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Locally Adaptive Non-Hydrostatic Shallow Water Extension for Moving Bottom-Generated Waves 移动底生波的局部自适应非静水浅水扩展
IF 1.8 4区 工程技术 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-10-02 DOI: 10.1002/fld.70021
Kemal Firdaus, Jörn Behrens

We propose a locally adaptive non-hydrostatic model and apply it to wave propagation generated by a moving bottom. This model is based on the non-hydrostatic extension of the shallow water equations (SWE) with a quadratic pressure relation, which is suitable for weakly dispersive waves. The approximation is mathematically equivalent to the Green-Naghdi equations. Applied globally, the extension requires solving an elliptic system of equations in the whole domain at each time step. Therefore, we develop an adaptive model that reduces the application area of the extension, thereby reducing the computational time. The elliptic problem is only solved in the area where the dispersive effect might play a crucial role. To define the non-hydrostatic area, we investigate several potential criteria based on the hydrostatic SWE solution. We validate and illustrate how our adaptive model works by first applying it to simulate a simple propagating solitary wave, where exact solutions are known. Following that, we demonstrate the accuracy and efficiency of our approach in more complicated cases involving moving bottom-generated waves, where measured laboratory data serve as reference solutions. The adaptive model yields similar accuracy as the global application of the non-hydrostatic extension while reducing the computational time by more than 50%$$ 50% $$.

