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1

Xu, Gang, Ting Ting Jiang, and Jie Hu. "Design and Experiment of Vortex Rings Umbrella Based on Finite Element Method." Advanced Materials Research 785-786 (September 2013): 1225–28. http://dx.doi.org/10.4028/www.scientific.net/amr.785-786.1225.

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In order to research and design the vortex rings umbrella, finite element analytical approach is integrated to design the complicated vortex rings umbrella. Three-dimensional geometrical model of vortex rings umbrella is constructed from the feature of non-linear ductile deformation, and it establish kinetic model of particle node at the stage of steady state rotary motion, finally build simulation model. The calculation shows that motion variation laws of its result and experiment result are basically same, the model is deemed effective and correct. This research can help rapid realization of
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2

G.S., Avinash, and S. Anil Lal. "Inverse Design of Airfoil Using Vortex Element Method." International Journal of Fluid Machinery and Systems 11, no. 2 (2018): 163–70. http://dx.doi.org/10.5293/ijfms.2018.11.2.163.

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3

Wang, H., K. Szekerczes, and A. Afanasev. "Electromagnetic vortex topologies from sparse circular phased arrays." Journal of Physics Communications 6, no. 2 (2022): 025005. http://dx.doi.org/10.1088/2399-6528/ac5089.

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Abstract Structured vortex waves have numerous applications in optics, plasmonics, radio-wave technologies and acoustics. We present a theoretical study of a method for generating vortex states based on coherent superposition of waves from discrete elements of planar phased arrays, given limitations on an element number. Using Jacobi-Anger expansion, we analyze emerging vortex topologies and derive a constraint for the least number of elements needed to generate a vortex with a given leading-order topological charge.
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4

Wong, L. H., and S. M. Calisal. "A Numerical Solution for Potential Flows Including the Effects of Vortex Shedding." Journal of Offshore Mechanics and Arctic Engineering 115, no. 2 (1993): 111–15. http://dx.doi.org/10.1115/1.2920099.

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This paper reports on an attempt to include vortex shedding effects into potential flow calculations using the boundary element method. Significant computational advantages result because of the relatively simple approach to handling separation at the sharp edges while working only with the boundary values. A discrete vortex method was incorporated into a time domain boundary element algorithm for the numerical simulation of oscillating flow past a normal flat plate. Separation from a sharp edge results in the formation of a vortex sheet issuing from the edge. This vortex sheet is modeled by a
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5

Stock, Mark J., and Adrin Gharakhani. "Graphics Processing Unit-Accelerated Boundary Element Method and Vortex Particle Method." Journal of Aerospace Computing, Information, and Communication 8, no. 7 (2011): 224–36. http://dx.doi.org/10.2514/1.52938.

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6

Uchiyama, Tomomi, and Tomohiro Degawa. "Vortex Simulation of the Bubbly Flow around a Hydrofoil." International Journal of Rotating Machinery 2007 (2007): 1–9. http://dx.doi.org/10.1155/2007/72697.

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This study is concerned with the two-dimensional simulation for an air-water bubbly flow around a hydrofoil. The vortex method, proposed by the authors for gas-liquid two-phase free turbulent flow in a prior paper, is applied for the simulation. The liquid vorticity field is discrerized by vortex elements, and the behavior of vortex element and the bubble motion are simultaneously computed by the Lagrangian approach. The effect of bubble motion on the liquid flow is taken into account through the change in the strength of vortex element. The bubbly flow around a hydrofoil of NACA4412 with a ch
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7

Lin, Hui-Fang, and Yi-Chern Hsieh. "Analysis of Vortex-Generation Using Adaptive Finite Element Method to Simulate Hemodynamics of Sigmoid Sinus Diverticulum." International Journal of Clinical Medicine and Bioengineering 2, no. 1 (2022): 33–40. http://dx.doi.org/10.35745/ijcmb2022v02.01.0006.

