半隐式弱可压缩方法（SI-WC）。SI-C通过计算由可压缩流体方程导出的压力泊松型方程，提高了迭代求解器的收敛性。在SI-WC中，通过计算弱可压缩泊松型方程可以进一步减少迭代次数，该方程使用由马赫数控制的人工声速。通过溃坝问题和气泡流分析验证了该方法的有效性，对比验证表明，与不可压缩相比，SI-C和SI-WC分别将压力泊松型方程求解器的求解速度提高了2倍和4倍，而得到的解几乎相同。

引用次数: 0

When surface evolution meets Fokker-Planck equation: A novel tangential velocity model for uniform parametrization 当表面演化满足Fokker-Planck方程时：一种新的均匀参数化切向速度模型

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

Journal of Computational Physics

Pub Date : 2025-12-22 DOI: 10.1016/j.jcp.2025.114604

Jiangong Pan , Guozhi Dong , Hailong Guo , Zuoqiang Shi

A common issue in simulating geometric evolution of surfaces is unexpected clustering of points that may cause numerical instability. We propose a novel artificial tangential velocity method for this matter. The artificial tangential velocity is generated from a surface density field governed by a Fokker-Planck equation to guide the point distribution. A target distribution matching algorithm is developed leveraging the surface Kullback-Leibler divergence of density functions. The numerical method is formulated within a fully meshless framework using the moving least squares approximation, thereby eliminating the need for mesh generation and allowing flexible treatment of unstructured point cloud data. Extensive numerical experiments are conducted to demonstrate the robustness, accuracy, and effectiveness of the proposed approach across a variety of surface evolution problems, including the mean curvature flow.

模拟曲面几何演化的一个常见问题是可能导致数值不稳定的点的意外聚类。我们提出了一种新的人工切向速度法。人造切向速度是由表面密度场产生的，该密度场由Fokker-Planck方程控制，以指导点的分布。利用密度函数的曲面Kullback-Leibler散度，提出了一种目标分布匹配算法。数值方法是在使用移动最小二乘近似的完全无网格框架内制定的，从而消除了网格生成的需要，并允许灵活处理非结构化点云数据。大量的数值实验证明了该方法在各种表面演化问题（包括平均曲率流）中的鲁棒性、准确性和有效性。

引用次数: 0

An unstructured block-based adaptive mesh refinement approach for discontinuous Galerkin method 一种基于非结构化块的非连续Galerkin法自适应网格细化方法

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

Journal of Computational Physics

Pub Date : 2025-12-22 DOI: 10.1016/j.jcp.2025.114613

Yun-Long Liu , Qi Kong , Le-Wen Chen , Qi-Hang Hao , Yuan Cao , A-Man Zhang

This paper presents an adaptive mesh refinement (AMR) approach specifically designed for the discontinuous Galerkin (DG) method for conservation laws. Our approach employs block-based AMR to keep local data structures simple and computationally efficient, while supporting an unstructured topology of the initial root blocks through a forest representation to handle complex geometries. We introduce inter-block communication via guard cells to simplify flux computations between cells at the same and different refinement levels. To preserve geometric fidelity of the computational domain with smooth boundaries during refinement, boundary nodes are projected onto either user-provided analytic surface functions or automatically reconstructed NURBS surfaces. The implementation includes MPI parallelization with dynamic load balancing using two alternatives: space-filling curve partitioning and graph partitioning. Numerical tests in 2D and 3D demonstrate the method’s expected order of accuracy, effective dynamic refinement control, and good parallel efficiency.

