Computers & Fluids最新文献_第7页

Generalization-aware structured mesh smoothing via graph neural networks 基于图神经网络的泛化感知结构网格平滑

IF 3 3区工程技术 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computers & Fluids

Pub Date : 2025-11-10 DOI: 10.1016/j.compfluid.2025.106895

Jingzhu Pei , Xinhai Chen , Yang Liu , Zhichao Wang , Qingyang Zhang , Qinglin Wang , Xiang Gao , Jie Liu

Structured meshes provide computationally efficient discretization for scientific simulations through geometrically ordered mesh units. Because of their strict orthogonality constraints, it is still challenging to generate high-quality structured meshes. Although traditional optimization techniques employ iterative node relocation to enhance element quality, they suffer from accuracy-efficiency trade-offs. Existing intelligent methods based on supervised learning attempt to circumvent these limitations through data-driven optimization. However, these methods are inherently limited by their dependence on domain-specific training data and their inability to generalize across diverse complex geometries. To overcome these problems, we propose Structured-Mesh Graph Neural Network-based smoothing(SMGNN-Smoothing), a generalization-aware unsupervised method for structured mesh optimization. Our method integrates three key innovations: (1) a graph neural network that aggregates neighborhood features to predict optimized node configurations, (2) an adaptive normalization technique enabling consistent processing of multi-resolution meshes, (3) a well-designed loss function controls the whole training process, StructureLoss. SMGNN-Smoothing realizes excellent optimization performance across multiple quality metrics. It outperforms existing supervised learning methods and shows strong generalization capability. Compared with optimization-based smoothing, it achieves an order-of-magnitude improvement in computational efficiency.

结构化网格通过几何有序的网格单元为科学模拟提供了高效的计算离散化。由于其严格的正交性约束，生成高质量的结构化网格仍然具有挑战性。虽然传统的优化技术采用迭代节点重新定位来提高元素质量，但它们受到精度和效率权衡的影响。现有的基于监督学习的智能方法试图通过数据驱动优化来规避这些限制。然而，这些方法本身就受到限制，因为它们依赖于特定领域的训练数据，并且无法泛化各种复杂几何形状。为了克服这些问题，我们提出了基于结构网格图神经网络的平滑（SMGNN-Smoothing），这是一种具有泛化意识的无监督结构网格优化方法。我们的方法集成了三个关键创新：(1)聚合邻域特征以预测优化节点配置的图神经网络；(2)实现多分辨率网格一致处理的自适应归一化技术；(3)设计良好的损失函数StructureLoss控制整个训练过程。SMGNN-Smoothing实现了跨多个质量指标的卓越优化性能。它优于现有的监督学习方法，具有较强的泛化能力。与基于优化的平滑相比，计算效率提高了一个数量级。

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引用次数: 0

Analysis and prediction of the pressure drop in corrugated plate heat exchangers based on numerical simulations 基于数值模拟的波纹板换热器压降分析与预测

IF 3 3区工程技术 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computers & Fluids

Pub Date : 2025-11-10 DOI: 10.1016/j.compfluid.2025.106910

Nicolas Montiel , Pierre Horgue , Mathieu Courtial , Benoît Sénéchal , Julien Sebilleau , Rémi Zamansky

We present simulations of flows in wavy channels, typical of corrugated plated exchangers (CPHE), using wall-resolved Large Eddy Simulation (LES) and the Reynolds Average Navier-Stokes (RANS) approach with the

k - ω SST

model. We consider three different corrugation angles (β) and a range of Reynolds numbers from 4721 to 47025. Using the LES, we analyze the evolution of the head loss across the CPHE and report that for moderate Re and β it is mainly caused by the wall-shear stress contribution, whereas at high Re and β it results from the wall-pressure contribution. Further wall-resolved LES simulations are used as a reference to assess and improve the quality of RANS modeling. The standard setting of the RANS

k - ω SST

model, considered as a now-day standard for RANS in the industry, clearly showed limitations for such complicated geometries, with errors for the mean pressure drop prediction, which can be as high as 40 %. Finally we show that, relying on genetic algorithms, we can find sets of model parameters able to significantly reduce the RANS errors on the pressure drop although some discrepancies in the prediction of the mean flow structure remain, emphasizing the inherent limitation of the

k - ω SST

model.