我们提出了一个局部自适应的非流体静力模型,并将其应用于由移动底部产生的波浪传播。该模型是基于二次压力关系的浅水方程(SWE)的非静力扩展,适用于弱色散波。这个近似在数学上等同于Green-Naghdi方程。推广应用于全局时,需要在每个时间步解出整个域内的一个椭圆方程组。因此,我们开发了一种自适应模型,减少了扩展的应用范围,从而减少了计算时间。椭圆问题只有在色散效应可能起关键作用的区域才能得到解决。为了定义非流体静力区域,我们研究了基于流体静力SWE解决方案的几个潜在标准。我们验证并说明了我们的自适应模型是如何工作的,首先应用它来模拟一个简单的传播孤立波,其中精确的解是已知的。接下来,我们在涉及移动底部产生的波的更复杂的情况下展示了我们方法的准确性和效率,其中测量的实验室数据可作为参考解决方案。该自适应模型与非静力扩展的全局应用具有相似的精度,同时将计算时间减少50%以上 % $$ 50% $$ .
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引用次数: 0
Spatial Analysis of Hydrodynamic Instabilities With Spectral-Collocation Methods Using Chebyshev Polynomials 用切比雪夫多项式谱配方法分析水动力不稳定性
IF 1.8 4区 工程技术 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-10-02 DOI: 10.1002/fld.70020
Diego Armando Landínez Capacho, Guillermo Andrés Jaramillo Pizarro
<div> <p>An open and fully reproducible numerical procedure to solve the Rayleigh stability equation is presented in this work for the spatial analysis of hydrodynamic instabilities in an inviscid shear flow using the Chebyshev spectral-collocation method. The resulting cubic polynomial eigenvalue problem is linearized via a companion matrix and solved efficiently, from which the most unstable spatial growth rate and its frequency are identified. Verification against the classical reference [1] at dimensionless temporal frequency <span></span><math> <semantics> <mrow> <mi>ω</mi> <mo>=</mo> <mn>0</mn> <mo>.</mo> <mn>2</mn> </mrow> <annotation>$$ omega =0.2 $$</annotation> </semantics></math> demonstrates spectral (exponential) convergence of the dispersion relation <span></span><math> <semantics> <mrow> <mi>α</mi> <mo>(</mo> <mi>ω</mi> <mo>)</mo> </mrow> <annotation>$$ alpha left(omega right) $$</annotation> </semantics></math>; in practice, a resolution of <span></span><math> <semantics> <mrow> <mi>N</mi> <mo>=</mo> <mn>300</mn> </mrow> <annotation>$$ N=300 $$</annotation> </semantics></math> yields grid-independent predictions. Across the unstable band, the maximum relative difference is <span></span><math> <semantics> <mrow> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mo>−</mo> <mn>4</mn> </mrow> </msup> <mspace></mspace> <mo>%</mo> </mrow> <annotation>$$ 1{0}^{-4}kern0.3em % $$</annotation> </semantics></math> for the real component of the wavenumber <span></span><math> <semantics> <mrow> <msub> <mrow> <mi>α</mi> </mrow> <mrow> <mi>r</mi> </mrow> </msub> <mo>(</mo> <mi>ω</mi> <mo>)</mo> </mrow> <annotation>$$ {alpha}_rleft(omega right) $$</annotation> </semantics></math> and <span></span><math> <semantics> <mrow> <mn>2</mn> <mspace></mspace> <mo>×</mo> <mspace></mspace> <mn>1</mn>
本文采用切比雪夫谱配点法对无粘剪切流的水动力不稳定性进行了空间分析,提出了一种开放的、完全可重复的求解瑞利稳定性方程的数值方法。由此得到的三次多项式特征值问题通过伴矩阵线性化并有效求解,从中识别出最不稳定的空间增长率及其频率。在无量纲时间频率ω = 0时对经典参考[1]的验证。2 $$ omega =0.2 $$展示了色散关系α (ω) $$ alpha left(omega right) $$的谱(指数)收敛性;在实践中,N = 300 $$ N=300 $$的分辨率产生与网格无关的预测。在不稳定波段,最大的相对差值为1 0−4 % $$ 1{0}^{-4}kern0.3em % $$ for the real component of the wavenumber α r ( ω ) $$ {alpha}_rleft(omega right) $$ and 2 × 1 0 − 4 % $$ 2times kern0.3em 1{0}^{-4}kern0.3em % $$ for the dimensionless imaginary component of the complex streamwise wavenumber − α i ( ω ) $$ -{alpha}_ileft(omega right) $$ , with the peak growth rate and its frequency matching the reference. The computed real and imaginary eigenfunctions closely reproduce the reported mode shapes. An additional comparison with a shooting method implementation (method used by Michalke) indicated that the spectral formulation attains the same accuracy with superior conditioning and reduced parameter tuning. The proposed workflow thus offers a computationally practical and fully reproducible route to assess shear-flow stability — complementary to large eddy and direct numeric simulation LES/DNS — while enabling straightforward verification against canonical benchmarks.
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引用次数: 0
CFD Study of Indian Coal to Assess the Severity of Coal Dust Explosion and Its Classification as Per Explosibility 印度煤炭煤尘爆炸严重程度评价及可爆性分级的CFD研究
IF 1.8 4区 工程技术 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-10-01 DOI: 10.1002/fld.70015
Niroj Kumar Mohalik, Asfar Mobin Khan, Santosh Kumar Ray, Debashish Mishra, Jai Krishna Pandey

This paper presents a comprehensive study using computational fluid dynamics (CFD) to evaluate the explosibility of Indian coals and classify their explosion severity. A Siwek 20 L explosion chamber was simulated by ASTM standard 1226-19 to analyze coal samples collected from 24 coal mines across various coalfields of India. The explosibility parameters that is, maximum explosion pressure (Pmax), maximum rate of pressure rise ((dP/dt)max), explosion delay time (Ted), time to reach Pmax (Tep), and deflagration index (Kst) were estimated for each coal sample to evaluate the deflagration index, which measures the severity of explosions. The deflagration index (Kst) of all coal samples varied significantly between 47.90 bar·ms−1 and 109.43 bar·ms−1 indicating weak explosion potentials (0 < Kst < 200) as per OSHA 2009 standards. Based on this result, a classification system can be proposed for Indian coals depending on shared characteristics, which may be helpful in identifying coal according to their deflagration index (degree of severity). Presently, no formal classification system exists for Indian coal, and current assessments rely on USA OSHA regulations. Hence, multivariate statistical techniques, including feature selection, correlation analysis, multiple regression, and hierarchical clustering, were employed to identify the factors influencing explosion severity and to categorize the coal samples. Volatile matter dry (VMd) and crossing point temperature (CPT) were the most influential factors impacting Kst. A non-linear regression model yielded a polynomial equation with a strong fit (R2 = 0.909, std. error of estimate = 5.19%) for predicting the deflagration index and validated with test results. Hierarchical clustering further classified the coal samples into three distinct groups based on their explosion susceptibility: highly susceptible, moderately susceptible, and potentially susceptible. The proposed classification and prediction model can guide industry stakeholders to implement more effective explosion mitigation strategies and safety protocols.

