Journal of Computational Physics最新文献_第7页

Improved phase field model for two-phase incompressible flows: Sharp interface limit, universal mobility and surface tension calculation 改进的两相不可压缩流相场模型：锐界面极限、通用迁移率和表面张力计算

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

Journal of Computational Physics

Pub Date : 2025-12-30 DOI: 10.1016/j.jcp.2025.114638

Jing-Wei Chen, Chun-Yu Zhang, Hao-Ran Liu, Hang Ding

In this paper, we propose an improved phase field model for interface capturing in simulating two-phase incompressible flows. The model incorporates a second-order diffusion term, which utilizes a nonlinear coefficient to assess the degree of deviation of interface profile from its equilibrium state. In particular, we analyze the scale of the mobility in the model, to ensure that the model asymptotically approaches the sharp interface limit as the interface thickness approaches zero. For accurate calculations of surface tension, we introduce a generalized form of smoothed Dirac delta functions that can adjust the thickness of the tension layer, while strictly maintaining that its integral equals one, even when the interface profile is not in equilibrium. Furthermore, we theoretically demonstrate that the ‘spontaneous shrinkage’ of under-resolved interface structures encountered in the Cahn-Hilliard phase field method does not occur in the improved phase field model. Through various numerical experiments, we determine the range of the optimal mobility, confirm the theoretical analysis of the improved phase field model, verify its convergence, and examine the performance of different surface tension models. The numerical experiments include Rayleigh-Taylor instability, axisymmetric rising bubbles, droplet migration due to the Marangoni effect, partial coalescence of a droplet into a pool, oscillating sessile droplet, and deformation of three-dimensional droplet in shear flow. In all these cases, numerical results are validated against experimental data and/or theoretical predictions. Moreover, the recommended range of dimensionless mobility (

1 / P e \sim 100 C n^{2} - 333 C n^{2}

) has been shown to be universal, as it can be effectively applied to the simulations of a wide range of two-phase flows and exhibits excellent performance.

本文提出了一种改进的相场模型，用于模拟两相不可压缩流的界面捕获。该模型引入了一个二阶扩散项，利用非线性系数来评价界面轮廓偏离平衡状态的程度。特别地，我们分析了模型中迁移率的尺度，以确保模型在界面厚度趋近于零时渐近于锐界面极限。为了精确计算表面张力，我们引入了一种广义形式的光滑狄拉克函数，它可以调整张力层的厚度，同时严格保持其积分等于1，即使在界面轮廓不平衡的情况下。此外，我们从理论上证明了Cahn-Hilliard相场方法中遇到的未分解界面结构的“自发收缩”不会发生在改进的相场模型中。通过各种数值实验，确定了最优迁移率范围，验证了改进相场模型的理论分析，验证了其收敛性，并检验了不同表面张力模型的性能。数值实验包括瑞利-泰勒不稳定性、轴对称上升气泡、马兰戈尼效应引起的液滴迁移、液滴局部聚并成池、无根液滴振荡、三维液滴剪切变形等。在所有这些情况下，数值结果与实验数据和/或理论预测相对照。此外，推荐的无量纲迁移率范围（1/Pe ~ 100Cn2−333Cn2）已被证明是通用的，因为它可以有效地应用于大范围的两相流的模拟，并表现出优异的性能。

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引用次数: 0

Learning non-separable Hamiltonian systems with pseudo-symplectic neural network 用伪辛神经网络学习不可分哈密顿系统

