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Meso-scale investigation on the permeability of frozen soils with the lattice Boltzmann method 用晶格玻尔兹曼法对冻土的渗透性进行中尺度研究
IF 4.6 2区 工程技术 Q1 MECHANICS Pub Date : 2024-09-20 DOI: 10.1063/5.0222658
Huxi Xia, Yuanming Lai, Mohaddeseh Mousavi-Nezhad
Complex composition and intricate pore-scale structure of frozen soils poses significant challenges in reliably and efficiently obtaining their permeability. In this study, we propose a modified quartet structure generation set (QSGS) numerical tool for generating frozen soils and present the development of a computational simulation code based on the multiple-relaxation-time lattice Boltzmann method (LBM). In the modified QSGS, the arc-shaped water-ice interface is depicted, and the influence of pore-scale geometry on freezing temperature is considered. The validity of combining the proposed QSGS model and the LBM code is proved by comparing calculated results to analytical and experimental results of porous media. Our objective was to investigate the effects of soil features, including porosity, grain diameter, shape anisotropy of soil particles, and ice content on the intrinsic permeability of frozen soil. Additionally, we examined the relationship between these features and the specific surface area and tortuosity. Numerical results show that the intrinsic permeability of frozen soils increases with increasing porosity, larger granular diameter, and anisotropy, which is identical with the pressure gradient. The presence of ice led to clogging flow pathways and drastically decreased the intrinsic permeability, which is significantly less than unfrozen soil with same effective porosity. This study provides a useful tool to investigate the intricate interplay between the pore-scale structure and the intrinsic permeability of frozen soils.
冻土成分复杂,孔隙尺度结构错综复杂,给可靠有效地获取其渗透率带来了巨大挑战。在本研究中,我们提出了一种用于生成冻土的改进型四元结构生成集(QSGS)数值工具,并介绍了基于多松弛时间晶格玻尔兹曼法(LBM)的计算模拟代码的开发情况。在改进的 QSGS 中,描绘了弧形水冰界面,并考虑了孔隙尺度几何形状对冻结温度的影响。通过将计算结果与多孔介质的分析和实验结果进行比较,证明了将所提出的 QSGS 模型与 LBM 代码相结合的有效性。我们的目标是研究土壤特性(包括孔隙度、颗粒直径、土壤颗粒形状各向异性和含冰量)对冻土内在渗透性的影响。此外,我们还研究了这些特征与比表面积和迂回度之间的关系。数值结果表明,冻土的内在渗透性随着孔隙度、颗粒直径增大和各向异性的增加而增加,这与压力梯度相同。冰的存在导致流动通道堵塞,本征渗透率急剧下降,明显低于有效孔隙度相同的未冻结土壤。这项研究为研究冻土孔隙尺度结构与固有渗透性之间错综复杂的相互作用提供了有用的工具。
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引用次数: 0
Overlapping effect of detonation driving during multi-point initiation 多点起爆期间起爆驱动的重叠效应
IF 4.6 2区 工程技术 Q1 MECHANICS Pub Date : 2024-09-19 DOI: 10.1063/5.0231221
Yuan Li, Yuan Guo, Tao Suo, Xiaogang Li, Yuquan Wen
Employing multi-point initiation in warhead structures produces a detonation wave aiming warhead. Numerous studies have concentrated on enhancing the velocity and analyzing its distribution in this type of warhead. Researchers have developed formulas for the velocity distribution of asymmetrically one-line initiated warheads; however, a reliable and complete calculation method for the velocity distribution in asymmetrically two-line initiated warheads is yet to be established. A new idea is proposed and verified in this work: the velocity distribution for the asymmetric two-line initiation can be derived from that of the one-line initiation. Initial efforts include conducting experimentally verified numerical modeling to examine the propagation and interaction of detonation waves in asymmetrically two-line initiated warheads. Subsequently, using the principle of independent propagation, a model is formulated to use the velocity distribution from asymmetric one-line initiation to predict that of asymmetric two-line initiations. Finally, arena tests are performed to corroborate the overlapping model. This research can provide valuable insights for lethality assessment, protection design, and security analysis.