我们利用壁面分辨大涡模拟（LES）和k−ω海温模型的Reynolds平均Navier-Stokes （RANS）方法，对波纹板式换热器（CPHE）的典型波浪通道中的流动进行了模拟。我们考虑了三种不同的波纹角（β）和4721到47025的雷诺数范围。利用LES，我们分析了整个CPHE的水头损失的演变，并报告了中等Re和β的水头损失主要是由壁面剪切应力贡献引起的，而在高Re和β的水头损失则是由壁面压力贡献引起的。进一步的壁面分辨LES模拟可作为评估和改进RANS建模质量的参考。RANS k−ωSST模型的标准设置，被认为是当今行业中RANS的标准，清楚地显示出这种复杂几何形状的局限性，平均压降预测的误差可高达40%。最后，我们表明，依靠遗传算法，我们可以找到能够显著降低压降的RANS误差的模型参数集，尽管平均流结构的预测仍然存在一些差异，这强调了k−ω海表温度模型的固有局限性。

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引用次数: 0

Central-differencing quasi-Newton method for solving the Eikonal equation with application to wall distance computation 求解Eikonal方程的中心差分拟牛顿法及其在壁距计算中的应用

IF 3 3区工程技术 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computers & Fluids

Pub Date : 2025-11-09 DOI: 10.1016/j.compfluid.2025.106897

Yair Mor-Yossef

A new implicit method for solving the Eikonal equation on unstructured grids is proposed. The implicit Jacobian is obtained by modifying a direct linearization of the residual. The modified Jacobian is designed to form an M-matrix without the artificial time derivative commonly used. Namely, no artificial time step is involved in solving the Eikonal equation. Moreover, the algorithm guarantees the solution’s positivity and the linearized problem’s convergence. Usually, upwinding is introduced into the algorithm to enhance its stability. However, a second-order, central-differencing method is proposed in the present work for solving the Eikonal equation. It relies on a newly developed weighted least-squares scheme. Common weighting depends on the inverse of the distance between the sought cell and its neighboring cells. The new scheme adds directional weighting. This scheme was found to outperform the common weighted least-squares in terms of solution accuracy. An artificial diffusion term is introduced to smooth the solution. A dynamic smoothing coefficient is developed to control spurious oscillations. It distinguishes between freely propagating and colliding solution fronts. Moreover, it allows the artificial diffusion to be minimized, thereby increasing solution accuracy, while maintaining the stability of the algorithm. The numerical simulations demonstrated the algorithm’s robustness. It exhibits consistent and rapid residual convergence across various cases involving high aspect-ratio grid elements.

提出了求解非结构网格上的Eikonal方程的一种新的隐式方法。隐式雅可比矩阵是通过修改残差的直接线性化得到的。将改进的雅可比矩阵设计成一个不需要通常使用的人工时间导数的m矩阵。也就是说，在求解Eikonal方程时不涉及人工的时间步长。该算法保证了解的正性和线性化问题的收敛性。通常在算法中引入上绕来增强算法的稳定性。然而，本文提出了求解Eikonal方程的二阶中心差分方法。它依赖于一种新开发的加权最小二乘格式。通用加权取决于所寻单元与其相邻单元之间距离的倒数。新方案增加了定向加权。该方案在求解精度方面优于普通加权最小二乘方案。引入人工扩散项使解光滑化。提出了一种动态平滑系数来控制杂散振荡。它区分了自由传播和碰撞的解阵。此外，它可以使人工扩散最小化，从而提高求解精度，同时保持算法的稳定性。数值仿真结果表明了该算法的鲁棒性。它在涉及高纵横比网格元素的各种情况下表现出一致和快速的残差收敛。

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引用次数: 0

Implicit-PointSAGE: Neural implicit representation based superresolution for computational fluid dynamics 隐式点：基于神经隐式表示的计算流体动力学超分辨率

IF 3 3区工程技术 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computers & Fluids