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

Journal of Computational Physics

Pub Date : 2025-12-29 DOI: 10.1016/j.jcp.2025.114630

Xupeng Cheng , Lijin Wang , Yanzhao Cao , Chen Chen

Hamiltonian systems are fundamental and crucial in both classical and quantum mechanics. Extracting governing differential equations of Hamiltonian systems from observed data can enhance understanding complex systems and predict their dynamical behavior, compensating the limitations of first-principle-modeling. Recent research on data-based neural network detection of Hamiltonian systems has focused on structure-preserving learning that incorporates the intrinsic properties such as the symplecticity into the neural network architecture. However, these approaches either apply only to separable Hamiltonian systems, or to non-separable ones but require more complex computational tools such as dimension augmentation and implicit prediction. In this paper we propose a novel one layer explicit Pseudo-Symplectic Neural Network (PSNN) model for learning non-separable Hamiltonian systems. To enhance the accuracy of neural network simulation and compensate the loss of accuracy due to non-exact symplecticity, we design the learnable Padé-type activation function for neural network output. With shorter training period, smaller sample size and fewer network parameters, we demonstrate through numerical experiments that the proposed PSNN model with Padé-type activation is versatile in learning and forecasting a wide array of Hamiltonian systems, surpassing benchmark neural networks including the ODE-net, HNN, SympNets, NSSNN and Taylor-net, in terms of prediction accuracy, long-term stability and energy-preservation.

哈密顿系统在经典力学和量子力学中都是基础和关键的。从观测数据中提取哈密顿系统的控制微分方程可以增强对复杂系统的理解和预测其动力学行为，弥补第一原理建模的局限性。近年来，基于数据的神经网络哈密顿系统检测的研究主要集中在结构保持学习上，该学习将辛性等固有特性融入到神经网络结构中。然而，这些方法要么只适用于可分哈密顿系统，要么适用于不可分哈密顿系统，但需要更复杂的计算工具，如维增和隐式预测。本文提出了一种新的一层显式伪辛神经网络（PSNN）模型，用于学习不可分哈密顿系统。为了提高神经网络仿真的精度，弥补非精确辛性导致的精度损失，我们设计了可学习的padsami型激活函数作为神经网络输出。通过数值实验，我们证明了PSNN模型具有更短的训练周期、更小的样本量和更少的网络参数，在学习和预测广泛的哈密顿系统方面是通用的，在预测精度、长期稳定性和能量保存方面超过了基准神经网络，包括ODE-net、HNN、SympNets、NSSNN和Taylor-net。

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引用次数: 0

Uncertainty quantification and stability of neural operators for prediction of three-dimensional turbulence 三维湍流预测神经算子的不确定性量化与稳定性

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

Journal of Computational Physics

Pub Date : 2025-12-28 DOI: 10.1016/j.jcp.2025.114640

Xintong Zou , Zhijie Li , Yunpeng Wang , Huiyu Yang , Jianchun Wang

The uncertain and chaotic nature of turbulence poses significant challenges for numerical simulation, particularly in capturing multiscale dynamics and managing high computational costs. Conventional numerical methods with turbulence modeling face limitations in accuracy, long-term stability, and efficiency, especially in complex physical scenarios. Recent advances in scientific machine learning (SciML), including surrogate models such as the Fourier neural operator (FNO), have shown promise in solving partial differential equations (PDEs). FNO-based models typically adopt a one-step-ahead prediction framework, where the model predicts the system state at the next time step based solely on the current state. However, many of these models primarily focus on short-term pointwise accuracy and often struggle to maintain stability over long temporal horizons, particularly in three-dimensional turbulent flows. To evaluate the reliability of neural operator approaches in general turbulent flow problems, this paper presents a theoretical framework for assessing the trustworthiness and robustness of neural operator models. Three-dimensional forced homogeneous isotropic turbulence (HIT) is employed as a representative example to demonstrate and validate the proposed methodology. Uncertainty quantification (UQ) is conducted to assess predictive variability across different time resolutions and spatial Fourier modes, where the statistical distributions of prediction errors are utilized to compare the performance and reliability of different models. Stability is further assessed from a statistical perspective, focusing on error propagation through time-marching and sensitivity to initial perturbations. Notably, certain FNO-based models demonstrate superior statistical stability compared to conventional large eddy simulation (LES) methods. The autocorrelation function (ACF) is utilized to explore the connection between temporal coherence in the flow field and the reliability of model predictions. The results demonstrate that the proposed factorized-implicit FNO (F-IFNO) offers a trade-off between accuracy, long-term stability, and computational efficiency, outperforming conventional numerical solvers and other FNO-based models. In particular, modifying the one-step-ahead paradigm through implicit factorization helps mitigate error accumulation and enhances long-term prediction capability. The findings underscore that incorporating prediction constraints and selecting appropriate time intervals are crucial for enhancing the robustness and reliability of FNO-based models. The study highlights the importance of UQ, stability, and temporal correlation in the development of robust operator learning frameworks for turbulent flows and other multi-scale nonlinear dynamic systems.