本文提出了一种针对不连续伽辽金守恒律法的自适应网格细化方法。我们的方法采用基于块的AMR来保持本地数据结构的简单性和计算效率，同时通过森林表示支持初始根块的非结构化拓扑来处理复杂的几何形状。我们通过保护单元引入块间通信，以简化相同和不同细化级别单元之间的通量计算。为了在精化过程中保持具有光滑边界的计算域的几何保真度，边界节点被投影到用户提供的解析曲面函数或自动重建的NURBS曲面上。该实现包括MPI并行化和动态负载平衡，使用两种替代方案：空间填充曲线分区和图分区。二维和三维数值试验表明，该方法具有预期的精度、有效的动态精细化控制和良好的并行效率。

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引用次数: 0

Semi-Lagrangian SAV method for Vlasov-Maxwell equations Vlasov-Maxwell方程的半拉格朗日SAV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 : 2025-12-21 DOI: 10.1016/j.jcp.2025.114606

Nicolas Crouseilles , Hongtao Liu , Yukun Yue

In this work, a new numerical method to approximate the solution of the Vlasov-Maxwell equations is presented. The method uses a phase space discretization and its main properties are: energy and charge conservation thanks to a semi-implicit treatment of the Maxwell equations, but allowing for an explicit and efficient update of the unknown. One of the main ingredients lies in the introduction of an auxiliary scalar variable inspired from the Scalar Auxiliary Variable (SAV) approach [1] together with a suitable splitting inspired from [2] which enables the use of a semi-Lagrangian method.

本文提出了一种新的近似求解Vlasov-Maxwell方程组的数值方法。该方法使用相空间离散化，其主要特性是：由于对麦克斯韦方程的半隐式处理，能量和电荷守恒，但允许对未知进行显式和有效的更新。其中一个主要的组成部分是引入了从标量辅助变量（SAV）方法[1]启发的辅助标量变量，以及从[2]启发的合适的分裂，从而可以使用半拉格朗日方法。

引用次数: 0

Online optimisation of machine learning collision models to accelerate direct molecular simulation of rarefied gas flows 在线优化机器学习碰撞模型，加速稀薄气体流动的直接分子模拟

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

Journal of Computational Physics

Pub Date : 2025-12-21 DOI: 10.1016/j.jcp.2025.114601

Nicholas Daultry Ball , Jonathan F. MacArt , Justin Sirignano

We develop an online optimisation algorithm for in situ calibration of collision models in simulations of rarefied gas flows. The online optimised collision models are able to achieve similar accuracy to Direct Molecular Simulation (DMS) at significantly reduced computational cost for 1D normal shocks in argon across a wide range of temperatures and Mach numbers. DMS is a method of simulating rarefied gases which numerically integrates the trajectories of colliding molecules. It often achieves similar fidelity to Molecular Dynamics (MD) simulations, which fully resolve the trajectories of all particles at all times. However, DMS is substantially more computationally expensive than the popular Direct Simulation Monte Carlo (DSMC) method, which uses simple phenomenological models of the collisions. We aim to accelerate DMS by replacing the computationally costly Classical Trajectory Calculations (CTC) with a neural network collision model. A key feature of our approach is that the machine learning (ML) collision model is optimised online during the simulation on a small dataset of CTC trajectories generated in situ during simulations. The online Machine Learning DMS (ML-DMS) is able to reproduce the accuracy of MD and CTC-DMS for 1D normal shocks in argon at a significantly lower computational cost (by a factor of  ∼ 5–15), at a wide range of physical conditions (Mach numbers 1.55 ≤ Ma ≤ 50, densities

\sim 1 \times 10^{- 4} k g m^{- 3}

1 k g m^{- 3}

, and temperatures 16 K to 300 K). We also derive an online optimisation method for calibration of DSMC collision models given a model of the interatomic forces. In our numerical evaluations for 1D normal shocks, the online optimisation method matches or significantly improves the accuracy of VHS (Variable Hard Sphere) DSMC with respect to CTC-DMS (with a  ∼ 20 ×  lower computational cost).