本文采用计算流体力学(CFD)方法对印度煤的爆炸危险性进行了综合评价,并对其爆炸严重程度进行了分类。采用ASTM 1226-19标准模拟了Siwek 20 L爆炸室,对印度不同煤田的24个煤矿的煤样进行了分析。通过估算各煤样的爆炸参数,即最大爆炸压力(Pmax)、最大升压速率(dP/dt)max、爆炸延迟时间(Ted)、到达Pmax的时间(Tep)和爆燃指数(Kst),来评价衡量爆炸严重程度的爆燃指数。所有煤样的爆燃指数(Kst)在47.90 bar·ms - 1和109.43 bar·ms - 1之间变化显著,表明弱爆炸电位(0 < Kst < 200)符合OSHA 2009标准。在此基础上,可以根据印度煤的共同特征提出一种分类系统,这可能有助于根据其爆燃指数(严重程度)对煤进行识别。目前,印度煤炭没有正式的分类系统,目前的评估依赖于美国OSHA法规。为此,采用特征选择、相关分析、多元回归、分层聚类等多元统计技术识别影响爆炸严重程度的因素,对煤样进行分类。挥发分干度(VMd)和过点温度(CPT)是影响Kst的主要因素。利用非线性回归模型对爆燃指数进行预测,得到了一个强拟合的多项式方程(R2 = 0.909,标准差估计误差= 5.19%),并与试验结果进行了验证。分层聚类进一步将煤样根据其爆炸易感性分为高易感性、中等易感性和潜在易感性三组。提出的分类和预测模型可以指导行业利益相关者实施更有效的爆炸缓解战略和安全协议。
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引用次数: 0
A Semi-Implicit Numerical Method for Simultaneous Fluid-Structure Interaction 流固耦合的半隐式数值方法
IF 1.8 4区 工程技术 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-10-01 DOI: 10.1002/fld.70019
Vincenzo Casulli

A one-dimensional shallow water model is coupled with a floating boat which is assumed to be in hydrostatic equilibrium with the underlying water. Numerically, a semi-implicit discretization of the shallow water equations also includes the Archimedes' floating conditions in such a fashion that the boat's vertical position and pitch slope are simultaneously adjusted to the computed flow field. The resulting algorithm is well-posed, physically consistent, numerically stable, extremely efficient, and fully conservative. A few numerical tests are included to confirm the model's accuracy and performance.

在一维浅水模型中,假定浮船与底层水处于流体静力平衡状态。在数值上,浅水方程的半隐式离散化也包括阿基米德漂浮条件,以这样一种方式,船的垂直位置和俯仰斜率同时调整到计算的流场。所得到的算法是适定的、物理上一致的、数值上稳定的、极其高效的和完全保守的。通过数值试验验证了模型的准确性和性能。
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引用次数: 0
Comparative Analysis of the Impact of Two Flow Control Methods on the Stall Characteristics of NACA0021 Airfoil Using DMD and POD Methods 采用DMD和POD两种流动控制方法对NACA0021翼型失速特性影响的对比分析
IF 1.8 4区 工程技术 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-09-24 DOI: 10.1002/fld.70018
Zelin Liu, Kaidi Li, Xiaojing Sun

