{"title":"Vortex Panel Method in Axisymmetric Cylindrical Coordinates: Inviscid Formulation","authors":"Suguru Shiratori, Kosuke Kimata, Masaya Katoh, Hideaki Nagano, Kenjiro Shimano","doi":"10.1002/fld.5400","DOIUrl":null,"url":null,"abstract":"<p>This study addresses the vortex panel method, which is an efficient solution for inviscid flow around a body. For Cartesian coordinates, the panel method has been developed and widely applied. However, a formulation has not been proposed for axisymmetric cylindrical coordinates. This study derives a Green's function corresponding to the governing equation of the potential flow in axisymmetric cylindrical coordinates by modifying the Green's function provided by Cohl and Tohline [doi:10.1086/308062]. The derived Green's function <span></span><math>\n \n <semantics>\n <mrow>\n <mi>G</mi>\n </mrow>\n <annotation>$$ G $$</annotation>\n </semantics></math> is significantly compact and is composed of a single term of the half-integer degree Legendre function of the second type. The derivation of Green's function <span></span><math>\n <semantics>\n <mrow>\n <mi>G</mi>\n </mrow>\n <annotation>$$ G $$</annotation>\n </semantics></math> is confirmed by analytically evaluating the requirement <span></span><math>\n <semantics>\n <mrow>\n <mi>ℒ</mi>\n <mi>G</mi>\n <mo>=</mo>\n <mn>0</mn>\n </mrow>\n <annotation>$$ \\mathit{\\mathcal{L}G}=0 $$</annotation>\n </semantics></math>, where <span></span><math>\n <semantics>\n <mrow>\n <mi>ℒ</mi>\n </mrow>\n <annotation>$$ \\mathcal{L} $$</annotation>\n </semantics></math> is a linear operator of the governing equation. Under the derived <span></span><math>\n <semantics>\n <mrow>\n <mi>G</mi>\n </mrow>\n <annotation>$$ G $$</annotation>\n </semantics></math>, the vortex panel method is formulated by discretizing the vorticity distribution along the body surface. The validity of the constructed panel method is confirmed through calculations of the flow past a sphere, an ellipsoid, a torus, and a teardrop-like object by comparison with analytical or numerical solutions.</p>","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":"97 9","pages":"1161-1170"},"PeriodicalIF":1.8000,"publicationDate":"2025-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/fld.5400","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal for Numerical Methods in Fluids","FirstCategoryId":"5","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/fld.5400","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
Abstract
This study addresses the vortex panel method, which is an efficient solution for inviscid flow around a body. For Cartesian coordinates, the panel method has been developed and widely applied. However, a formulation has not been proposed for axisymmetric cylindrical coordinates. This study derives a Green's function corresponding to the governing equation of the potential flow in axisymmetric cylindrical coordinates by modifying the Green's function provided by Cohl and Tohline [doi:10.1086/308062]. The derived Green's function is significantly compact and is composed of a single term of the half-integer degree Legendre function of the second type. The derivation of Green's function is confirmed by analytically evaluating the requirement , where is a linear operator of the governing equation. Under the derived , the vortex panel method is formulated by discretizing the vorticity distribution along the body surface. The validity of the constructed panel method is confirmed through calculations of the flow past a sphere, an ellipsoid, a torus, and a teardrop-like object by comparison with analytical or numerical solutions.
期刊介绍:
The International Journal for Numerical Methods in Fluids publishes refereed papers describing significant developments in computational methods that are applicable to scientific and engineering problems in fluid mechanics, fluid dynamics, micro and bio fluidics, and fluid-structure interaction. Numerical methods for solving ancillary equations, such as transport and advection and diffusion, are also relevant. The Editors encourage contributions in the areas of multi-physics, multi-disciplinary and multi-scale problems involving fluid subsystems, verification and validation, uncertainty quantification, and model reduction.
Numerical examples that illustrate the described methods or their accuracy are in general expected. Discussions of papers already in print are also considered. However, papers dealing strictly with applications of existing methods or dealing with areas of research that are not deemed to be cutting edge by the Editors will not be considered for review.
The journal publishes full-length papers, which should normally be less than 25 journal pages in length. Two-part papers are discouraged unless considered necessary by the Editors.