我们开发了一种在线优化算法，用于在稀薄气体流动模拟中现场校准碰撞模型。在线优化的碰撞模型能够在广泛的温度和马赫数范围内实现与直接分子模拟（DMS）相似的精度，同时显著降低了氩气一维正常冲击的计算成本。DMS是一种模拟稀薄气体的方法，它对碰撞分子的运动轨迹进行数值积分。它经常达到与分子动力学（MD）模拟相似的保真度，这完全解决了所有粒子在任何时候的轨迹。然而，DMS比流行的直接模拟蒙特卡罗（DSMC）方法在计算上要昂贵得多，后者使用简单的碰撞现象模型。我们的目标是通过用神经网络碰撞模型取代计算量大的经典轨迹计算（CTC）来加速DMS。我们的方法的一个关键特征是，在模拟过程中，机器学习（ML）碰撞模型在模拟过程中对原位生成的CTC轨迹的小数据集进行在线优化。在线机器学习DMS （ML-DMS）能够在广泛的物理条件下（马赫数1.55 ≤ Ma ≤ 50，密度~ 1×10−4kgm−3至1kgm−3，温度16 K至300 K），以显著降低的计算成本（ ~ 5-15）重现MD和CTC-DMS在氩气中一维正常冲击的精度。在给定原子间相互作用力模型的情况下，我们还推导了一种用于校准DSMC碰撞模型的在线优化方法。在我们对一维正常冲击的数值评估中，在线优化方法匹配或显着提高了VHS（可变硬球）DSMC相对于CTC-DMS的精度（计算成本降低 ~ 20 × ）。

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引用次数: 0

Improving Yee’s scheme with asymptotic dispersion correction for time-harmonic Maxwell’s equations 用渐近色散校正改进时谐Maxwell方程组的Yee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 : 2025-12-21 DOI: 10.1016/j.jcp.2025.114602

Pierre-Henri Cocquet , Martin J. Gander

In this paper, we show how to reduce the dispersion error associated to Yee’s finite difference scheme applied to time-harmonic Maxwell’s equations in one, two and three spatial dimensions. Our method, called asymptotic dispersion correction, is based on the introduction of a shifted angular frequency depending on a free parameter in the Yee stencil. The optimal parameter, called the asymptotically optimal shift, is next explicitly determined by minimizing the dispersion error for small enough meshsize or, equivalently, for large enough number of grid points per wavelength. Numerical experiments are provided and show that the relative error is reduced when using the optimal shifted angular frequency as soon as the number of grid points per wavelength is large enough.

在本文中，我们展示了如何减少与Yee有限差分格式相关的色散误差应用于一维、二维和三维的时谐麦克斯韦方程组。我们的方法，称为渐近色散校正，是基于引入一个移位的角频率依赖于Yee模板中的自由参数。最优参数，称为渐近最优位移，接下来明确地通过最小化色散误差来确定足够小的网格尺寸，或者等效地，对于每个波长足够多的网格点。数值实验结果表明，只要每个波长的网格点数量足够大，采用最优位移角频率可以减小相对误差。

引用次数: 0

A generalized fundamental solution technique for the regularized 13-moment system in rarefied gas flows 稀薄气体流动中正则13矩系统的广义基本解技术

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

Journal of Computational Physics

Pub Date : 2025-12-20 DOI: 10.1016/j.jcp.2025.114591

Himanshi , Lambert Theisen , Anirudh Singh Rana , Manuel Torrilhon , Vinay Kumar Gupta

In this work, we explore a generalized method of fundamental solutions (MFS) for solving the regularized 13-moment (R13) equations for rarefied monatomic gases. While previous applications of the MFS in rarefied gas flows relied on problem-specific fundamental solutions, we propose a generic approach that systematically computes the fundamental solutions for any linear moment system without predefined source terms. The proposed framework is first introduced using a simple example involving the Stokes equations, and is then extended to the R13 equations. The results obtained from the generic MFS are validated against an analytical solution for the R13 equations. Following validation, the framework is applied to the case of thermally-induced flow between two noncoaxial cylinders. Since no analytical solution exists for this case, we compare the results obtained from the MFS with those obtained from the finite element method (FEM). To further assess computational efficiency, we analyze the runtimes of the FEM and MFS. The results indicate that the MFS converges faster than the FEM and serves as a promising alternative to conventional meshing-based techniques. The documented code for the generic MFS validated against the analytical solution for R13 equations is publicly available.

