Computers & Fluids最新文献_第5页

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 : 2026-02-15 Epub 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

A Markov matrix iterative splitting algorithm for incompressible flow 不可压缩流的马尔可夫矩阵迭代分裂算法

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

Computers & Fluids

Pub Date : 2026-02-15 Epub Date: 2025-12-15 DOI: 10.1016/j.compfluid.2025.106943

Manuel A. Ramirez-Cabrera , Eduardo Ramos , Manira E. Narvaez-Saucedo , Patricio J. Valades-Pelayo

We present a Monte Carlo method for the incompressible Navier-Stokes equations, enforcing divergence-free solutions through a probabilistic projection framework. Using short random walks embedded in Markov matrices, the method sequentially solves diffusion, convection, and pressure projection steps at each timestep. The method achieves near-linear CPU scaling (O(N^1.18)) for transient simulations through pre-computed transition probability matrices for linear operators, with Multi-Level Monte Carlo acceleration improving steady-state convergence to (O(N^1.58)). Validation on lid-driven cavity flows (Re=100, 1000) shows differences below 3 % versus benchmarks. Additionally, the mesh-free nature of the Monte Carlo approach handles complex geometries simply by tagging random walkers within non-conforming obstacles, bypassing traditional meshing requirements. The method combines accuracy, unconditional stability, and inherent parallelizability, offering a compelling alternative to deterministic approaches.

我们提出了不可压缩Navier-Stokes方程的蒙特卡罗方法，通过概率投影框架强制无散度解。使用嵌入在马尔可夫矩阵中的短随机漫步，该方法在每个时间步上依次解决扩散，对流和压力投影步骤。该方法通过预先计算线性算子的转移概率矩阵，实现暂态模拟的近线性CPU缩放（O(N1.18)），多级蒙特卡罗加速将稳态收敛提高到（O(N1.58)）。对盖子驱动的空腔流动（Re= 100,1000）的验证表明，与基准相比，差异低于3%。此外，蒙特卡罗方法的无网格特性仅通过在不符合障碍物内标记随机步行者来处理复杂的几何形状，绕过传统的网格划分要求。该方法结合了准确性、无条件稳定性和固有的并行性，为确定性方法提供了令人信服的替代方案。

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引用次数: 0

Tackling compressible turbulent multi-component flows with dynamic hp-adaptation 动态hp自适应处理可压缩湍流多组分流动

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

Computers & Fluids

Pub Date : 2026-02-15 Epub Date: 2025-11-26 DOI: 10.1016/j.compfluid.2025.106928

Pascal Mossier , Philipp Oestringer , Steven Jöns , Jens Keim , Catherine Mavriplis , Andrea D. Beck , Claus-Dieter Munz

In this paper, we present an hp-adaptive hybrid Discontinuous Galerkin/Finite Volume method for simulating compressible, turbulent multi-component flows. Building on a previously established hp-adaptive strategy for hyperbolic gas- and droplet-dynamics problems, this study extends the hybrid DG/FV approach to viscous flows with multiple species and incorporates non-conforming interfaces, enabling enhanced flexibility in grid generation. A central contribution of this work lies in the computation of both convective and dissipative fluxes across non-conforming element interfaces of mixed discretizations. To achieve accurate shock localization and scale-resolving representation of turbulent structures, the operator dynamically switches between an h-refined FV sub-cell scheme and a p-adaptive DG method, based on an a priori modal solution analysis. The method is implemented in the high-order open-source framework FLEXI and validated against benchmark problems, including the supersonic Taylor-Green vortex and a triplepoint shock interaction, demonstrating its robustness and accuracy for under-resolved shock-turbulence interactions and compressible multi-species scenarios. Finally, the method’s capabilities are showcased through an implicit large eddy simulation of an under-expanded hydrogen jet mixing with air, highlighting its potential for tackling challenging compressible multi-species flows in engineering.

本文提出了一种用于模拟可压缩、湍流多组分流动的自适应间断Galerkin/有限体积混合方法。在先前建立的双曲气体和液滴动力学问题的hp自适应策略的基础上，本研究将混合DG/FV方法扩展到具有多物种的粘性流动，并包含非一致性界面，从而增强了网格生成的灵活性。这项工作的核心贡献在于计算混合离散化的非协调单元界面上的对流和耗散通量。为了实现精确的激波定位和湍流结构的尺度解析表示，该算子基于先验模态解分析，在h精细FV子单元方案和p自适应DG方法之间动态切换。该方法在高阶开源框架FLEXI中实现，并针对基准问题进行了验证，包括超音速Taylor-Green涡旋和三点激波相互作用，证明了其在欠分解激波-湍流相互作用和可压缩多物种场景下的鲁棒性和准确性。最后，通过对膨胀不足的氢气射流与空气混合的隐式大涡模拟，展示了该方法的能力，突出了其在解决工程中具有挑战性的可压缩多组分流动方面的潜力。