在弹头结构中采用多点起爆会产生一个起爆波瞄准弹头。大量研究集中于提高这类弹头的速度并分析其分布。研究人员已经建立了非对称单线起爆弹头的速度分布公式,但对于非对称双线起爆弹头的速度分布,尚未建立可靠而完整的计算方法。本研究提出并验证了一个新想法:非对称双线起爆弹头的速度分布可以从单线起爆弹头的速度分布推导出来。最初的工作包括进行经过实验验证的数值建模,以研究非对称双线起爆弹头中引爆波的传播和相互作用。随后,利用独立传播原理,建立了一个模型,利用非对称单线起爆的速度分布来预测非对称双线起爆的速度分布。最后,进行了竞技场试验,以证实重叠模型。这项研究可为致命性评估、防护设计和安全分析提供有价值的见解。
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引用次数: 0
Computational investigation of both geometric and fluidic compressible turbulent thrust vectoring, using a Coanda based nozzle 利用科恩达喷嘴对几何和流体可压缩湍流推力矢量进行计算研究
IF 4.6 2区 工程技术 Q1 MECHANICS Pub Date : 2024-09-19 DOI: 10.1063/5.0222070
Alireza Nayebi, Mohammad Taeibi Rahni
This study addresses the challenge of enhancing aircraft maneuverability, particularly for vertical landing and takeoff, focusing on the fluidic aerial Coanda high efficiency orienting jet nozzle that employs the Coanda effect to achieve thrust vectoring. This research advances understanding of the interplay between geometric and fluidic factors in thrust vectoring. Stationary, turbulent, and compressible flow conditions are assumed, employing Favre-averaged Reynolds-averaged Navier–Stokes approach with the standard k-ε model. Computational solutions were obtained using a pressure-based finite volume method and a structured computational grid. The key findings include thrust vectoring enhancement due to an increase in the total mass flow rate, septum position (at no shock wave-related issues), and Reynolds number. In addition, shock wave formation (at specific mass flow rates and septum positions) considerably affects thrust vectoring. These insights are crucial for optimizing Coanda-based nozzle design in advanced propulsion systems, including in unmanned aircraft vehicles.
本研究针对提高飞机机动性(尤其是垂直起降)的挑战,重点研究了利用科恩达效应实现推力矢量的流体航空科恩达高效定向喷嘴。这项研究加深了人们对推力矢量中几何因素和流体因素之间相互作用的理解。假定流动条件为静止、湍流和可压缩流动,采用法夫尔平均雷诺平均纳维-斯托克斯方法和标准 k-ε 模型。使用基于压力的有限体积法和结构化计算网格获得了计算结果。主要发现包括由于总质量流量、隔膜位置(无冲击波相关问题时)和雷诺数的增加而导致的推力矢量增强。此外,冲击波的形成(在特定的质量流量和隔膜位置)对推力矢量有很大影响。这些见解对于优化先进推进系统(包括无人驾驶飞行器)中基于科恩达喷嘴的设计至关重要。
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引用次数: 0
Directional self-migration of droplets on an inclined surface driven by wettability gradient 由润湿梯度驱动的液滴在倾斜表面上的定向自迁移
IF 4.6 2区 工程技术 Q1 MECHANICS Pub Date : 2024-09-19 DOI: 10.1063/5.0228546
Ying Zhang, Shuting Zhao, Yao Liu, Deji Sun, Zhaoqing Ke, Yuan Tian
In the current study, the anti-gravity directional self-migration of droplets on an inclined surface driven by wettability gradient (ω) was investigated using a front-tracking method. A unified mechanical model of droplet motion on an inclined wettability gradient wall was derived, considering the driving force generated by ω (Fd), gravity (G), and flow resistance (Ff). The model demonstrates that ω, G, and inclination angle (α) are key parameters affecting droplet motion. By varying ω, Bond number (Bo), and α, the droplet dynamic characteristics were analyzed, and a real-time Capillary number (Ca) was introduced to measure the droplet migration speed. The results indicate that a larger ω generates a greater Fd, leading to faster migration and more pronounced spreading. When the ratio of the channel width to the droplet diameter is 0.7, the droplet can cross three regions, obtaining double Fd, and Ca curve exhibits a bimodal structure. When the ratio of the channel width to the droplet diameter is 1.2, the droplet slides and spreads in the middle region without ω, resulting in a trimodal Ca curve. A larger Bo implies a stronger gravity effect, reducing the net driving force for upward migration and slowing the migration speed. At α=30° and ω=0.54, Bo reaches its critical value at 0.5, where G exceeds Fd, causing the droplet to slide downward along the wall. α affects droplet motion by controlling the gravitational component along the wall (Gx). A larger α results in a smaller net driving force for upward migration, reducing the migration speed.