Pub Date : 2025-11-08 DOI: 10.1016/j.compfluid.2025.106900

Rajat Kumar Sarkar , Vishal Jadhav , Venkataramana Runkana

High-resolution computational fluid dynamics (CFD) simulations are essential for capturing complex fluid flow phenomena such as turbulent flows and shock-boundary layer interactions that are critical for aerospace applications. However, the high computational cost of obtaining simulation results at high resolution often limits their practicality. Traditional deep learning-based super-resolution methods such as UNets have been explored to predict fine-mesh simulation results from coarse-mesh simulations, but they face challenges with unstructured meshes and require extensive amounts of training data. To address these limitations, we propose Implicit-PointSAGE, a mesh-independent super-resolution framework that leverages unordered, mesh-less structure of point clouds to simulate intricate fluid dynamics. By integrating the strengths of PointSAGE with a Neural Implicit Learning module employing Galerkin-based attention, the framework efficiently captures the underlying physics and accurately predicts fine-mesh data directly from coarse-mesh inputs. Implicit-PointSAGE demonstrates significant computational efficiency, scalability to diverse point cloud sizes, and adaptability across various CFD scenarios. It matches the performance of state-of-the-art surrogate models in solving problems represented by PDEs, achieving high accuracy with 10 to 100 times fewer data samples-sometimes requiring as few as 100 samples-while delivering substantial computational acceleration. These results position Implicit-PointSAGE as a transformative tool for super-resolution modeling and efficient high-resolution CFD simulations.

高分辨率计算流体动力学（CFD）模拟对于捕捉复杂的流体流动现象（如湍流和激波边界层相互作用）至关重要，这对航空航天应用至关重要。然而，获得高分辨率模拟结果的计算成本高，往往限制了其实用性。传统的基于深度学习的超分辨率方法（如UNets）已经被用于从粗网格模拟中预测细网格模拟结果，但它们面临着非结构化网格的挑战，并且需要大量的训练数据。为了解决这些限制，我们提出了Implicit-PointSAGE，这是一个网格无关的超分辨率框架，利用点云的无序，无网格结构来模拟复杂的流体动力学。通过将PointSAGE的优势与基于galerkin注意力的神经内隐学习模块相结合，该框架有效地捕获底层物理，并直接从粗网格输入中准确预测细网格数据。Implicit-PointSAGE展示了显著的计算效率，不同点云大小的可扩展性，以及各种CFD场景的适应性。在解决由pde表示的问题时，它与最先进的代理模型的性能相匹配，用10到100倍的数据样本（有时只需要100个样本）实现高精度，同时提供大量的计算加速。这些结果使Implicit-PointSAGE成为超分辨率建模和高效高分辨率CFD模拟的变革性工具。

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引用次数: 0

A stochastic front tracking method for compressible flows with interfaces 具有界面的可压缩流动的随机前沿跟踪方法

IF 3 3区工程技术 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computers & Fluids

Pub Date : 2025-11-08 DOI: 10.1016/j.compfluid.2025.106888

Philippe Helluy , Olivier Hurisse

A front tracking method is proposed to deal with compressible flows involving sharp interfaces. It relies on a first-order finite-volumes scheme of Lagrange-Projection type. While the Lagrangian step of the method is classical, the projection step is based on a pseudo-random sampling technique in the spirit of the one used in the Glimm’s scheme. The scheme allows reducing the numerical diffusion at the interface, in the sense that they remain sharp. It has robustness and convergence properties that are not present in most of the schemes proposed previously, and it can be applied to unstructured meshes. While this new method works very well on structured meshes, improvements are still needed in order to achieve accurate results on unstructured meshes (triangles).

针对含有尖锐界面的可压缩流，提出了一种前沿跟踪方法。它依赖于拉格朗日投影型的一阶有限体积格式。虽然该方法的拉格朗日步骤是经典的，但投影步骤是基于在Glimm方案中使用的精神中的伪随机抽样技术。该方案允许减少界面上的数值扩散，在某种意义上说，它们保持锋利。它具有鲁棒性和收敛性，这是以前提出的大多数方案所不具备的，并且可以应用于非结构化网格。虽然这种新方法在结构化网格上工作得很好，但为了在非结构化网格（三角形）上获得准确的结果，仍然需要改进。

引用次数: 0

Three-dimensional super-resolution reconstruction of turbulent flow using 3D-ESRGAN with random sampling strategy 基于随机采样策略的3D-ESRGAN湍流三维超分辨率重建

IF 3 3区工程技术 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computers & Fluids