湍流的不确定性和混沌性对数值模拟提出了重大挑战，特别是在捕获多尺度动力学和管理高计算成本方面。传统的湍流数值模拟方法在精度、长期稳定性和效率方面存在局限性，特别是在复杂的物理场景下。科学机器学习（SciML）的最新进展，包括替代模型，如傅立叶神经算子（FNO），在求解偏微分方程（PDEs）方面显示出了希望。基于fno的模型通常采用一步前预测框架，其中模型仅根据当前状态预测下一个时间步的系统状态。然而，许多这些模型主要关注短期的点精度，往往难以保持长期的稳定性，特别是在三维湍流中。为了评估神经算子方法在一般湍流问题中的可靠性，本文提出了一个评估神经算子模型可信度和鲁棒性的理论框架。以三维强迫均匀各向同性湍流（HIT）为例，对所提出的方法进行了验证。不确定性量化（UQ）用于评估不同时间分辨率和空间傅里叶模式下的预测变异性，其中预测误差的统计分布用于比较不同模型的性能和可靠性。从统计角度进一步评估稳定性，重点关注通过时间行进的误差传播和对初始扰动的敏感性。值得注意的是，与传统的大涡模拟（LES）方法相比，某些基于fno的模型显示出优越的统计稳定性。利用自相关函数（ACF）探讨了流场时间相干性与模型预测可靠性之间的关系。结果表明，所提出的分解隐式FNO （F-IFNO）提供了精度，长期稳定性和计算效率之间的权衡，优于传统的数值求解器和其他基于FNO的模型。特别是，通过隐式因式分解修改一步先行范式有助于减少错误积累并增强长期预测能力。研究结果强调，纳入预测约束和选择适当的时间间隔对于提高基于fno的模型的鲁棒性和可靠性至关重要。该研究强调了UQ、稳定性和时间相关性在开发湍流和其他多尺度非线性动态系统的鲁棒算子学习框架中的重要性。

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引用次数: 0

Adaptive sampling accelerates the hybrid deviational particle simulations 自适应采样加速了混合偏差粒子模拟

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

Journal of Computational Physics

Pub Date : 2025-12-27 DOI: 10.1016/j.jcp.2025.114616

Zhengyang Lei, Sihong Shao

To avoid ineffective collisions between the equilibrium states, the hybrid method with deviational particles (HDP) has been proposed to integrate the Vlasov-Poisson-Landau system, while leaving a new issue in sampling deviational particles from the high-dimensional source term. In this paper, we present an adaptive sampling (AS) strategy that first adaptively reconstructs a piecewise constant approximation of the source term based on sequential clustering via discrepancy estimation, and then samples deviational particles directly from the resulting adaptive piecewise constant function without rejection. The mixture discrepancy, which can be easily calculated thanks to its explicit analytical expression, is employed as a measure of uniformity instead of the star discrepancy the calculation of which is NP-hard. The resulting method, dubbed the HDP-AS method, samples deviational particles through adaptive sampling instead of the acceptance-rejection method in the original HDP method. In the Landau damping, two stream instability, bump on tail and Rosenbluth’s test problems, the HDP-AS method runs approximately ten times faster than the HDP method while keeping the same accuracy.