本研究采用前沿跟踪法研究了液滴在润湿梯度(ω)驱动下在倾斜表面上的反重力定向自迁移。考虑到ω(Fd)、重力(G)和流动阻力(Ff)产生的驱动力,推导出了液滴在倾斜的润湿性梯度壁上运动的统一力学模型。模型表明,ω、G 和倾角 (α) 是影响液滴运动的关键参数。通过改变ω、邦德数(Bo)和α,分析了液滴的动态特性,并引入了实时毛细管数(Ca)来测量液滴的迁移速度。结果表明,ω 越大,Fd 越大,迁移速度越快,扩散越明显。当通道宽度与液滴直径之比为 0.7 时,液滴可穿过三个区域,获得双倍 Fd,Ca 曲线呈现双峰结构。当通道宽度与液滴直径之比为 1.2 时,液滴在中间区域滑动和扩散,不需要 ω,从而形成三峰型 Ca 曲线。Bo 越大,意味着重力效应越强,向上迁移的净驱动力就越小,迁移速度就越慢。当 α=30° 和 ω=0.54 时,Bo 在 0.5 时达到临界值,此时 G 超过 Fd,导致液滴沿壁向下滑动。α 越大,向上迁移的净驱动力就越小,从而降低迁移速度。
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引用次数: 0
Study on the Karman gait kinematics of an airfoil in an asymmetrical vortex street 非对称涡街中机翼的卡曼步态运动学研究
IF 4.6 2区 工程技术 Q1 MECHANICS Pub Date : 2024-09-18 DOI: 10.1063/5.0228852
Wenbo Wu, Runpeng Gu, Zhongming Hu, Yuankun Sun
To understand fish swimming behavior in unsteady flows, this paper introduces the Kármán gait model to numerically investigate the hydrodynamics of fish-like swimming in an asymmetric vortex environment, specifically the P + S mode (a pair of vortices are shed from one side of the cylinder and a single vortex from the other side during one oscillation period) created by an oscillating cylinder. The immersed boundary method is employed to model both the fish-like airfoil and the vibrating cylinder. Through simulations across a broad range of controlling parameters, we analyze the advancement efficiency of the airfoil in the P + S mode, the force coefficients, Fourier spectra of hydrodynamic forces, and the interactions between the airfoil and vortices. Our findings reveal that the fundamental phase Φ0 is crucial, as it directly influences the airfoil's position relative to the vortex and affects the forces exerted. Other parameters play a secondary role, primarily reinforcing the effect of the fundamental phase on airfoil–vortex interactions. Furthermore, the vortex pair boosting effect, unique to the P + S mode, enhances the airfoil's thrust and swimming efficiency. The wake environment behind the airfoil is also vital for maximizing benefits from the P + S mode. When the fundamental mode fs, indicative of the airfoil's ability to extract energy from vortices, dominates the Fourier spectra of hydrodynamic forces, it supports the airfoil's motion in the P + S mode. Conversely, when the first harmonic mode 2fs dominates the drag spectrum, it hinders propulsion by reducing the airfoil's thrust in the swimming direction.
为了理解鱼类在非稳定流中的游动行为,本文引入了卡尔曼步态模型,对鱼类在非对称漩涡环境中游动的流体力学进行数值研究,特别是由振动圆柱体产生的 P + S 模式(在一个振动周期内,一对漩涡从圆柱体的一侧流出,另一个漩涡从另一侧流出)。采用沉浸边界法对鱼形机翼和振动圆柱体进行建模。通过在广泛的控制参数范围内进行模拟,我们分析了机翼在 P + S 模式下的推进效率、力系数、流体动力的傅里叶频谱以及机翼和涡流之间的相互作用。我们的研究结果表明,基本相位Φ0 至关重要,因为它直接影响机翼相对于涡旋的位置,并影响施加的力。其他参数起次要作用,主要是加强基本相位对机翼与涡旋相互作用的影响。此外,P + S 模式特有的涡对助推效应增强了机翼的推力和游动效率。机翼后的尾流环境对于最大限度地发挥 P + S 模式的优势也至关重要。当基本模式 fs(表明机翼从涡流中提取能量的能力)在流体动力的傅里叶频谱中占主导地位时,它将支持机翼在 P + S 模式下的运动。相反,当第一次谐波模式 2fs 在阻力谱中占主导地位时,则会减少机翼在游动方向上的推力,从而阻碍推进力。
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引用次数: 0
Performance prediction and design optimization of a transonic rotor based on deep transfer learning 基于深度迁移学习的跨音速转子性能预测与设计优化
IF 4.6 2区 工程技术 Q1 MECHANICS Pub Date : 2024-09-18 DOI: 10.1063/5.0221767
Hefang Deng, Songan Zhang, Kailong Xia, Xiaoqing Qiang, Mingmin Zhu, Jinfang Teng