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引用次数: 0

Data-driven regression of thermodynamic models in entropic form using physics-informed machine learning 使用物理信息机器学习的熵形式的热力学模型的数据驱动回归

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

Computers & Fluids

Pub Date : 2026-02-15 Epub Date: 2025-11-30 DOI: 10.1016/j.compfluid.2025.106932

Evert Bunschoten, Alessandro Cappiello, Matteo Pini

This article presents a data-driven method to evaluate thermodynamic properties of pure fluids and mixtures of fixed composition in the ideal- and nonideal thermodynamic states. Thermodynamic consistency is ensured by computing the fluid properties on the basis of the entropy potential and its first- and second- order derivatives, calculated with a physics-informed neural network. The computational performance of the method was investigated by implementing the resulting data-driven model in the open-source SU2 CFD software and by performing RANS simulations of the nonideal compressible flows through an organic Rankine cycle turbine cascade. Compared to using a multiparameter equation of state through a thermodynamic library coupled with SU2, the method was found to be 60 % more computationally efficient while maintaining high accuracy.

本文提出了一种数据驱动的方法来评估纯流体和固定成分混合物在理想和非理想热力学状态下的热力学性质。基于熵势及其一阶和二阶导数，通过物理信息神经网络计算流体性质，从而确保热力学一致性。通过在开源的SU2 CFD软件中实现所得到的数据驱动模型，并对有机朗肯循环涡轮叶栅中的非理想可压缩流动进行RANS模拟，研究了该方法的计算性能。结果表明，该方法在保持较高的计算精度的同时，计算效率提高了60%。

引用次数: 0

Intermittency-based transition models for different flow conditions in a high-order framework 高阶框架下不同流动条件下基于间歇的过渡模型

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

Computers & Fluids

Pub Date : 2026-02-15 Epub Date: 2025-11-24 DOI: 10.1016/j.compfluid.2025.106918

A. Crivellini , A. Ghidoni , E. Mantecca , G. Noventa

This work proposes a modified formulation of the Spalart-Allmaras and

k - \tilde{ω}

turbulence models for predicting transition in subsonic, supersonic, and hypersonic flows. Both models are algebraic and correlation-based, where the intermittency function includes corrections for pressure gradients and compressibility effects, using only local and free-stream flow conditions. Both models are implemented in a high-order discontinuous Galerkin solver, with particular attention to compressibility corrections to overcome the limitations of turbulence models in high-supersonic and hypersonic flows and/or with cold-wall conditions. The accuracy of the models is proved for turbulent and transitional flows on flat plates with different free-stream flow conditions, transition modes, and pressure gradients. Results are in agreement with experiments and high-fidelity simulations in terms of transition onset location and skin friction and/or heat transfer distribution on the plate. Both models are characterized by ease of implementation and robustness, and are suitable for high-order solvers.

这项工作提出了用于预测亚音速、超音速和高超音速流动过渡的Spalart-Allmaras和k−ω ~湍流模型的修改公式。这两种模型都是基于代数和相关性的，其中间歇函数包括压力梯度和压缩性效应的校正，仅使用局部和自由流动条件。这两个模型都是在高阶不连续伽辽金解算器中实现的，特别注意可压缩性修正，以克服高超音速和高超音速流动和/或冷壁条件下湍流模型的局限性。对不同自由流动条件、过渡模式和压力梯度的平板湍流和过渡流动，验证了模型的准确性。结果与实验和高保真模拟在过渡开始位置和板上的皮肤摩擦和/或传热分布方面一致。这两种模型都具有易于实现和鲁棒性强的特点，适用于高阶求解器。

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引用次数: 0

Effect of wall-collision models on the transport of rigid, elongated non-spherical particles in a turbulent channel flow using an Euler/Lagrange approach 用欧拉/拉格朗日方法研究了壁面碰撞模型对湍流通道中刚性、细长非球形颗粒输运的影响