为了避免平衡态之间的无效碰撞，提出了带有偏差粒子的混合方法（HDP）来整合Vlasov-Poisson-Landau系统，但留下了从高维源项中采样偏差粒子的新问题。在本文中，我们提出了一种自适应采样（AS）策略，该策略首先通过差异估计自适应重构源项的分段常数近似，然后直接从产生的自适应分段常数函数中采样偏离粒子而不拒绝。混合差由于其明确的解析表达式而易于计算，因此被用作均匀性的度量，而不是计算np困难的星差。由此产生的方法被称为HDP- as方法，通过自适应采样来采样偏离粒子，而不是原HDP方法中的接受-拒绝方法。在Landau阻尼、两流不稳定性、尾部碰撞和Rosenbluth的测试问题中，HDP- as方法的运行速度比HDP方法快10倍左右，同时保持相同的精度。

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引用次数: 0

A sharp cartesian grid method for simulating flow past viscous droplets of arbitrary shape and viscosity 一种模拟流过任意形状和粘度的粘性液滴的锐笛卡尔网格方法

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

Journal of Computational Physics

Pub Date : 2025-12-27 DOI: 10.1016/j.jcp.2025.114632

Bo-Lin Wei , Jie Zhang , Ming-Jiu Ni

We present a sharp Cartesian grid method for simulating flow past viscous droplets of arbitrary shape and viscosity. The method proposes a height function approach to compute the Weingarten matrix, enabling the accurate estimation of principal curvatures and directions on discretized curved interfaces of the droplet. These geometric quantities are then used to impose space- and time-dependent slip conditions at the interface. The incompressible Navier-Stokes equations are solved separately in the internal and external domains and coupled through the slip conditions using an embedded boundary method coupled with a synchronous iterative approach, ensuring a sharp representation of the interface. A key innovation of this approach is its ability to handle droplets with arbitrary geometries, including complex topologies imported directly from STL files, eliminating the need for analytical interface descriptions. By operating on a Cartesian grid, the method offers enhanced flexibility while preserving sharp interfacial dynamics. Numerical validation demonstrates the method’s accuracy and robustness. The height function approach is shown to reliably compute principal curvatures and directions, while simulations of flow past spheroidal droplets - spanning inviscid bubbles to rigid particles - exhibit excellent agreement with body-fitted benchmark solutions. Further, simulations of popcorn- and blob-shaped droplets highlight the method’s versatility in handling arbitrarily complex interfaces. This solver provides a powerful and flexible tool for investigating interfacial flow phenomena involving droplets with irregular geometries and viscosity variations.

我们提出了一种精确的笛卡尔网格方法来模拟任意形状和粘度的粘性液滴的流动。该方法采用高度函数法计算Weingarten矩阵，能够准确估计液滴离散曲面界面上的主曲率和方向。然后使用这些几何量在界面上施加与空间和时间相关的滑移条件。不可压缩的Navier-Stokes方程在内外域中分别求解，并通过滑移条件进行耦合，采用内嵌边界法与同步迭代法相结合，保证了界面的清晰表示。该方法的一个关键创新之处在于它能够处理任意几何形状的液滴，包括直接从STL文件导入的复杂拓扑，从而消除了对分析接口描述的需求。通过在笛卡尔网格上操作，该方法提供了增强的灵活性，同时保持了尖锐的界面动力学。数值验证验证了该方法的准确性和鲁棒性。高度函数方法被证明可以可靠地计算主曲率和方向，而通过球体液滴的流动模拟-跨越无粘气泡到刚性颗粒-与体贴合基准解表现出极好的一致性。此外，爆米花状和斑点状液滴的模拟突出了该方法在处理任意复杂界面方面的通用性。该求解器为研究具有不规则几何形状和粘度变化的液滴的界面流动现象提供了一个强大而灵活的工具。

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引用次数: 0

Efficient numerical integration for finite element trunk spaces in 2D and 3D using machine learning: A new optimisation paradigm to construct application-Specific quadrature rules 利用机器学习对二维和三维有限元主干空间进行有效的数值集成：构建特定应用正交规则的新优化范例

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

Journal of Computational Physics

Pub Date : 2025-12-27 DOI: 10.1016/j.jcp.2025.114634

Tomas Teijeiro , Pouria Behnoudfar , Jamie M. Taylor , David Pardo , Victor M. Calo