Deep transfer learning is frequently employed to address the challenges arising from limited or hard-to-obtain training data in the target domain, but its application in axial compressors has been scarcely explored thus far. In this paper, a multi-objective optimization framework of a transonic rotor is established using deep transfer learning. This framework first pre-trains deep neural networks based on the peak efficiency condition of 100% design speed and then fine-tunes the networks to predict the performance of off-design conditions based on the small training dataset. Finally, the design optimization of the transonic rotor is carried out through non-dominated sorting genetic algorithm II. Compared to neural networks that are trained directly, transfer learning models can achieve higher prediction accuracy, particularly in scenarios with small training datasets. This is because the pre-trained weights can offer a better initial state for transfer learning models. Moreover, transfer learning models can use fewer samples to obtain an approximate Pareto front, making the optimized rotor increase the isentropic efficiency at both peak efficiency and high loading conditions. The efficiency improvement of the optimized rotor is attributed to the reduction of the loss associated with the tip leakage flow by adjusting the tip loading distribution. Overall, this study fully demonstrates the effectiveness of transfer learning in predicting compressor performance, which provides a promising approach to solving high-cost compressor design problems.
深度迁移学习经常被用来解决目标领域训练数据有限或难以获得所带来的挑战,但其在轴流压缩机中的应用迄今为止还鲜有探索。本文利用深度迁移学习建立了跨音速转子的多目标优化框架。该框架首先基于 100% 设计转速的峰值效率条件对深度神经网络进行预训练,然后根据小型训练数据集对网络进行微调,以预测非设计条件下的性能。最后,通过非支配排序遗传算法 II 对跨音速转子进行设计优化。与直接训练的神经网络相比,迁移学习模型可以获得更高的预测精度,尤其是在训练数据集较小的情况下。这是因为预训练的权重可以为迁移学习模型提供更好的初始状态。此外,迁移学习模型可以使用更少的样本获得近似帕累托前沿,从而使优化后的转子在峰值效率和高负载条件下都能提高等熵效率。优化转子效率的提高归功于通过调整尖端负载分布减少了与尖端漏流相关的损失。总之,本研究充分展示了迁移学习在预测压缩机性能方面的有效性,为解决高成本压缩机设计问题提供了一种前景广阔的方法。
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引用次数: 0
A novel variable-coefficient extended Davey–Stewartson system for internal waves in the presence of background flows 存在背景流情况下的新型可变系数扩展戴维-斯图沃特森内波系统
IF 4.6 2区 工程技术 Q1 MECHANICS Pub Date : 2024-09-18 DOI: 10.1063/5.0219224
Jun-Chao Sun, Xiao-Yan Tang, Yong Chen
We propose a novel variable-coefficient Davey–Stewartson type system for studying internal wave phenomena in finite-depth stratified fluids with background flows, where the upper- and lower-layer fluids possess distinct velocity potentials, and the variable-coefficient terms are primarily controlled by the background flows. This realizes the first application of variable-coefficient DS-type equations in the field of internal waves. Compared to commonly used internal wave models, this system not only describes multiple types of internal waves, such as internal solitary waves, internal breathers, and internal rogue waves, but also aids in analyzing the impact of background flows on internal waves. We provide the influence of different background flow patterns on the dynamic behavior and spatial position of internal waves, which contribute to a deeper understanding of the mechanisms through which background flows influence internal waves. Furthermore, the system is capable of capturing variations in the velocity potentials of the upper and lower layers. We discover a connection between internal waves under the influence of background flows and velocity potentials. Through the variations in velocity potentials within the flow field, the dynamic behaviors of internal waves can be indirectly inferred, their amplitude positions located, and different types of internal waves distinguished. This result may help address the current shortcomings in satellite detection of internal wave dynamics and internal rogue waves.