Pub Date : 2025-11-07 DOI: 10.1016/j.compfluid.2025.106890

Linqi Yu, Yanyun Chen, Mustafa Z. Yousif, Hee-Chang Lim

This study introduces a deep learning framework that uses an enhanced three-dimensional super-resolution generative adversarial network (3D-ESRGAN) to reconstruct high-resolution turbulent flow fields from low-resolution data. To minimize the reliance on complete datasets during training, a random sampling strategy is used. In each training epoch, approximately 1 % of spatial points are randomly chosen from both the predicted and ground-truth fields for loss computation. This method mimics sparse sensor measurements in real-world experiments, allowing the model to learn accurate mappings based on limited spatial observations. Furthermore, physics-guided loss functions are incorporated to ensure consistency with the underlying physical laws, thereby improving the reliability of the reconstructed flow fields. Subsequently, the framework is tested on two typical flow scenarios: (1) flow over a finite wall-mounted square cylinder at

{Re}_{d} = 500

, and (2) fully developed turbulent channel flow at

{Re}_{τ} = 180

and 500. Both scenarios are generated using direct numerical simulation (DNS). Finally, the results are presented and analyzed both qualitatively and quantitatively. The qualitative findings show that the reconstructed fields effectively restore the key vortex structures and turbulence features absent in the coarse data. Quantitative comparisons with the ground-truth data confirm high accuracy in terms of velocity profiles, Reynolds stresses, probability density functions (PDFs), and energy spectra. Additionally, the relative error regarding the streamwise velocity magnitude is calculated, and all cases show a low error rate of approximately 5 %. In summary, the findings confirm the efficacy of combining GAN-based super-resolution with a random sampling strategy for accurate and data-efficient 3D turbulence reconstruction. The results suggest that the proposed framework can be successfully applied in real-world scenarios where only sparse measurements are accessible.

本研究引入了一种深度学习框架，该框架使用增强的三维超分辨率生成对抗网络（3D-ESRGAN）从低分辨率数据重建高分辨率湍流流场。为了减少训练过程中对完整数据集的依赖，使用了随机抽样策略。在每个训练历元中，从预测场和真值场中随机选择大约1%的空间点进行损失计算。该方法模拟了真实世界实验中的稀疏传感器测量，使模型能够基于有限的空间观测学习精确的映射。此外，为了保证与底层物理规律的一致性，还引入了物理导向损失函数，从而提高了重建流场的可靠性。随后，该框架在两种典型的流动场景下进行了测试：(1)在Red=500处流过有限壁挂式方形圆柱体，以及(2)在Reτ=180和500处完全发育的湍流通道。这两种场景都是使用直接数值模拟（DNS）生成的。最后，对研究结果进行了定性和定量分析。定性结果表明，重建场有效地恢复了粗糙数据中缺失的关键涡结构和湍流特征。与地面真实数据的定量比较证实了在速度剖面、雷诺应力、概率密度函数（pdf）和能谱方面的高精度。此外，计算了沿流速度大小的相对误差，所有情况的误差率都在5%左右。总之，研究结果证实了将基于gan的超分辨率与随机采样策略相结合的有效性，可以实现准确且数据高效的三维湍流重建。结果表明，所提出的框架可以成功地应用于只有稀疏测量可访问的现实场景。

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引用次数: 0

Actuator Line – Interpolated bounce back approach in lattice Boltzmann method for wind turbine wake simulation 风力发电机尾流仿真的晶格玻尔兹曼法中致动器线插值回弹方法

IF 3 3区工程技术 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computers & Fluids

Pub Date : 2025-11-07 DOI: 10.1016/j.compfluid.2025.106901

Seiya Watanabe , Hiroaki Kuranaga , Changhong Hu

Wind turbine wakes affect the power output of a wind farm. Unsteady turbulent simulations are a powerful approach to predicting turbine wake and wake loss in wind farms. This study proposes a novel wind turbine wake simulation based on an actuator line (AL) model for the lattice Boltzmann method. The standard AL model represents only blades, and the absence of turbine structures, such as a nacelle and a tower, impairs the precision of wake calculations. In this study, the interpolated bounce-back method, a wall boundary condition commonly used in the lattice Boltzmann method, represents a nacelle and a tower and is combined with the AL model. The proposed hybrid approach is validated by a stand-alone turbine calculation of the NTNU “Blind Test” 1. A mesh convergence study is conducted with five simulation cases at varying grid spacing, confirming that the results converge with a grid spacing of D/96 for the velocity deficit and D/128 for the turbulent kinetic energy, where the rotor diameter is D. Comparisons of simulations with and without modeling the nacelle and tower show that including the full turbine structure improves wake prediction accuracy. The proposed method is further evaluated against eight previous CFD studies that used blade-resolved or actuator-line models. The lattice Boltzmann simulations with the proposed turbine model reproduce the experimental wake profiles of mean velocity deficit and turbulent kinetic energy with accuracy comparable to these studies, except under stall-mode operation.