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In various practical physical problems, the formation of the vortical flow inside the flow field has different effects and consequences. The diverticular vortex has been considered one of the causative factors of venous pulsatile tinnitus (PT). Thus, we aimed to solve the diverticular vortex by using the adaptive finite element method. We investigated the physical phenomena of the diverticular flow field generated during the cardiac cycles and transient changes of various physical phenomena before and after the vortex. The three-dimensional (3D) computational reconstructive geometry was create
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8

Gerasimov, V. V., N. D. Osintseva, V. S. Pavelyev, and A. N. Agafonov. "Generation of Bessel vortex beams in the subterahertz range using reflecting diffractive optical elements." Computer Optics 48, no. 3 (2024): 334–41. http://dx.doi.org/10.18287/2412-6179-co-1410.

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In this work, we propose a simple method for generating Bessel vortex beams in the subterahertz (subTHz) range with the orbital angular momentum with l = 1 based on reflecting metal diffractive optical elements with a continuous helical microrelief. The elements are fabricated by micromilling in a polished duralumin substrate and by tin casting, and tested using a backward wave oscillator (wavelength λ = 855 µm). When using the micromilled element, Bessel vortex beams are shown to be generated and retain a Bessel intensity profile at a distance of 20–50 mm from the reflecting element, which is
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9

Liang, Shin-Jye, Dong-Jiing Doong, and Wei-Ting Chao. "Solution of Shallow-Water Equations by a Layer-Integrated Hydrostatic Least-Squares Finite-Element Method." Water 14, no. 4 (2022): 530. http://dx.doi.org/10.3390/w14040530.

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A multi-layer hydrostatic shallow-water model was developed in the present study. The layer-integrated hydrostatic nonlinear shallow-water was solved with θ time integration and the least-squares finite element method. Since the least-squares formulation was employed, the resulting system of equations was symmetric and positive–definite; therefore, it could be solved efficiently by the preconditioned conjugate gradient method. The model was first applied to simulate the von Karman vortex shedding. A well-organized von Karman vortex street was reproduced. The model was then applied to simulate
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10

Dewanto, Gamaliel, Wati Pranoto, Jack Widjajakusuma, and Hans-Georg Matuttis. "Simulation of incompressible viscous flow using finite element method." E3S Web of Conferences 429 (2023): 02012. http://dx.doi.org/10.1051/e3sconf/202342902012.

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This study focused on simulating incompressible viscous flow using the finite element method. This study used velocity and pressure as unknowns known as primitive variable formulations. Simulation of incompressible fluid flow poses numerical challenges due to the presence of nonlinear convective terms in Navier-Stokes equations and the incompressible nature of the fluid. If the connection between velocities and pressure is not discretized correctly, the stable and convergent velocities might be gained, but the obtained pressure will be oscillatory. To avoid these difficulties, continuous quadr
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11

Dutt, H. N. V. "Analysis of multi-element airfoils by a vortex panel method." AIAA Journal 27, no. 5 (1989): 658–60. http://dx.doi.org/10.2514/3.10159.

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12

Gharakhani, Adrin, and Ahmed F. Ghoniem. "Massively parallel implementation of a 3D vortex-boundary element method." ESAIM: Proceedings 1 (1996): 213–23. http://dx.doi.org/10.1051/proc:1996011.

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13

Kuzmina, Kseniia, Ilia Marchevsky, and Victoriya Moreva. "Parallel Implementation of Vortex Element Method on CPUs and GPUs." Procedia Computer Science 66 (2015): 73–82. http://dx.doi.org/10.1016/j.procs.2015.11.010.

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14

Kostecki, Stanisław. "Random Vortex Method in Numerical Analysis of 2D Flow Around Circular Cylinder." Studia Geotechnica et Mechanica 36, no. 4 (2015): 57–63. http://dx.doi.org/10.2478/sgem-2014-0036.

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Abstract A combination of the vortex method and the boundary element method is used here to predict the two-dimensional flow field around a circular cylinder. Cylindrical structures experience strong hydrodynamic loading, due to vortex detachment from the both sides of cylinder during the flow. Thus, the practical meaning of such calculation is significant particularly in offshore oil and gas engineering as well as in the bridge and hydraulic structure engineering. This paper presents the mathematical formulation of the vortex method for the velocity and vorticity field calculation. The calcul
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15

R., Maiti P., and Bhattacharyya S. K. "Numeric evaluation from cantilever beam and plate." INTERNATIONAL JOURNAL ENGINEERING AND APPLIED TECHNOLOGY (IJEAT) 1, no. 2 (2022): 1–10. http://dx.doi.org/10.52005/ijeat.v1i2.8.