我们提出了一种新的可变系数戴维-斯图沃特森(Davey-Stewartson)型系统,用于研究具有背景流的有限深度分层流体中的内波现象,其中上层和下层流体具有不同的速度势,可变系数项主要受背景流控制。这实现了变系数 DS 型方程在内波领域的首次应用。与常用的内波模型相比,该系统不仅能描述多种类型的内波,如内孤波、内呼吸波和内流氓波,还有助于分析背景流对内波的影响。我们提供了不同背景流模式对内波动态行为和空间位置的影响,有助于加深对背景流影响内波机制的理解。此外,该系统还能捕捉上下两层速度势的变化。我们发现了背景流影响下的内波与速度势之间的联系。通过流场内速度势的变化,可以间接推断内波的动态行为,定位内波的振幅位置,并区分不同类型的内波。这一结果可能有助于解决目前卫星探测内波动力学和内流氓波的不足。
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引用次数: 0
Influence of different factors on gap breakdown process with hot electrode and high temperature gas medium in low voltage circuit breaker chamber based on particle-in-cell/Monte-Carlo collision simulation 基于粒子入室/蒙特卡洛碰撞模拟的低压断路器室中热电极和高温气体介质对间隙击穿过程不同因素的影响
IF 4.6 2区 工程技术 Q1 MECHANICS Pub Date : 2024-09-18 DOI: 10.1063/5.0207871
Lijun Wang, Runze Hu, Zhuo Chen, Zhiwei Wang, Yile Wang
Different factors such as gas composition inside the low voltage circuit breaker (LVCB) chamber and the residual plasma in the post-arc stage affect the breakdown process, which in turn affects the breaking capacity of LVCBs. In this paper, the effects of non-parallel electrode structure, gas temperature and pressure, electrode temperature, and gap distance on gap breakdown of hot electrode under high temperature gas conditions were studied, for which a particle-in-cell/Monte-Carlo collision simulation model has been established, which takes into account the effects of high-temperature gas components, cathode electron thermal emission, electron collision ionization and other effects, and simulation studies have been conducted. The simulation results show that the increase in gap gas temperature, the decrease in air pressure, and the increase in electrode temperature will lead to the gap breakdown more easily. With the increase in the gap length, the breakdown voltage increases, but the average electric field intensity required for breakdown decreases. In the non-parallel electrode structure, the breakdown occurs first at the position with the shortest gap distance, then the cathode sheath forms and extends along the electrode surface to other areas, and finally, the entire gap breaks down.
低压断路器(LVCB)腔体内的气体成分和弧后阶段的残余等离子体等不同因素会影响击穿过程,进而影响低压断路器的分断能力。本文研究了非平行电极结构、气体温度和压力、电极温度和间隙距离对高温气体条件下热电极间隙击穿的影响,为此建立了粒子在电池/蒙特卡洛碰撞模拟模型,考虑了高温气体成分、阴极电子热发射、电子碰撞电离等效应,并进行了模拟研究。仿真结果表明,间隙气体温度升高、气压降低、电极温度升高更容易导致间隙击穿。随着间隙长度的增加,击穿电压会增加,但击穿所需的平均电场强度会降低。在非平行电极结构中,击穿首先发生在间隙距离最短的位置,然后形成阴极鞘,并沿着电极表面延伸到其他区域,最后整个间隙击穿。
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引用次数: 0
Wetting and pressure gradient performance in a lattice Boltzmann color gradient model 晶格玻尔兹曼颜色梯度模型中的润湿和压力梯度性能
IF 4.6 2区 工程技术 Q1 MECHANICS Pub Date : 2024-09-18 DOI: 10.1063/5.0228835
M. Sedahmed, R. C. V. Coelho
An accurate implementation of wetting and pressure drop is crucial to correctly reproduce fluid displacement processes in porous media. Although several strategies have been proposed in the literature, a systematic comparison of them is needed to determine the most suitable for practical applications. Here, we carried out numerical simulations to investigate the performance of two widely used wettability schemes in the lattice Boltzmann color gradient model, namely, the geometrical wetting scheme by Leclaire et al. [Phys. Rev. E 95(3), 033306 (2017)](scheme-I) and the modified direction of the color gradient scheme by Akai et al. [Adv. Water Resour. 116, 56–66 (2018)] (scheme-II). We showed that scheme-II was more accurate in simulating static contact angles of a fluid droplet on a solid surface. However, scheme-I was more accurate in simulating a dynamic case of a binary fluid flow in a horizontal capillary tube described by the Washburn equation. Moreover, we investigated the performance of two popular pressure gradient implementation types. Type-I used the so-called Zou–He pressure boundary conditions at the inlet and the outlet of the domain, while type-II used an external body force as a pressure gradient. We showed that the type-I implementation was slightly more accurate in simulating a neutrally wetting fluid in a horizontal capillary tube described by the Washburn equation. We also investigated the differences between the two types of pressure gradient implementation in simulating two fluid displacement processes in a Bentheimer sandstone rock sample: the primary drainage and the imbibition displacement processes.