Finite element methods usually construct basis functions and quadrature rules for multidimensional domains via tensor products of one-dimensional counterparts. While straightforward, this approach results in integration spaces larger than necessary, especially as the polynomial degree p or the spatial dimension increases, leading to considerable and avoidable computational overhead. This work starts from the hypothesis that reducing the dimensionality of the polynomial space can lead to quadrature rules with fewer points and lower computational cost, while preserving the exactness of numerical integration. We use trunk spaces that exclude high-degree monomials that do not improve the approximation quality of the discrete space. These reduced spaces retain sufficient expressive power and allow us to construct smaller (more economical) integration domains. Given a maximum degree p, we define trial and test spaces U and V as 2D or 3D trunk spaces and form the integration space

S = U \otimes V

.We then construct exact quadrature rules by solving a non-convex optimisation problem over the number of points q, their coordinates, and weights. We use a shallow neural network with linear activations to parametrise the rule, and a random restart strategy to mitigate the risk of converging to poor local minima. When necessary, we dynamically increase q to achieve exact integration. Our construction reaches machine-precision accuracy (errors below

10^{- 22}

) using significantly fewer points than standard tensor-product Gaussian quadrature: up to 30% reduction in 2D for p ≤ 10, and 50% in 3D for p ≤ 6. These results show that combining the mathematical understanding of polynomial structure with numerical optimisation can lead to a practical and extensible methodology for improving the adaptiveness, efficiency, and scalability of quadrature rules for high-order finite element simulations.

有限元法通常通过一维域的张量积来构造多维域的基函数和正交规则。虽然简单，但这种方法会导致积分空间比必要的大，特别是当多项式度p或空间维度增加时，这会导致相当大的可避免的计算开销。本工作的出发点是假设降低多项式空间的维数可以得到点更少、计算成本更低的正交规则，同时保持数值积分的准确性。我们使用排除不能改善离散空间近似质量的高次单项式的主干空间。这些简化的空间保留了足够的表现力，并允许我们构建更小（更经济）的集成域。在给定最大度p的情况下，我们将试验和测试空间U和V定义为二维或三维主干空间，形成了积分空间S=U⊗V。然后，我们通过解决一个关于点的数量q、它们的坐标和权重的非凸优化问题来构建精确的正交规则。我们使用具有线性激活的浅神经网络来参数化规则，并使用随机重启策略来降低收敛到较差的局部最小值的风险。必要时，我们动态地增加q以达到精确积分。我们的构造使用比标准张量积高斯正交更少的点达到机器精度（误差低于10−22）：p ≤ 10时，2D减少30%，p ≤ 6时，3D减少50%。这些结果表明，将多项式结构的数学理解与数值优化相结合，可以产生一种实用且可扩展的方法，用于提高高阶有限元模拟的正交规则的适应性、效率和可扩展性。

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引用次数: 0

FieldTNN-based machine learning method for Maxwell eigenvalue problems 基于fieldtnn的Maxwell特征值问题机器学习方法

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

Journal of Computational Physics

Pub Date : 2025-12-26 DOI: 10.1016/j.jcp.2025.114605

Jiantao Jiang , Yanli Wang , Yifan Wang , Hehu Xie

The aim of this paper is to introduce a FieldTNN-based machine learning method for solving the Maxwell eigenvalue problem in both 2D and 3D domains, including tensor and non-tensor computational regions. First, we extend the existing TNN-based approach to the Maxwell eigenvalue problem, a fundamental challenge in electromagnetic field theory. Second, we extend the existing TNN framework to non-tensor computational domains, this is a novel and significant contribution of this work. Third, we incorporate the divergence-free constraint into the optimization process, allowing the automatic filtering of spurious eigenpairs. Numerical examples are presented to demonstrate the efficiency and accuracy of our algorithm, underscoring its potential for broader applications in computational electromagnetics.