In aerospace engineering and wind turbine applications, flow control technologies improve the behavior of separated flows around airfoils by employing diverse methods. However, the effectiveness of these methods varies significantly. Therefore, it is necessary to conduct an in-depth analysis of the flow structure over the airfoil surface after applying flow control. This helps to gain a deeper understanding of the underlying physical mechanisms, thereby providing a theoretical basis for optimizing flow control techniques and guiding the selection of the most appropriate flow control strategies according to specific requirements. This study utilized the delayed detached eddy simulation (DDES) technique to simulate the detailed flow field around a NACA0021 airfoil under two common flow control strategies: The Gurney flap and the combined leading- and trailing-edge flaps, both tested at a stall angle of attack of 20°. Subsequently, dynamic mode decomposition (DMD) and proper orthogonal decomposition (POD) were employed to analyze the flow structure characteristics derived from velocity field data. This analysis exposed the distinct patterns and mechanisms through which these two methods modulate the unsteady flow field on the airfoil surface during stall conditions and clarified the intrinsic differences in their impact on the airfoil's aerodynamic properties. Highly instructive for in-depth study of flow control methods.

在航空航天工程和风力涡轮机应用中,流动控制技术通过采用多种方法来改善翼型周围分离流动的行为。然而,这些方法的有效性差异很大。因此,应用气流控制后,有必要对翼型表面的流动结构进行深入分析。这有助于更深入地了解潜在的物理机制,从而为优化流动控制技术和指导根据具体要求选择最合适的流动控制策略提供理论依据。本研究利用延迟分离涡模拟(DDES)技术模拟了NACA0021翼型在两种常见的流动控制策略下的详细流场:Gurney襟翼和前后缘组合襟翼,均在失速攻角为20°的情况下进行了测试。随后,采用动态模态分解(DMD)和适当正交分解(POD)对速度场数据导出的流场结构特征进行分析。该分析揭示了这两种方法在失速条件下调节翼型表面非定常流场的不同模式和机制,并阐明了它们对翼型气动性能影响的内在差异。对流动控制方法的深入研究具有重要的指导意义。
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引用次数: 0
Airfoil Shape Optimization in Ultralow Reynolds Flows Applying a Deep Learning–Genetic Algorithm Framework on a Shear-Stress-Based Inverse Design Method 基于深度学习-遗传算法框架的基于剪切应力的反设计方法的超低雷诺数翼型优化
IF 1.8 4区 工程技术 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-09-24 DOI: 10.1002/fld.70016
Zakaria Drafsh, Mahdi Nili-Ahmadabadi, Man Yeong Ha

Pressure-based inverse design (ID) cannot converge in flow regimes with ultralow Reynolds numbers (Res). This study proposes a shear-stress-based ID method for airfoil design at Re = 1000 at the optimal angle of attack (AOA) in the presence of a laminar separation bubble. The proposed method applies the difference between the existing and target shear stress distributions (SSDs) to a deformable surface. The Navier–Stokes equations are solved to calculate the wall SSD during each iteration of the ID process. This process modifies the airfoil geometry until the abovementioned difference becomes negligible, achieving convergence to the target geometry. Achieving the maximum lift-to-drag ratio by manually correcting the wall SSD involves extensive trial and error, making it almost impossible. Thus, in the second part of this research, we trained Gaussian process regression and an ensemble of trees deep learning (DL) models using data generated during ID at the optimal AOA to predict lift and drag coefficients, respectively. The SSD was optimized throughout the ID process by coupling the DL models with a genetic algorithm (GA). Optimization was performed in several consecutive cycles, with the DL models becoming more accurate and updated as more data were gathered, helping the GA obtain the optimal SSD and geometry precisely. Finally, the performance curves of different geometries obtained through the optimization cycles were evaluated and compared using the Fluent solver. The results demonstrated a 22.42% increase in the lift-to-drag ratio relative to the initial population at the optimal AOA.