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As soon as fluid passes over a solid surface vortices are formed at the surface of structure to satisfy the no slip boundary conditions at the fluid-structure interface. Vortices that are formed at fluid-structure interface diffuse in fluid domain. In the present study, the strength of vortices is evaluated on the surface of an oscillating structural element (cantilever beam and plate) that is interacting with oscillating fluid flow. In the analysis, the analysis of structural element is carried out by finite element method and analysis of fluid domain is carried out by panel method. It is ass
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16

Epstein, Ronald J., Anthony Leonard, and Alan B. Cain. "Hybrid discrete vortex method (DVM)/boundary element method (BEM) calculations for cavity acoustics." Journal of the Acoustical Society of America 105, no. 2 (1999): 1372. http://dx.doi.org/10.1121/1.426495.

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17

Han, Chenchen, Weidong Gao, and Lifen Chen. "Study on the Trajectory of Free-End Fiber in Jet Vortex Spinning Based on the Elastic Thin-Rod Finite Element Model of Flexible Fiber." Autex Research Journal 20, no. 1 (2020): 43–48. http://dx.doi.org/10.2478/aut-2019-0005.

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AbstractDuring the air flow twisting process of jet vortex spinning, the moving characteristics of flexible free-end fiber are complex. In this paper, the finite element model of the fiber is established based on elastic thin rod element. According to the air pressure and velocity distribution in the airflow twisting chamber of jet vortex spinning, this paper analyzes the undetermined coefficients of the finite element kinetic differential equation of the free-end fiber following the principle of mechanical equilibrium, energy conservation, mass conservation and momentum conservation. Based on
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18

Deglaire, P., O. Ågren, H. Bernhoff, and M. Leijon. "Conformal mapping and efficient boundary element method without boundary elements for fast vortex particle simulations." European Journal of Mechanics - B/Fluids 27, no. 2 (2008): 150–76. http://dx.doi.org/10.1016/j.euromechflu.2007.03.005.

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19

NADAOKA, KAZUO. "Analysis of an interaction process between wave and vortex using boundary element and discrete vortex method." PROCEEDINGS OF COASTAL ENGINEERING, JSCE 36 (1989): 41–45. http://dx.doi.org/10.2208/proce1989.36.41.

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20

Mondal, Partha. "Prediction of Moment Using a Modified Discrete Vortex Method in Ground Effect." Defence Science Journal 71, no. 2 (2021): 146–52. http://dx.doi.org/10.14429/dsj.71.16127.

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The aerodynamics around a wing is modified when it comes near the ground. This is generally referred to as ground effect. In this work, a discrete vortex method based model which can predict two-dimensional (2D) ground effect from its free flight data is proposed. The required data in free flight could be generated either from high fidelity CFD solver or experiments. In this method, strength of the vortex distribution as obtained from discrete vortex based method is modified using a constrained optimisation procedure to match the free flight aerodynamic data. This vortex distribution is furthe
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21

Hirgeto, Dereje Haile, Guo-Wei Qian, Xuan-Yi Zhou, and Wei Wang. "Numerical Study of the Effect of Unsteady Aerodynamic Forces on the Fatigue Load of Yawed Wind Turbines." Machines 13, no. 7 (2025): 607. https://doi.org/10.3390/machines13070607.

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The intentional yaw offset of wind turbines has shown potential to redirect wakes, enhancing overall plant power production, but it may increase fatigue loading on turbine components. This study analyzed fatigue loads on the NREL 5 MW reference wind turbine under varying yaw offsets using blade element momentum theory, dynamic blade element momentum, and the converging Lagrange filaments vortex method, all implemented in OpenFAST. Simulations employed yaw angles from −40° to 40°, with turbulent inflow generated by TurbSim, an OpenFAST tool for realistic wind conditions. Fatigue loads were calc
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22

SHONO, Hideaki, Akira OJIMA, and Kyoji KAMEMOTO. "Development of Virtual Two-Dimensional wind tunnel using Vortex Element Method." Proceedings of the JSME annual meeting 2003.2 (2003): 277–78. http://dx.doi.org/10.1299/jsmemecjo.2003.2.0_277.