本文的目的是介绍一种基于fieldtnn的机器学习方法，用于解决二维和三维域中的Maxwell特征值问题，包括张量和非张量计算区域。首先，我们将现有的基于tnn的方法扩展到麦克斯韦特征值问题，这是电磁场理论中的一个基本挑战。其次，我们将现有的TNN框架扩展到非张量计算域，这是本工作的一个新颖而重要的贡献。第三，我们将无散度约束纳入优化过程，允许虚假特征对的自动过滤。数值例子证明了我们的算法的效率和准确性，强调了它在计算电磁学中更广泛应用的潜力。

引用次数: 0

Topology optimization of actively moving rigid bodies in unsteady flows via grid separation 非定常流动中主动运动刚体的网格分离拓扑优化

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

Journal of Computational Physics

Pub Date : 2025-12-26 DOI: 10.1016/j.jcp.2025.114620

Yuta Tanabe , Kentaro Yaji , Kuniharu Ushijima

This study proposes a novel topology optimization method for unsteady fluid flows induced by actively moving rigid bodies. The key idea of the proposed method is to decouple the design and analysis domains by using separate grids. The design grid undergoes rigid body motion and is then overlapped onto the analysis grid. After the overlap, key quantities such as the Brinkman coefficient are transferred between the grids. This approach provides a direct and efficient means of representing object motion and facilitates the handling of more general and complex movements in unsteady flow conditions. Since the computational cost of solving unsteady fluid problems is substantial, we employ a solver based on the lattice kinetic scheme, which is the extended version of the lattice Boltzmann method, to evaluate the design sensitivity. The fundamental equations are derived, and the accuracy of the design sensitivity calculations is validated through comparison with finite difference approximations. The effectiveness of the method is demonstrated through numerical examples in two-dimensional and three-dimensional settings.

针对主动运动刚体引起的非定常流体流动，提出了一种新的拓扑优化方法。该方法的关键思想是通过使用单独的网格来解耦设计和分析域。设计网格经过刚体运动，然后重叠到分析网格上。重叠后，布林克曼系数等关键量在网格之间传递。这种方法提供了一种直接而有效的表示物体运动的方法，并有助于处理非定常流条件下更一般和更复杂的运动。由于求解非定常流体问题的计算成本很大，我们采用基于晶格动力学格式的求解器，即晶格玻尔兹曼方法的扩展版本，来评估设计灵敏度。推导了基本方程，并通过与有限差分近似的比较验证了设计灵敏度计算的准确性。通过二维和三维的数值算例验证了该方法的有效性。

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引用次数: 0

The tailored finite point scheme based on flux conservation for singularly perturbed eigenvalue problems 奇异摄动特征值问题的基于通量守恒的定制有限点格式

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

Journal of Computational Physics

Pub Date : 2025-12-25 DOI: 10.1016/j.jcp.2025.114628

Wang Kong , Zhongyi Huang

In this paper, we propose a new tailored finite point scheme to solve the singularly perturbed eigenvalue problem (SPEP), which arises in describing the semiclassical limit of the spectrum for the Schrödinger operator. However, the multi-scale structure of the eigenfunctions makes it difficult to solve these problems efficiently. With the idea of the tailored finite point method (TFPM), we employ a local linear approximation of the potential function and derive a local general solution representation for the resulting approximate equation. This enables a decomposition of the eigenfunctions into a linear combination of grid point values within each local region. For the one-dimensional case, a three-point nonlinear scheme is constructed based on the flux conservation at grid points. We rigorously prove that this scheme achieves second-order convergence uniformly with respect to the small parameter ε. In the two-dimensional case, by incorporating the finite volume scheme, we establish a flux conservation relationship in the vicinity of each grid point, leading to a five-point scheme for solving the two-dimensional SPEP. Finally, some numerical examples are given to demonstrate the validity of TFPM scheme and the correctness of theoretical analysis.