基于压力的反设计(ID)在超低雷诺数(Res)流型中不能收敛。本研究提出了一种基于剪切应力的ID方法的翼型设计在Re = 1000在最佳迎角(AOA)的层流分离泡的存在。该方法将现有剪切应力分布和目标剪切应力分布(ssd)之间的差异应用于可变形表面。求解了Navier-Stokes方程,计算了每次迭代ID过程中的壁面SSD。这个过程修改翼型几何形状,直到上述差异变得可以忽略不计,实现收敛到目标几何形状。通过手动校正壁面SSD来实现最大升阻比需要大量的试验和错误,这几乎是不可能的。因此,在本研究的第二部分中,我们分别使用最优AOA下ID期间生成的数据训练高斯过程回归和树深度学习(DL)模型集合来预测升力和阻力系数。通过将DL模型与遗传算法(GA)耦合,在整个ID过程中对SSD进行优化。优化在几个连续的周期中进行,随着收集到的数据越来越多,DL模型变得更加准确和更新,帮助遗传算法精确地获得最佳的SSD和几何形状。最后,利用Fluent求解器对优化周期得到的不同几何形状的性能曲线进行了评价和比较。结果表明,在最佳AOA下,相对于初始种群,升阻比增加了22.42%。
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引用次数: 0
A Hierarchical Multi-Resolution WENO Scheme for Hyperbolic Conservation Laws 双曲型守恒律的分层多分辨率WENO格式
IF 1.8 4区 工程技术 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-09-22 DOI: 10.1002/fld.70017
Qiushi Ding, Zhengxian Liu, Ming Zhao, Jingshuo Cao, Shixi Hao, Wei Liu, Xiaojian Li

To achieve the high-precision characteristics within the smooth regions while maintaining stable, non-oscillatory, and sharp discontinuity transitions, the weighted essentially non-oscillatory (WENO) scheme and its variants have been developed. However, when there are multiple discontinuities close to each other, the numerical accuracy and robustness of the traditional schemes are probably affected. To this end, a hierarchical multi-resolution WENO (MR-WENO) scheme is proposed in the present study to suppress the overshoot and improve the accuracy of the original MR-WENO scheme in the vicinity of discontinuities. It could achieve an adaptive selection of the substencils and optimal accuracy due to the hierarchical strategy and the new smoothness indicator. The performances of the hierarchical MR-WENO scheme have been tested in 1D and 2D cases. The accuracy has been validated and the influences of weights of both large stencils and small substencils have been comprehensively discussed. The linear weights are adjusted aiming at improving the resolution of discontinuities and suppressing the unexpected weight oscillations. As a result, discontinuities like shock waves and contact discontinuities could be accurately resolved, while overshoot phenomena in the MR-WENO scheme are effectively suppressed in both 1D and 2D cases. Especially, the numerical error of the Lax problem has been reduced by one or two orders of magnitude in the vicinity of discontinuities. With an implementation of the KXRCF indicator, the computational cost has been controlled while maintaining the present superiority of shock capturing capacity.

为了在光滑区域内实现高精度特性,同时保持稳定、非振荡和尖锐的不连续过渡,提出了加权基本非振荡(WENO)格式及其变体。然而,当存在多个相互接近的不连续点时,传统格式的数值精度和鲁棒性可能会受到影响。为此,本文提出了一种分层多分辨率WENO (MR-WENO)方案,以抑制不连续区域附近MR-WENO方案的超调并提高其精度。该方法采用分层策略和新的平滑度指标,实现了材料的自适应选择和最优精度。在一维和二维情况下测试了分层MR-WENO方案的性能。验证了该方法的准确性,并对大模板和小模板重量的影响进行了全面的讨论。对线性权值进行了调整,以提高不连续点的分辨率和抑制权值的非预期振荡。因此,可以准确地解决激波和接触不连续等不连续问题,而MR-WENO方案中的超调现象在一维和二维情况下都得到有效抑制。特别是在不连续面附近,Lax问题的数值误差减小了一到两个数量级。通过KXRCF指标的实现,在保持现有冲击捕获能力优势的同时,控制了计算成本。
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引用次数: 0
Towards Accurate Simulations of Infiltration in Homogeneous Soils Using Harmonic/Geometric Averaging 用调和/几何平均法精确模拟均匀土壤入渗
IF 1.8 4区 工程技术 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-09-14 DOI: 10.1002/fld.70014
Vishnu Prakash K, Ganesh Natarajan