风力发电机尾迹影响风力发电场的输出功率。非定常湍流模拟是预测风电场涡轮尾流和尾流损失的有效方法。本文提出了一种基于执行器线（AL）模型的网格玻尔兹曼方法的风力发电机尾迹模拟方法。标准的人工智能模型只代表叶片，而没有涡轮结构，如机舱和塔，损害了尾流计算的精度。在本研究中，插值反弹法是晶格玻尔兹曼方法中常用的壁面边界条件，它代表一个机舱和一个塔，并与AL模型相结合。通过NTNU“盲测”的单机涡轮计算验证了所提出的混合方法。采用不同网格间距的5个仿真实例进行了网格收敛研究，证实了速度亏缺的网格间距为D/96，湍流动能的网格间距为D/128，其中转子直径为D。模拟结果表明，在不模拟机舱和塔架的情况下，包括整个涡轮结构可以提高尾迹预测精度。该方法与先前使用叶片分解模型或执行器线模型的8项CFD研究进行了进一步评估。用所提出的涡轮模型进行的晶格玻尔兹曼模拟再现了平均速度赤字和湍流动能的实验尾迹曲线，其精度与这些研究相当，但在失速模式下除外。

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引用次数: 0

Adaptive criterion and modification of wave-particle decomposition in UGKWP method for high-speed flow simulation 高速流动模拟UGKWP法波粒分解自适应准则及修正

IF 3 3区工程技术 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computers & Fluids

Pub Date : 2025-11-06 DOI: 10.1016/j.compfluid.2025.106896

Junzhe Cao , Yufeng Wei , Wenpei Long , Chengwen Zhong , Kun Xu

Benefiting from its direct modeling of physical laws in discretized space and its automatic decomposition of hydrodynamic waves and particles, the unified gas-kinetic wave-particle (UGKWP) method provides significant advantages for a wide range of multiscale physical problems, including hypersonic flow, plasma transport, and radiation transport. To achieve a more effective and efficient wave-particle decomposition in high-speed flow simulations, particularly in regions with drastic scale variations, this work investigates a scale-adaptive criterion and introduces modifications to the flux evolution of the UGKWP method. In addition to the intrinsic time-based criterion embedded in the time-dependent distribution function of UGKWP, two further criteria-based on spatial resolution and local gradients–are employed to identify the local scale and reduce the computational overhead of particles in representing near-equilibrium gas distributions. Furthermore, by aligning the evolution of hydrodynamic waves with the coefficients in the time–integration flux of the unified gas-kinetic scheme (UGKS), the modified wave representation improves consistency with particle contributions, which is especially critical when flow scales vary significantly across computational cells. The effectiveness of the adaptive UGKWP method is demonstrated through a series of benchmark cases, including hypersonic flows around a cylinder at various inflow Knudsen numbers, hypersonic flow over a slender cavity, side-jet impingement in hypersonic flow, and three-dimensional hypersonic flows over a 70^∘ blunted cone with a cylindrical sting.

统一气动波粒（UGKWP）方法直接模拟离散空间中的物理规律，并能自动分解流体动力波粒，为高超声速流动、等离子体输运、辐射输运等广泛的多尺度物理问题提供了显著的优势。为了在高速流动模拟中实现更有效的波粒分解，特别是在尺度变化较大的地区，本文研究了一种尺度自适应准则，并对UGKWP方法的通量演化进行了修改。除了嵌入UGKWP时变分布函数中的固有时变准则外，还采用了基于空间分辨率和局部梯度的两个准则来识别局部尺度，并减少了粒子在表示近平衡气体分布时的计算开销。此外，通过将水动力波的演变与统一气体动力学格式（UGKS）的时间积分通量系数对齐，改进的波表示提高了与颗粒贡献的一致性，这在不同计算单元之间的流动尺度差异很大时尤为重要。自适应UGKWP方法的有效性通过一系列基准案例得到了证明，这些案例包括以不同努森数流入的高超声速绕圆柱体流动、在细长腔体上的高超声速流动、高超声速流动中的侧向射流撞击，以及在70°钝化圆锥体上的三维高超声速流动。