本文提出了一种新的定制有限点格式来解决描述Schrödinger算子谱的半经典极限时出现的奇异摄动特征值问题（SPEP）。然而，特征函数的多尺度结构给这些问题的有效求解带来了困难。利用定制有限点法（TFPM）的思想，我们采用势函数的局部线性逼近，并推导出所得近似方程的局部通解表示。这样可以将特征函数分解为每个局部区域内网格点值的线性组合。对于一维情况，基于网格点的通量守恒构造了一个三点非线性格式。我们严格地证明了该格式对小参数ε达到一致的二阶收敛性。在二维情况下，通过引入有限体积格式，我们在每个网格点附近建立了通量守恒关系，从而得到求解二维SPEP的五点格式。最后，通过数值算例验证了TFPM格式的有效性和理论分析的正确性。

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引用次数: 0

Sub-filter-scale (SFS) compressible turbulence modeling and shock capturing via the Block-Spectral-Stress (BSS) closure 子滤波尺度（SFS）可压缩湍流建模和冲击捕获通过块谱应力（BSS）关闭

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

Journal of Computational Physics

Pub Date : 2025-12-25 DOI: 10.1016/j.jcp.2025.114611

Matteo Ruggeri , Victor~C. B. Sousa , Carlo Scalo

A new Block-Spectral-Stress (BSS) sub-filter-scale (SFS) closure combining turbulence modeling and shock-capturing has been developed for flux-reconstruction numerics improving upon an earlier formulation named Legendre Spectral Viscosity or LSV (Sousa and Scalo, J. Comput. Phys. 2022, Vol 460). The BSS method relies on the Legendre spectral representation of the velocity gradients to estimate the SFS kinetic energy, used to compute the SFS momentum stresses, heat-flux, and pressure-work, based on the resolved field. The method is able to capture shocks in one-dimension with numerical order up to 20, with good agreement between a posteriori and exact SFS stresses. The same approach is able to adequately preserve the hydrodynamic structure of a vortex impinging on a Mach 1.5 shock in two dimensions and overcome symmetry violations and lack of Galilean invariance of the previous LSV method. Also, unlike LSV, BSS removes the need for explicit spectral modulations of the modeled SFS fluxes. It has been tested in three-dimensional turbulent calculations where it is compared against the Smagorinsky, dynamic Smagorinsky, and Vreman models, all adapted to flux reconstruction numerics. In subsonic and supersonic Taylor-Green Vortex calculations, the BSS model loses accuracy on coarse meshes (i.e. fewer mesh cells), while surpassing other closures on finer ones, making the increasing of polynomial order not advantageous. The same behavior was noticed also in a supersonic Taylor-Green Vortex test case; instead, in fully developed supersonic and hypersonic turbulent channel flow the opposite is observed, where a posteriori predictions improve with increasing polynomial order. BSS has proven to be versatile in achieving both shock capturing and turbulence modeling with no case-specific tuning of coefficients, while not necessarily being the best performing closure for anyone particular test case.

一种新的块谱应力（BSS）子滤波尺度（SFS）闭合结合了湍流建模和冲击捕获，用于通量重建数值，改进了早期的公式，称为勒让德谱粘度或LSV （Sousa和Scalo， J. Comput）。物理学。2022，卷460)。BSS方法依靠速度梯度的Legendre谱表示来估计SFS动能，用于计算基于解析场的SFS动量应力、热通量和压力功。该方法能够捕获一维冲击，其数值顺序高达20，后检和精确的SFS应力之间具有良好的一致性。同样的方法能够在二维上充分地保留撞击1.5马赫激波的涡旋的水动力结构，克服了以往LSV方法的对称性违反和伽利略不变性的不足。此外，与LSV不同，BSS不需要对模拟的SFS通量进行显式的光谱调制。它已经在三维湍流计算中进行了测试，并与Smagorinsky、动态Smagorinsky和freeman模型进行了比较，这些模型都适用于通量重建数值。在亚音速和超音速Taylor-Green Vortex计算中，BSS模型在粗网格（即较少的网格单元）上失去精度，而在细网格上优于其他闭包，使得多项式阶数的增加不有利。在一个超音速Taylor-Green Vortex测试案例中也注意到了同样的行为；相反，在完全发展的超音速和高超音速湍流通道流动中，观察到相反的情况，其中后测预测随着多项式阶数的增加而改善。事实证明，BSS在实现冲击捕获和湍流建模方面是通用的，无需特定情况下的系数调整，而不一定是任何特定测试用例的最佳性能关闭。

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