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23

Wang, Youjiang, Moustafa Abdel-Maksoud, and Baowei Song. "A boundary element-vortex particle hybrid method with inviscid shedding scheme." Computers & Fluids 168 (May 2018): 73–86. http://dx.doi.org/10.1016/j.compfluid.2018.03.062.

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24

Requerey, Iker S., Basilio Ruiz Cobo, Milan Gošić, and Luis R. Bellot Rubio. "Persistent magnetic vortex flow at a supergranular vertex." Astronomy & Astrophysics 610 (February 2018): A84. http://dx.doi.org/10.1051/0004-6361/201731842.

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Context. Photospheric vortex flows are thought to play a key role in the evolution of magnetic fields. Recent studies show that these swirling motions are ubiquitous in the solar surface convection and occur in a wide range of temporal and spatial scales. Their interplay with magnetic fields is poorly characterized, however. Aims. We study the relation between a persistent photospheric vortex flow and the evolution of a network magnetic element at a supergranular vertex. Methods. We used long-duration sequences of continuum intensity images acquired with Hinode and the local correlation-tracki
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25

H, Kalis, Kangro I, and Aboltins A. "Mathematical modeling of velocity field induced by the vortex." Annals of Mathematics and Physics 7, no. 1 (2024): 096–106. http://dx.doi.org/10.17352/amp.000113.

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In new technological applications, it is important to use vortex distributions in the area for obtaining large velocity fields. This paper, it was calculated the distribution of the velocity field and distribution of stream function for ideal incompressible fluid, induced by a different system of the finite number of vortex threads: 1) circular vortex lines in a finite cylinder, positioned on its inner, 2) spiral vortex threads, positioned on the inner surface of the finite cylinder or cone, and 3) linear vortex lines in the plane channel, positioned on its boundary. An original method was use
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26

Król, Przemysław, and Krzysztof Tesch. "Experimental and Numerical Validation of the Improved Vortex Method Applied to CP745 Marine Propeller Model." Polish Maritime Research 25, no. 2 (2018): 57–65. http://dx.doi.org/10.2478/pomr-2018-0054.

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Abstract The article presents a numerical analysis of the CP745 marine propeller model by means of the improved vortex method and CFD simulations. Both numerical approaches are validated experimentally by comparing with open water characteristics of the propeller. The introduced modification of the vortex method couples the lifting surface approach for the propeller blades and the boundary element method for the hub. What is more, a simple algorithm for determination of the propeller induced advance angles is established. The proposed modifications provide better results than the original vers
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27

Liu, Jing Shi, Ya Zhou Sun, Li Hua Lu, and Ying Chun Liang. "Factors Effect on Vortex Torque of Aerostatic Bearings." Advanced Materials Research 97-101 (March 2010): 3745–48. http://dx.doi.org/10.4028/www.scientific.net/amr.97-101.3745.

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In order to improve the drift accuracy of aerostatic bearings, the air supply pressure and manufacturing errors effect on vortex torque of aerostatic bearings were studied by using the finite element method. This paper analyzed the influence of air supply pressure on vortex torque, in view of elliptical error, incline error of throttle slit and radial eccentricity ratio exist. The quadratic regression orthogonal design was adopted to establish function expression of vortex torque among air supply pressure, elliptical error, incline error of throttle slit and radial eccentricity ratio. In resea
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28

Lee, Hanseong, and Spyros A. Kinnas. "Application of a Boundary Element Method in the Prediction of Unsteady Blade Sheet and Developed Tip Vortex Cavitation on Marine Propellers." Journal of Ship Research 48, no. 01 (2004): 15–30. http://dx.doi.org/10.5957/jsr.2004.48.1.15.

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Most marine propellers operate in nonaxisymmetric inflows, and thus their blades are often subject to an unsteady flow field. In recent years, due to increasing demands for faster and larger displacement ships, the presence of blade sheet and tip vortex cavitation has become very common. Developed tip vortex cavitation, which often appears together with blade sheet cavitation, is known to be one of the main sources of propeller-induced pressure fluctuations on the ship hull. The prediction of developed tip vortex cavity as well as blade sheet cavity is thus quite important in the assessment of
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29

Kinnas, Spyros A., Ye Tian, and Abhinav Sharma. "Numerical Modeling of a Marine Propeller Undergoing Surge and Heave Motion." International Journal of Rotating Machinery 2012 (2012): 1–8. http://dx.doi.org/10.1155/2012/257461.