在这项工作中，我们探索了求解稀有单原子气体正则化13矩方程的广义基本解方法（MFS）。虽然以前的MFS在稀薄气体流动中的应用依赖于特定问题的基本解，但我们提出了一种通用方法，可以系统地计算任何线性矩系统的基本解，而不需要预定义的源项。提出的框架首先通过一个涉及Stokes方程的简单示例进行介绍，然后将其推广到R13方程。对R13方程的解析解进行了验证。在验证之后，将该框架应用于两个非同轴圆柱体之间的热诱导流动情况。由于这种情况不存在解析解，我们将MFS得到的结果与有限元法得到的结果进行比较。为了进一步评估计算效率，我们分析了FEM和MFS的运行时间。结果表明，MFS的收敛速度比FEM快，是传统基于网格的技术的一个有希望的替代方案。针对R13方程的解析解验证的通用MFS的文档代码是公开的。

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引用次数: 0

The intrinsic filters of the finite volume methods and a new interpretation of the implicit large eddy simulation 有限体积法的内禀滤波器及隐式大涡模拟的新解释

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

Journal of Computational Physics

Pub Date : 2025-12-20 DOI: 10.1016/j.jcp.2025.114603

Wenzhi Huang , Yanhui Li , Rundong Zhang , Zhuohang Wu , Min Gao , Yu-Xin Ren

This paper proposes a novel interpretation of implicit large eddy simulation (ILES) based on high-order finite volume methods. When a finite volume scheme cannot resolve all solution scales on a given grid, an intrinsic filter arises from the scheme's cell averaging and reconstruction procedures. The paper identifies this filter and provides its explicit expression for the first time. This filter possesses unique characteristics that distinguish it from conventional filters employed in large eddy simulation (LES). Applying this filter to the governing equation yields a filtered differential equation resembling that in a standard LES. The corresponding unclosed "exact" subgrid-scale (SGS) stress is also identified. Similarly, the differential equation equivalent to a finite volume scheme is derived alongside the "numerical" SGS stress. These two equations form the theoretical framework of ILES, which governs the filtering and closure procedures. The mechanism underlying ILES using high-order finite volume schemes is analyzed. The rationality of utilizing the dissipative part of the Riemann flux to close the exact SGS stress is confirmed in terms of its magnitude and dissipation properties. Furthermore, two a priori criteria for optimizing the filtering and closure procedures are proposed to design finite volume schemes for ILES applications. Finally, one-dimensional forced Burgers turbulence is simulated to validate the new interpretation, and the numerical results provide clear support for the presented theoretical framework.

本文提出了一种基于高阶有限体积法的隐式大涡模拟（ILES）的新解释。当有限体积方案不能解决给定网格上的所有解决尺度时，该方案的单元平均和重建过程产生了一个内在滤波器。本文首次对该过滤器进行了识别，并给出了其显式表达式。该滤波器具有独特的特点，区别于大涡模拟（LES）中使用的传统滤波器。将此过滤器应用于控制方程，将得到一个类似于标准LES中的过滤微分方程。相应的未闭合“精确”亚网格尺度（SGS）应力也被确定。类似地，等效于有限体积格式的微分方程与“数值”SGS应力一起导出。这两个方程构成了ILES的理论框架，它支配着过滤和闭包过程。分析了基于高阶有限体积格式的ILES机制。从黎曼通量的大小和耗散特性两方面证实了利用黎曼通量的耗散部分来封闭精确SGS应力的合理性。此外，提出了优化滤波和闭合过程的两个先验准则，以设计适用于ILES应用的有限体积方案。最后，对一维强迫Burgers湍流进行了模拟以验证新的解释，数值结果为所提出的理论框架提供了明确的支持。

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