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

Computers & Fluids

Pub Date : 2026-02-15 Epub Date: 2025-12-04 DOI: 10.1016/j.compfluid.2025.106940

Manuel A. Taborda, Martin Sommerfeld

The present contribution focuses on an extended modelling of elongated, non-spherical particle transport in wall-bounded, particle-laden flows. A turbulent channel flow is considered using a point-particle Euler/Lagrange framework, with the fluid phase computed by a numerically filtered, scale-resolving approach. The developed method for inertial fibres was implemented in OpenFOAM^Ⓡ, neglecting two-way coupling. Particle tracking with respect to translation and rotation is conducted in different frames of reference which are transformed through the use of quaternions, so that the fibre centroid position and orientation are known along their trajectory. Aerodynamic resistance coefficients for drag, lift, and torque are taken from correlations dependent on fibre orientation at an aspect ratio of five. Wall collisions of fibres are treated with an extended hard-body collision model that includes fibre orientation and the actual contact point. By solving the impulse equations with the parameters for restitution ratio and Coulomb friction coefficient the momentum loss was modelled. The flow validation was carried out against DNS data for a turbulent channel. Particular consideration was focused on the fibre-wall interactions, comparing the extended model with reduced approaches, such as centre-of-gravity specular reflection and spherical particle wall collision for the same equivalent diameter. The results highlight the important role of realistic wall-collision modelling. Accounting for the actual fibre-wall contact point leads to significantly different predictions of near-wall mean concentration, particle flux, and orientation profiles. In particular, fibre tilting during wall interactions enhances wall contact, increasing collision rates and modifying rebound angles compared to simplified models.

目前的贡献集中在拉长，非球形颗粒输运的扩展模型在壁界，颗粒负载流。紊流通道流动采用点粒子欧拉/拉格朗日框架，流体相通过数值滤波、尺度解析方法计算。所开发的惯性光纤方法在OpenFOAMⓇ中实现，忽略了双向耦合。通过使用四元数变换，在不同的参照系中进行粒子的平移和旋转跟踪，从而知道纤维质心沿其轨迹的位置和方向。阻力、升力和扭矩的气动阻力系数取自与纤维取向相关的系数，长径比为5。采用包含纤维取向和实际接触点的扩展硬体碰撞模型处理纤维的壁面碰撞。通过求解以恢复比和库仑摩擦系数为参数的冲量方程，对动量损失进行了建模。对湍流通道的DNS数据进行了流量验证。特别考虑了纤维壁的相互作用，将扩展模型与简化方法进行了比较，例如相同等效直径的重心镜面反射和球形粒子壁碰撞。结果强调了真实的壁面碰撞建模的重要作用。考虑实际的纤维壁接触点会导致对近壁平均浓度、粒子通量和取向分布的显著不同的预测。特别是，与简化模型相比，纤维在壁面相互作用时的倾斜增强了壁面接触，增加了碰撞率并改变了回弹角。

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引用次数: 0

Leading-edge vortex monitoring in dynamically stalled flows via persistent homology 动态停滞流动中前缘涡监测的持续同源性

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

Computers & Fluids

Pub Date : 2026-02-15 Epub Date: 2025-11-29 DOI: 10.1016/j.compfluid.2025.106931

Quentin Martinez , Chetan Jagadeesh , Marinos Manolesos , Mohammad Omidyeganeh

A novel vortex core identification pipeline is developed based on template matching. Using persistent homology, a template similarity field is constructed from a sliding window template-target feature space distance. This scalar field is then used to accentuate localised regions of spanwise vorticity via nonlinear weighting. This method is successfully applied to track the leading-edge vortex trajectory in a stall flutter starting cycle for a pitching NACA 63(3)418 aerofoil. Trajectory results are compared with several user-based vortex core identifiers like local vorticity minimum, local Q-criterion maximum, local swirling strength maximum, and manual tracking. The results of this comparison are quite satisfactory as the developed method is capable of automatically monitoring the leading-edge vortex core through several critical stages of its lifecycle. The effects of template size and down sampling are also investigated with respect to the vortex core identification. It is found that a template radius of

r = 0.04 c

and down sampling factor

M = 10

are sufficient for accurate vortex core monitoring in dynamically stalled flows. In general, this method acts primarily as a field-based filter that can be useful for isolating highly vortical regions like the leading-edge vortex core in stall flutter or dynamic stall scenarios.