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A boundary element method (BEM) and a vortex-lattice method (VLM) are extended in order to predict the unsteady performance of propellers subject to rigid body motions. The methods are applied in the case of prescribed surge and heave motions, and the results are compared with those from other methods.
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Kirchhart, Matthias, and Shinnosuke Obi. "A Smooth Partition of Unity Finite Element Method for Vortex Particle Regularization." SIAM Journal on Scientific Computing 39, no. 5 (2017): A2345—A2364. http://dx.doi.org/10.1137/17m1116258.

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31

YOKOTA, Rio, and Shinnosuke OBI. "2016 Simulation of a Wake using a 3-D Vortex Element Method." Proceedings of the JSME annual meeting 2006.1 (2006): 31–32. http://dx.doi.org/10.1299/jsmemecjo.2006.1.0_31.

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32

Jiang, Fei, Kangping Liao, Kazuki Matsumura, Junji Ohgi, and Xian Chen. "Simulation of Fluid–Structure Interaction Problems with Thin Elastic Plate via the Coupling of Finite Element and Lattice Boltzmann Methods." International Journal of Computational Methods 17, no. 10 (2020): 2050013. http://dx.doi.org/10.1142/s0219876220500139.

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A numerical framework is proposed to couple the finite element (FE) and lattice Boltzmann methods (LBM) for simulating fluid–structure interaction (FSI) problems. The LBM is used as an efficient method for solving the weakly-compressible fluid flows. The corotational FE method for beam elements is used to solve the thin plate deformation. The two methods are coupled via a direct-forcing immersed boundary (IB) method with a sub-iteration scheme. A virtual structure method has been developed to improve the computational accuracy. Validations of the proposed coupling method have been carried out
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33

TIAN, FANG-BAO, YUAN-QING XU, XIAO-YING TANG, and YU-LIN DENG. "STUDY ON A SELF-PROPELLED FISH SWIMMING IN VISCOUS FLUID BY A FINITE ELEMENT METHOD." Journal of Mechanics in Medicine and Biology 13, no. 06 (2013): 1340012. http://dx.doi.org/10.1142/s0219519413400125.

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A self-propelled fish swimming in viscous fluid is investigated by solving the incompressible Navier–Stokes equations numerically with the space-time finite element method to understand the mechanisms of aquatic animal locomotion. Two types of propulsion strategies, undulatory body and traveling wave surface (TWS), are considered. Based on the simulations, we find that by performing lateral undulation, the fish is able to move forward with a reverse von Kármán vortex street in its wake. In addition, there is no vortex street in the wake of the fish using TWS. In this case, the thrust of the fi
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34

Chen, Cichang, Tohru Fukano, and Yoshinori Hara. "Flow Analysis in a Cross-Flow Fan by Boundary Element Method and Discrete Vortex Method." Transactions of the Japan Society of Mechanical Engineers Series B 61, no. 587 (1995): 2387–92. http://dx.doi.org/10.1299/kikaib.61.2387.

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35

Kim, Yoo-Chul, Jung-Chun Suh, and Kyung-Jun Lee. "Vortex-in-cell method combined with a boundary element method for incompressible viscous flow analysis." International Journal for Numerical Methods in Fluids 69, no. 10 (2011): 1567–83. http://dx.doi.org/10.1002/fld.2649.

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36

Huyer, S. A., and J. R. Grant. "Computation of Unsteady Separated Flow Fields Using Anisotropic Vorticity Elements." Journal of Fluids Engineering 118, no. 4 (1996): 839–49. http://dx.doi.org/10.1115/1.2835518.

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A novel computational methodology to compute two-dimensional unsteady separated flow fields using a vorticity based formulation is presented. Unlike traditional vortex methods, the elements used in this method are designed to take advantage of the natural anisotropy of most external flows. These vortex elements are disjoint and of compact support. The vorticity is uniform over rectangular elements whose initial thickness is set by a diffusion length scale. The elements are a mathematical construction which enables the vorticity of the flow to be created and followed numerically, and the Biot-S
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37

Goryanikov, Danil. "INVESTIGATION OF THE DEPENDENCE OF THE FREQUENCY OF WINDAGE ON THE SHAPE OF THE BODY OF THE FLOW." Energy Systems 9, no. 3 (2024): 80–83. https://doi.org/10.34031/es.2024.3.008.