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引用次数: 0

Grid resolution requirements for DNS of shock/boundary-layer interactions 激波/边界层相互作用DNS的网格分辨率要求

IF 3 3区工程技术 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computers & Fluids

Pub Date : 2025-11-04 DOI: 10.1016/j.compfluid.2025.106892

Alessandro Ceci , Andrea Palumbo , Sergio Pirozzoli

Direct Numerical Simulation (DNS) of shock-boundary-layer interactions (SBLI) is critical for accurate prediction of turbulence, heat transfer, and separation in high-speed flows. One of the main challenges is selecting a grid resolution that properly resolves both pre- and post-interaction states while maintaining computational efficiency. This study systematically examines the impact of grid resolution on DNS accuracy, with particular focus on the post-interaction region, where turbulence length scales undergo a dramatic reduction-especially under hypersonic flow conditions. Through a series of high-fidelity simulations using grids of increasing resolution, we quantify the consequences of under-resolution on turbulence statistics, skin friction, and heat transfer, and demonstrate that classical DNS criteria remain applicable in SBLI once the viscous length scale reduction across the shock is properly accounted for. To support mesh design, we propose and validate a simple predictive scaling law, based solely on inviscid flow quantities, that estimates this reduction and thus enables a priori resolution requirements to be determined across different configurations. These results go beyond confirming the need for fine grids, providing a predictive tool to guide future DNS and wall-modeled LES of hypersonic SBLI.

激波边界层相互作用（SBLI）的直接数值模拟（DNS）对于准确预测高速流动中的湍流、传热和分离至关重要。其中一个主要的挑战是选择一种网格分辨率，在保持计算效率的同时，适当地解决前交互和后交互状态。本研究系统地考察了网格分辨率对DNS精度的影响，特别关注了相互作用后区域，其中湍流长度尺度经历了显着减少-特别是在高超声速流动条件下。通过一系列使用增加分辨率网格的高保真度模拟，我们量化了分辨率不足对湍流统计、表面摩擦和传热的影响，并证明了经典的DNS标准在SBLI中仍然适用，一旦在激波上的粘性长度尺度减小得到了适当的考虑。为了支持网格设计，我们提出并验证了一个简单的预测缩放定律，该定律仅基于无粘流量，可以估计这种减少，从而可以在不同的配置中确定先验的分辨率要求。这些结果不仅证实了对精细网格的需求，还为指导未来高超声速SBLI的DNS和壁面建模LES提供了预测工具。

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引用次数: 0

A generalized Active Flux method of arbitrarily high order in two dimensions 二维任意高阶的广义有源通量方法

IF 3 3区工程技术 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computers & Fluids

Pub Date : 2025-11-04 DOI: 10.1016/j.compfluid.2025.106886

Wasilij Barsukow , Praveen Chandrashekar , Christian Klingenberg , Lisa Lechner

The Active Flux method can be seen as an extended finite volume method. The degrees of freedom of this method are cell averages, as in finite volume methods, and in addition shared point values at the cell interfaces, giving rise to a globally continuous reconstruction. Its classical version was introduced as a one-stage fully discrete, third-order method. Recently, a semi-discrete version of the Active Flux method was presented with various extensions to arbitrarily high order in one space dimension. In this paper we extend the semi-discrete Active Flux method on two-dimensional Cartesian grids to arbitrarily high order, by including moments as additional degrees of freedom (hybrid finite element–finite volume method). The stability of this method is studied for linear advection. For a fully discrete version, using an explicit Runge-Kutta method, a CFL restriction is derived. We end by presenting numerical examples for hyperbolic conservation laws.

主动通量法可以看作是一种扩展的有限体积法。与有限体积法一样，该方法的自由度是单元平均值，并且在单元界面处共享点值，从而产生全局连续重建。它的经典版本是作为一阶完全离散的三阶方法引入的。近年来，提出了一种半离散版本的有源通量法，并在一维空间上进行了各种扩展，达到任意高阶。本文通过将矩作为附加自由度（有限元-有限体积混合法），将二维笛卡尔网格上的半离散有源通量法扩展到任意高阶。研究了该方法对线性平流的稳定性。对于完全离散的版本，使用显式龙格-库塔方法，导出了CFL限制。最后，我们给出双曲守恒定律的数值例子。

引用次数: 0