提出了一种基于模板匹配的涡核识别方法。利用持久同源性，从滑动窗口模板-目标特征空间距离构造模板相似域。然后用这个标量场通过非线性加权来强调展向涡度的局部区域。该方法成功地应用于NACA 63(3)418俯仰型机翼失速颤振启动周期的前缘涡轨迹跟踪。轨迹结果与几种基于用户的涡核标识符进行了比较，如局部涡量最小值、局部q准则最大值、局部旋流强度最大值和手动跟踪。该方法能够对前缘涡芯生命周期的几个关键阶段进行自动监测，比较结果令人满意。研究了模板尺寸和下采样对涡核识别的影响。研究发现，模板半径r=0.04c，下采样因子M=10足以实现动态停滞流动中涡芯的精确监测。一般来说，这种方法主要作为一种基于场的过滤器，可用于隔离高旋涡区域，如在失速颤振或动态失速情况下的前缘涡核。

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引用次数: 0

Accelerating CFD-driven training of transition and turbulence models for turbine flows by one-shot and real-time transformer integration 通过一次性和实时变压器集成加速cfd驱动的涡轮流动过渡和湍流模型的训练

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

Computers & Fluids

Pub Date : 2026-02-15 Epub Date: 2025-11-29 DOI: 10.1016/j.compfluid.2025.106927

Yuan Fang , Maximilian Reissmann , Roberto Pacciani , Yaomin Zhao , Andrew S.H. Ooi , Michele Marconcini , Harshal D. Akolekar , Richard D. Sandberg

Recent studies have demonstrated the effectiveness of applying the computational fluid dynamics (CFD)-driven symbolic machine learning (ML) frameworks to assist in the development of explicit physical models within Reynolds-averaged Navier-Stokes (RANS), particularly for modeling transition, turbulence, and heat flux. These approaches can yield improved flow predictions with marginal increase in computational cost compared to baseline models. Nevertheless, a key limitation lies in the substantial computational expense during the training phase, which often requires thousands of RANS evaluations. This challenge becomes severe in training models for complex industrial applications, where each RANS run is computationally intensive, and is further exacerbated when attempting to develop more generalizable and coupled multiple models across multiple product designs. Take the development of general transition and turbulence model corrections for both low- and high-pressure turbines as the study case, this work introduces two transformer-assisted strategies to accelerate model training. In the first, previously trained models are stored and used as inputs to the transformer, which generates new models informed by prior knowledge to partially replace randomly initialized models at the first training iteration. Results show that leveraging prior knowledge trained from different turbine configurations all effectively guide the search toward more promising regions of the solution space, thereby accelerating the training process. In the second scenario, when no prior knowledge is available, the transformer is integrated into the training loop to dynamically generate candidate models based on the small error models from the last training iteration and discarding high-error models. Results indicate that more frequent transformer updates, such as after every training iteration, further enhance the acceleration effect.

最近的研究已经证明了应用计算流体动力学（CFD）驱动的符号机器学习（ML）框架在reynolds -average Navier-Stokes （RANS）中帮助开发显式物理模型的有效性，特别是对于过渡、湍流和热通量的建模。与基线模型相比，这些方法可以产生更好的流量预测，但计算成本略有增加。然而，一个关键的限制在于训练阶段的大量计算费用，这通常需要数千次RANS评估。在复杂工业应用的训练模型中，这一挑战变得非常严峻，因为每个ran的运行都是计算密集型的，当试图在多个产品设计中开发更通用和耦合的多个模型时，这一挑战会进一步加剧。本文以低压和高压涡轮的一般过渡和湍流模型修正的发展为研究案例，介绍了两种变压器辅助策略来加速模型训练。在第一种方法中，存储先前训练的模型并将其用作变压器的输入，变压器根据先验知识生成新模型，以部分替换第一次训练迭代中随机初始化的模型。结果表明，利用从不同涡轮配置训练的先验知识都能有效地引导搜索到解决空间中更有希望的区域，从而加快了训练过程。在第二种场景中，当没有可用的先验知识时，将变压器集成到训练循环中，根据上次训练迭代的小误差模型动态生成候选模型，并丢弃高误差模型。结果表明，频繁的变压器更新，如每次训练迭代后，进一步增强了加速效果。

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引用次数: 0

An improved immersed boundary method for investigating flows over multiple irregular geometries with fractal interpolation 基于分形插值的多不规则几何体流动研究的改进浸入边界法

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

Computers & Fluids

Pub Date : 2026-02-15 Epub Date: 2025-12-08 DOI: 10.1016/j.compfluid.2025.106942

Dongheng Lai , Xingyu Zhu

In this study, we propose an improved immersed boundary method with dual-layer local triangulation. A novel code was developed for high-order numerical simulations of supersonic flows over multiple complex irregular geometries. A fifth-order weighted essentially non-oscillatory scheme was implemented to capture any steep gradients in the flow created by the geometries. The simulations were carried out on Cartesian grids and the Delaunay triangulation method was implemented twice near the boundary to refine the object boundary discretization and improve the numerical simulation robustness for complex irregular geometries. The proposed method could successfully evaluate various two- and three-dimensional compressible flows with immersed boundaries. Moreover, we studied the flow mechanism over irregularly shaped debris generated by multiple disintegrations during spacecraft re-entry in near-space, with a particular focus on spherical debris objects. We also propose a self-affine fractal interpolation surface method for spherical surfaces to effectively characterize the near-space debris. The improved immersed boundary method with the dual-layer local triangulation was used to simulate the supersonic flow over multiple side-by-side fractal spherical objects. Numerical examples conclusively verified the effectiveness, generality, and robustness of the proposed method.