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The article presents the results of a study of the influence of the shape of the flow body (TO) on the frequency of vortex formation in a vortex flowmeter with an external sensitive element. Numerical simulation using CFD (Computational Fluid Dynamics), implemented in the program for modeling physical phenomena using the Comsol Multiphysics finite element method (Femlab), was performed for three modifications of a cylindrical body of flow at three different flow velocities (0.11, 0.27 and 0.44 m/s) and a distance of 40 mm from the starting point equal to 0.017965 m. The obtained data on the fr
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38

Lee, Hanseong, and Spyros A. Kinnas. "Unsteady Wake Alignment for Propellers in Nonaxisymmetric Flows." Journal of Ship Research 49, no. 03 (2005): 176–90. http://dx.doi.org/10.5957/jsr.2005.49.3.176.

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A low-order boundary element method is applied to predict the trailing wake geometries shedding from hydrofoil and marine propellers in steady and unsteady flows, as well as the vortex motions of the classical lifting line problem with elliptic loading distribution. In order to prevent the numerical instability near the vortex roll-up region, a tip vortex with finite core size is introduced at the end of the vortex line (or at the tip of the wake sheet in the case of a three-dimensional problem), and the induced velocities are evaluated at the displaced control points instead of the actual con
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Марчевский, И. К., К. С. Кузьмина, and С. Р. Гречкин-Погребняков. "An implementation of vortex methods for modeling 2D incompressible flows using the CUDA technology." Numerical Methods and Programming (Vychislitel'nye Metody i Programmirovanie), no. 1 (April 2, 2015): 165–76. http://dx.doi.org/10.26089/nummet.v16r117.

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Исследована возможность ускорения вычислений в методе вихревых элементов - бессеточном лагранжевом методе вычислительной гидродинамики - за счет использования графических ускорителей. Реализован алгоритм, основанный на авторской модификации метода вихревых элементов, позволяющий проводить все необходимые вычисления непосредственно на графическом ускорителе с использованием технологии CUDA. Скорость решения типичной задачи на одном ускорителе GeForce GTX 970 или Tesla C2050 оказывается соизмеримой со скоростью решения аналогичной задачи на кластере, содержащем 30-40 ядер, при использовании техн
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40

Zou, Jiahe, Bo Zhou, Wenxin Yi, Conghong Lu, Hui Liu, and Wenqing Luo. "Numerical Study of Vortex-Induced Vibration Characteristics of a Long Flexible Marine Riser." Journal of Marine Science and Engineering 12, no. 11 (2024): 1892. http://dx.doi.org/10.3390/jmse12111892.

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In ocean engineering, interactions between ocean currents and risers lead to regular vortex shedding on both sides of the riser, causing structural deformation. When the frequency of vortex shedding approaches the natural frequency of the structure, resonance occurs, significantly increasing deformation. This phenomenon is a critical cause of riser failure. Therefore, the dynamic response of flexible risers to vortex-induced vibrations (VIV) is crucial for their structural safety. This paper employs the finite-volume method to integrate over control volumes to solve for forces, such as pressur
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41

WANG, Zimo, Qidong CHEN, and Siyang ZHONG. "A rapid aerodynamic noise prediction model for multi-rotor unmanned aircraft systems with inclusion of wake effect." INTER-NOISE and NOISE-CON Congress and Conference Proceedings 270, no. 10 (2024): 1199–209. http://dx.doi.org/10.3397/in_2024_2841.

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In this work, the effect of wake on the rotor aerodynamics and aeroacosutics is studied based on an efficient rapid prediction model, which incorporates the induced effects of tip vortex on the blades into the blade element momentum theory. The tip vortex model is estimated using the free vortex wake method. The aerodynamic flow variables, as well as the unsteady loadings due to the radial flow and induction of tip vortices, are employed to model to equivalent sources and, therefore, noise emission, using Goldstein's acoustic analogy. The comparison between the hybrid algorithm and blade eleme
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42

Lin, Lin, and Yan Ying Wang. "Nonlinear Analysis of Vortex Induced Dynamic Response of Marine Riser." Applied Mechanics and Materials 353-356 (August 2013): 2736–40. http://dx.doi.org/10.4028/www.scientific.net/amm.353-356.2736.

