{"title":"Interface analysis of magnetic fluids by the boundary element method considering multiplicity and singularity","authors":"","doi":"10.1016/j.enganabound.2024.105889","DOIUrl":null,"url":null,"abstract":"<div><p>The present paper is devoted for numerical analysis of interface phenomena of magnetic fluids in real space and time, when the Boundary Element Method (BEM) is employed. The BEM obtains not only the magnetic potential and the normal magnetic induction for static magnetic fields but also the fluid velocity potential and the normal fluid velocity for incompressible–irrotational fluids, on arbitrary-shaped interfaces. During the discretizing process, one of the problems is the multiplicity, that is, multi-valued physical quantities at the edges and corners of the domains, or sharp-pointed peaks on the interface. Another problem is the singularity in the diagonal discretization terms, which is inherent to the BEM. Discretization elements at the same position are grouped for the multiplicity. The sum rules for discretization coefficients are used to avoid the singularity, which is derived from the uniform vector field conditions as the extension from the conventional one. Based on the formulated equations, a computational code was produced, and applied for simplified and more general conditions. This code generates magnetic fields on the interface between the fluid and the vacuum as intended with the least numerical effects. It also generates the fluid velocity caused by ununiform distribution of the sum of interface stresses. The applicability for the stability analysis on the Rosensweig instability is also discussed.</p></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":null,"pages":null},"PeriodicalIF":4.2000,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Engineering Analysis with Boundary Elements","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0955799724003631","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
The present paper is devoted for numerical analysis of interface phenomena of magnetic fluids in real space and time, when the Boundary Element Method (BEM) is employed. The BEM obtains not only the magnetic potential and the normal magnetic induction for static magnetic fields but also the fluid velocity potential and the normal fluid velocity for incompressible–irrotational fluids, on arbitrary-shaped interfaces. During the discretizing process, one of the problems is the multiplicity, that is, multi-valued physical quantities at the edges and corners of the domains, or sharp-pointed peaks on the interface. Another problem is the singularity in the diagonal discretization terms, which is inherent to the BEM. Discretization elements at the same position are grouped for the multiplicity. The sum rules for discretization coefficients are used to avoid the singularity, which is derived from the uniform vector field conditions as the extension from the conventional one. Based on the formulated equations, a computational code was produced, and applied for simplified and more general conditions. This code generates magnetic fields on the interface between the fluid and the vacuum as intended with the least numerical effects. It also generates the fluid velocity caused by ununiform distribution of the sum of interface stresses. The applicability for the stability analysis on the Rosensweig instability is also discussed.
本文采用边界元法(BEM)对磁性流体在实际空间和时间中的界面现象进行数值分析。BEM 不仅可以获得静态磁场的磁势和法向磁感应强度,还可以获得不可压缩旋转流体在任意形状界面上的流体速度势和法向流体速度。在离散化过程中,其中一个问题是多值性,即域的边缘和角落或界面上的尖峰处存在多值物理量。另一个问题是 BEM 固有的对角离散项的奇异性。同一位置上的离散化元素会因多重性而分组。离散化系数的求和规则用于避免奇异性,而奇异性是由均匀矢量场条件推导出来的,是传统矢量场条件的延伸。根据所制定的方程,编制了计算代码,并应用于简化和更一般的条件。该代码以最小的数值效应在流体和真空之间的界面上产生磁场。它还生成了由界面应力总和的不均匀分布引起的流体速度。此外,还讨论了罗森斯魏格不稳定性稳定性分析的适用性。
期刊介绍:
This journal is specifically dedicated to the dissemination of the latest developments of new engineering analysis techniques using boundary elements and other mesh reduction methods.
Boundary element (BEM) and mesh reduction methods (MRM) are very active areas of research with the techniques being applied to solve increasingly complex problems. The journal stresses the importance of these applications as well as their computational aspects, reliability and robustness.
The main criteria for publication will be the originality of the work being reported, its potential usefulness and applications of the methods to new fields.
In addition to regular issues, the journal publishes a series of special issues dealing with specific areas of current research.
The journal has, for many years, provided a channel of communication between academics and industrial researchers working in mesh reduction methods
Fields Covered:
• Boundary Element Methods (BEM)
• Mesh Reduction Methods (MRM)
• Meshless Methods
• Integral Equations
• Applications of BEM/MRM in Engineering
• Numerical Methods related to BEM/MRM
• Computational Techniques
• Combination of Different Methods
• Advanced Formulations.