要正确再现多孔介质中的流体位移过程,准确实现润湿和压降至关重要。虽然文献中已经提出了几种策略,但需要对它们进行系统比较,以确定最适合实际应用的策略。在此,我们进行了数值模拟,研究了晶格玻尔兹曼颜色梯度模型中两种广泛使用的润湿方案的性能,即 Leclaire 等人的几何润湿方案[Phys. Rev. E 95(3), 033306 (2017)](方案-I)和 Akai 等人的颜色梯度修正方向方案[Adv. Water Resour. 116, 56-66 (2018)](方案-II)。我们的研究表明,方案-II 在模拟流体液滴在固体表面的静态接触角方面更为精确。然而,在模拟由瓦什伯恩方程描述的二元流体在水平毛细管中流动的动态情况时,方案一更为精确。此外,我们还研究了两种常用压力梯度实施类型的性能。类型 I 在域的入口和出口处使用了所谓的 Zou-He 压力边界条件,而类型 II 则使用了外部体力作为压力梯度。我们发现,在模拟由瓦什伯恩方程描述的水平毛细管中的中性润湿流体时,I 型实施方案的精确度略高。我们还研究了在模拟本特海默砂岩岩石样本中的两种流体位移过程(原生排水和浸润位移过程)时,两种压力梯度实现方式之间的差异。
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引用次数: 0
Three-dimensional compact multi-resolution weighted essentially non-oscillatory reconstruction under the Arbitrary Lagrange–Euler framework 任意拉格朗日-欧拉框架下的三维紧凑型多分辨率加权基本非振荡重构
IF 4.6 2区 工程技术 Q1 MECHANICS Pub Date : 2024-09-18 DOI: 10.1063/5.0226237
Ningyu Zhan, Rongqian Chen, Yancheng You
A third-order compact multi-resolution weighted essentially non-oscillatory (CMR-WENO) reconstruction method for three-dimensional (3D) hybrid unstructured grids is developed using the Arbitrary Lagrange–Euler framework. The finite volume method is used to discretize the governing equations, and some turbulent and moving boundary problems are simulated. Only one compact center stencil comprising the neighboring cells of each control cell is required to construct the polynomials in the algorithm. As a result, the number of stencils and stencil cells is significantly reduced when compared with the traditional WENO scheme. This simplifies the code and improves the robustness of the algorithm. By ensuring the cell average and first-order derivatives are consistent with that in stencil cells an over-determined system of equations can be used to reconstruct the polynomials. This system can then be solved using the compact least squares method to avoid an ill-conditioned coefficient matrix. Furthermore, a coupled implicit iteration strategy is used to solve for the unknown coefficients, so no extra determination is required for the derivatives of each control cell. The final interpolation function for discontinuities in the flow field is obtained using CMR-WENO to nonlinearly combine polynomials of different orders, which further improves the stability of the algorithm. The CMR-WENO can be implemented on 3D hybrid unstructured grids and can be used to simulate complex problems such as those involving turbulence and moving boundaries. Finally, the algorithm presented here is verified to be third-order accurate and to exhibit good robustness when used on several representative numerical examples.
利用任意拉格朗日-欧拉框架,为三维(3D)混合非结构网格开发了一种三阶紧凑型多分辨率加权本质非振荡(CMR-WENO)重建方法。该方法采用有限体积法对控制方程进行离散化,并模拟了一些湍流和移动边界问题。在算法中,只需要一个由每个控制单元的相邻单元组成的紧凑中心模板来构建多项式。因此,与传统的 WENO 方案相比,模板和模板单元的数量大大减少。这不仅简化了代码,还提高了算法的鲁棒性。通过确保单元平均值和一阶导数与模版单元中的平均值和一阶导数一致,可以使用一个超定方程组来重建多项式。然后,可以使用紧凑最小二乘法求解该系统,以避免系数矩阵条件不良。此外,耦合隐式迭代策略用于求解未知系数,因此无需额外确定每个控制单元的导数。利用 CMR-WENO 对不同阶的多项式进行非线性组合,可获得流场不连续处的最终插值函数,从而进一步提高算法的稳定性。CMR-WENO 可在三维混合非结构网格上实现,并可用于模拟复杂问题,如涉及湍流和移动边界的问题。最后,本文介绍的算法在几个有代表性的数值示例中得到验证,具有三阶精度和良好的鲁棒性。
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引用次数: 0
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Physics of Fluids
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