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Vortex-induced dynamic response is the most important issue influencing marine riser. This paper presents an investigation on the vortex-induced nonlinear dynamic response of marine riser subjected to combined waves,currents and platform movement. The in-line force was solved by Morison equation under combined waves,currents and platform movement while cross-flow force was solved by wake oscillator model. Updated Lagrangianmethod was used to solve the nonlinear problem.The governing equations were discretized by finite element method and solved by Newmark-β method in time domain. Influence of
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43

Kudrov, M. A., A. S. Shcheglov, and V. S. Bugaev. "Study of vortex element method parameters and their effect on rigid rotation bodies aerodynamic computations." Journal of «Almaz – Antey» Air and Space Defence Corporation, no. 1 (March 30, 2019): 51–58. http://dx.doi.org/10.38013/2542-0542-2019-1-51-58.

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The purpose of this study was to implement a software package that allows non-stationary aerodynamic computations of fixed rotation bodies using the vortex element method. In the course of the work, we developed an algorithm for rigid rotation bodies aerodynamic computations by means of this method. Furthermore, we studied the influence of calculation parameters on the results obtained.
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44

Kummer, Florian, Martin Oberlack, Roozbeh Mousavi, Nehzat Emamy, and Zahra Niroobakhsh. "Numerical investigation of laminar vortex shedding applying a discontinuous Galerkin Finite Element method." Progress in Computational Fluid Dynamics, An International Journal 1, no. 1 (2015): 1. http://dx.doi.org/10.1504/pcfd.2015.10001170.

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45

Niroobakhsh, Zahra, Nehzat Emamy, Roozbeh Mousavi, Florian Kummer, and Martin Oberlack. "Numerical investigation of laminar vortex shedding applying a discontinuous Galerkin finite element method." Progress in Computational Fluid Dynamics, An International Journal 17, no. 3 (2017): 131. http://dx.doi.org/10.1504/pcfd.2017.084346.

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46

Krakov, M. S. "CONTROL VOLUME FINITE-ELEMENT METHOD FOR NAVIER-STOKES EQUATIONS IN VORTEX-STREAMFUNCTION FORMULATION." Numerical Heat Transfer, Part B: Fundamentals 21, no. 2 (1992): 125–45. http://dx.doi.org/10.1080/10407799208944913.

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47

Farrant, T., M. Tan, and W. G. Price. "A cell boundary element method applied to laminar vortex shedding from circular cylinders." Computers & Fluids 30, no. 2 (2001): 211–36. http://dx.doi.org/10.1016/s0045-7930(00)00009-8.

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48

Jiang, Jin, Quanyong Ju, and Yue Yang. "Finite Element Vortex Method for Hydrodynamic Analysis of Vertical Axis Cycloidal Tidal Turbine." Journal of Coastal Research 93, sp1 (2019): 988. http://dx.doi.org/10.2112/si93-143.1.

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49

Ghoniem, Ahmed F., Ghassem Heidarinejad, and Anantha Krishnan. "Numerical simulation of a thermally stratified shear layer using the vortex element method." Journal of Computational Physics 79, no. 1 (1988): 135–66. http://dx.doi.org/10.1016/0021-9991(88)90008-3.

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50

Papakalodoukas, Ioannis, and Kostas Belibassakis. "Performance Prediction of Bow-Foil Thrusters in Waves Using Unsteady Vortex Element Method." Journal of Marine Science and Engineering 13, no. 6 (2025): 1152. https://doi.org/10.3390/jmse13061152.

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In this study, an unsteady vortex element method is applied to the analysis of a horizontal wing in order to investigate its propulsive performance when operating as a biomimetic thruster. The foil undergoes a combined heaving and pitching motion at the same frequency, in a uniform inflow condition, due to its advance at a constant speed. The numerical results are presented and compared to experimental measurements for the propulsion thrust coefficient and the efficiency of the system over a range of motion parameters. The results indicate the significance of 3D effects and show that the prese
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