本文提出了一种改进的双层局部三角剖分浸入边界法。开发了一种新颖的程序，用于多种复杂不规则几何形状的超音速流动的高阶数值模拟。采用了一种五阶加权本质上无振荡的方案来捕捉由几何形状产生的气流中的陡峭梯度。仿真在直角网格上进行，在边界附近采用两次Delaunay三角剖分方法，以细化目标边界离散化，提高复杂不规则几何的数值模拟鲁棒性。该方法可以成功地计算各种浸入边界的二维和三维可压缩流。此外，我们研究了航天器在近空间再入过程中多次解体产生的不规则形状碎片的流动机制，特别关注球形碎片物体。我们还提出了一种球面自仿射分形插值曲面方法来有效地表征近空间碎片。采用改进的浸入边界法和双层局部三角剖分法，模拟了多个并列分形球面物体的超音速流动。数值算例验证了该方法的有效性、通用性和鲁棒性。

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引用次数: 0

RANS-CNN: A physics-informed convolutional neural network for solving reynolds-averaged Navier-Stokes equations in duct flows ranss - cnn：一个物理信息卷积神经网络，用于解决管道流动中的reynolds-average Navier-Stokes方程

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

Computers & Fluids

Pub Date : 2026-02-15 Epub Date: 2025-12-15 DOI: 10.1016/j.compfluid.2025.106946

Gaurav Bokil, Sebastian Merbold, Stefanie De Graaf

Classical Computational Fluid Dynamics (CFD) simulations of turbulent flows in aerospace applications are computationally demanding and limit rapid design exploration. Convolutional Neural Networks (CNN) are being employed as surrogate models to overcome this challenge. Physics-informed approaches have also been applied to CNNs albeit only for simple flow fields such as laminar flow and heat conduction. This study advances Physics-Informed Convolutional Neural Networks (PICNN) to solve the steady incompressible Reynolds-Averaged Navier-Stokes (RANS) equations in wall-bounded geometries. The proposed method employs a higher-order finite difference scheme for computing spatial gradients, thus enhancing numerical accuracy. Additionally, the Dirichlet boundary conditions are strongly enforced in the network architecture using custom output layers and boundary masks. Numerical stabilisation is incorporated to enable the CNN to simulate high Reynolds number flows without losing stability. To assess the capabilities of this approach on aerospace use cases, it is tested on three data-free cases: S-shaped duct, a ducted body force heat exchanger, and flow over a forward facing step along with a backward facing step geometry with sparse labelled data. Moreover, a comparison between zero-equation and one-equation turbulence models is presented when employed in this framework. The RANS-CNN models performed with over 95 % accuracy on geometries with attached flow and 80 % on separated flow cases. The results obtained from the case studies confirm the capability of the RANS-CNN method in developing a robust and computationally efficient surrogate model with sparse data for smooth ducts.

经典计算流体动力学（CFD）在航空航天应用中的湍流模拟计算要求很高，限制了快速设计探索。卷积神经网络（CNN）被用作替代模型来克服这一挑战。物理信息的方法也被应用于cnn，尽管只是简单的流场，如层流和热传导。本研究推进了基于物理信息的卷积神经网络（PICNN）在有壁几何中求解稳定不可压缩的reynolds - average Navier-Stokes （RANS）方程。该方法采用高阶有限差分格式计算空间梯度，提高了数值精度。此外，Dirichlet边界条件在使用自定义输出层和边界掩码的网络架构中被强制执行。数值稳定纳入使CNN能够模拟高雷诺数流动而不失去稳定性。为了评估这种方法在航空航天用例中的能力，我们在三种无数据的情况下对其进行了测试：s形管道，导管式体力热交换器，以及通过具有稀疏标记数据的前向台阶和后向台阶几何形状的流动。此外，还比较了零方程和单方程湍流模型在此框架下的应用。ranss - cnn模型在具有附加流的几何形状上的准确率超过95%，在分离流情况下的准确率超过80%。从案例研究中获得的结果证实了ranss - cnn方法在为光滑管道开发具有稀疏数据的鲁棒且计算效率高的代理模型方面的能力。

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引用次数: 0