The one-dimensional Richards equation has been widely employed to model water flow in porous media, but the effect of averaging soil diffusivity/hydraulic conductivity on the computed solutions has received comparatively less attention than the numerical approaches to solve the equation. The use of non-arithmetic (harmonic and geometric) averaging of diffusivity in finite volume simulations of the Richards equation is known to produce numerical artifacts that include the lagging of the wetting front in time and even “locked” fronts with no flow, depending on the type of soil and the constitutive relation. In this work, we propose a new and simple approach to define the interfacial diffusivity or hydraulic conductivity based on “modified” non-arithmetic averages that mitigates the spurious artifacts at minimal computational cost. Numerical studies with unsaturated soils using different soil diffusivity models (for horizontal infiltration) and different hydraulic conductivity models (for vertical infiltration) conclusively demonstrate that the m$$ m $$-harmonic and m$$ m $$-geometric averages defined in this work lead to physically consistent solutions of the Richards equation.

一维理查兹方程已被广泛用于模拟多孔介质中的水流,但平均土壤扩散系数/导水率对计算解的影响相对较少受到数值方法求解该方程的关注。在有限体积的Richards方程模拟中,使用非算术(谐波和几何)平均扩散系数会产生数值伪像,其中包括湿润锋在时间上的滞后,甚至是没有流动的“锁定”锋,这取决于土壤的类型和本构关系。在这项工作中,我们提出了一种新的简单方法来定义基于“修正”非算术平均值的界面扩散率或水力导电性,该方法以最小的计算成本减轻了虚假工件。采用不同土壤扩散率模型(水平入渗)和不同导电性模型(垂直入渗)对非饱和土进行的数值研究最终表明,本文定义的m $$ m $$ -谐波和m $$ m $$ -几何平均导致了物理上的影响理查兹方程的一致解。
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引用次数: 0
A Comparative Study on Heat Transfer and Entropy Generation of Ferrofluid Flowing Through a Double-Tube Heat Exchanger Subjected to Various Magnetic Fields 不同磁场作用下双管换热器铁磁流体传热与熵产的比较研究
IF 1.8 4区 工程技术 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-09-11 DOI: 10.1002/fld.70013
Ali Jalayeri, Reza Rahimi

Double-tube heat exchangers using ferrofluids under magnetic fields, which induce vortices, improve heat transfer and reduce irreversibilities. This study analyzes heat transfer and entropy generation of Fe3O4/water in a double-tube heat exchanger at Re = 100, subjected to magnetic fields. Key parameters, including inner tube cross-sectional geometry and magnetic field characteristics (intensity, wire distance, configuration, and number), are examined and optimized. The flow structure, heat transfer, friction factor coefficient, performance evaluation criterion (PEC), and entropy generation are evaluated based on thermodynamic principles. A finite volume numerical code is developed to solve the governing equations and consider the magnetic field through a UDF code on thermal and entropy performance using the SIMPLE algorithm. The investigation is evaluated: (1) the impact of the inner tube's cross-sectional geometry, (2) the effect of the current-carrying wire and outer tube distance, and (3) the influence of the magnetic field's arrangement and number. Altering the cross-sectional geometry shows that a vertically elliptical shape increases heat transfer by 81%, while the horizontally elliptical shape achieves the best overall performance. Adjusting the wire distance to d/r0 = 0.125 offers better overall operational performance by considering the heat transfer and entropy simultaneously. Additionally, a horizontal arrangement with two magnetic fields, which represents the optimal configuration, improves heat transfer and pressure drop by 2.8 and 21 times at Mn = 2 × 1010, and enhances the PEC by 39%. These findings can be applied in the field of energy system optimization, especially where compact design and high thermal efficiency are critical requirements.

在磁场作用下使用铁磁流体的双管换热器,可以诱导涡旋,改善传热并减少不可逆性。本研究分析了Re = 100时双管换热器中Fe3O4/水在磁场作用下的传热和熵产。对关键参数,包括内管截面几何形状和磁场特性(强度、导线距离、结构和数量)进行了检查和优化。基于热力学原理对流动结构、传热、摩擦系数、性能评价标准(PEC)和熵产进行了评价。开发了一个有限体积的数值程序,利用SIMPLE算法求解控制方程,并通过UDF程序考虑磁场对热和熵性能的影响。研究评估了:(1)内管截面几何形状的影响,(2)载流导线和外管距离的影响,(3)磁场排列和数量的影响。改变截面几何形状表明,垂直椭圆形状的传热能力提高81%,而水平椭圆形状的整体性能最好。将导线间距调整为d/r0 = 0.125,同时考虑传热和熵,可以获得更好的整体运行性能。另外,在Mn = 2 × 1010时,两磁场水平布置的传热和压降分别提高了2.8倍和21倍,PEC提高了39%。这些发现可以应用于能源系统优化领域,特别是在紧凑设计和高热效率是关键要求的领域。
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引用次数: 0
A Geometric Multigrid Solver for the Incompressible Navier–Stokes Equations Using Discretely Divergence-Free Finite Elements in 3D 三维离散无散度有限元的不可压缩Navier-Stokes方程几何多网格求解器
IF 1.8 4区 工程技术 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-09-04 DOI: 10.1002/fld.70008
Christoph Lohmann

A geometric multigrid solution technique for the incompressible Navier–Stokes equations in three dimensions is presented, utilizing the concept of discretely divergence-free finite elements without requiring the explicit construction of a basis on each mesh level. For this purpose, functions are constructed in an a priori manner spanning the subspace of discretely divergence-free functions for the Rannacher–Turek finite element pair under consideration. Compared to mixed formulations, this approach yields smaller system matrices with no saddle point structure. This prevents the use of complex Schur complement solution techniques, and more general preconditioners can be employed. While constructing a basis for discretely divergence-free finite elements may pose significant challenges and prevent the use of a structured assembly routine, a basis is utilized only on the coarsest mesh level of the multigrid algorithm. On finer grids, this information is extrapolated to prescribe boundary conditions efficiently. Here, special attention is required for geometries introducing bifurcations in the flow. In such cases, so-called “global” functions with an extended support are defined, which can be used to prescribe the net flux through different branches. Various numerical examples for meshes with different shapes and boundary conditions illustrate the strengths, limitations, and future challenges of this solution concept.

提出了一种三维不可压缩Navier-Stokes方程的几何多网格求解技术,该技术利用离散无散度有限元的概念,无需在每个网格层上明确构建基础。为此,对于所考虑的Rannacher-Turek有限元对,以先验的方式在离散无散度函数的子空间上构造函数。与混合公式相比,这种方法产生更小的系统矩阵,没有鞍点结构。这可以防止使用复杂的舒尔补溶液技术,并可以采用更一般的预调节器。虽然构建离散无散度有限元的基础可能会带来重大挑战,并阻碍结构化装配程序的使用,但基础仅在多网格算法的最粗网格级别上使用。在更细的网格上,这些信息被外推以有效地规定边界条件。在这里,需要特别注意在流中引入分岔的几何形状。在这种情况下,定义了具有扩展支持的所谓“全局”函数,可用于规定通过不同分支的净通量。具有不同形状和边界条件的网格的各种数值示例说明了该解决方案概念的优势,局限性和未来挑战。
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International Journal for Numerical Methods in Fluids
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