Analytical evaluation of the BEM singular integrals for 3D Laplace and Stokes flow equations using coordinate transformation

被引：5
|
作者：
Ren, Qinlong [1 ]
Chan, Cho Lik [1 ]
机构：
[1] Univ Arizona, Dept Aerosp & Mech Engn, Tucson, AZ 85721 USA
来源：
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS | 2015年 / 53卷
关键词：
Boundary element method; Coordinate transformation; Analytical integration; Laplace's equation; Stokes flow; FORMULATIONS;
D O I：
10.1016/j.enganabound.2014.11.018
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
It is well-known that singular integrals arise when the source point and field point are in the same element in boundary element method. To improve the accuracy, analytical evaluation of the singular integral should be carried out whenever possible. However, the analytical formulas for the BEM singular integrals are always quite complicated in 3D problems. In this paper, by applying a coordinate transformation, the analytical formulas of the singular integrals for 3D Laplace's and Stokes flow equations are obtained for arbitrary triangular boundary elements with constant elements approximation. In addition, numerical examples will be presented to demonstrate the improvement on accuracy. Published by Elsevier Ltd.
引用
收藏
页码：1 / 8
页数：8
相关论文
共 50 条
  • [21] Analytical removal of singularity and direct evaluation of singular integrals in 3-D elastoplastic finite deformation analysis by BEM
    Lu, Shan
    Ye, Tian-Qi
    Chen, Bai-Ping
    Acta Mechanica Solida Sinica, 1993, 6 (04): : 387 - 399
  • [22] Potentially Singular Behavior of the 3D Navier–Stokes Equations
    Thomas Y. Hou
    Foundations of Computational Mathematics, 2023, 23 : 2251 - 2299
  • [23] A new smoothing strategy for computing nearly singular integrals in 3D Galerkin BEM
    Scuderi, Letizia
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2009, 225 (02) : 406 - 427
  • [24] BEM computation of 3D Stokes flow including moving front
    M.-Q. Thai
    F. Schmidt
    G. Dusserre
    A. Cantarel
    L. Silva
    International Journal of Material Forming, 2017, 10 : 567 - 580
  • [25] BEM computation of 3D Stokes flow including moving front
    Thai, M. -Q.
    Schmidt, F.
    Dusserre, G.
    Cantarel, A.
    Silva, L.
    INTERNATIONAL JOURNAL OF MATERIAL FORMING, 2017, 10 (04) : 567 - 580
  • [26] The FMM-BEM Method for the 3D Particulate Stokes Flow
    Selmi, Hassib
    Abdelwahed, Mohamed
    Hamda, Hatem
    El Asmi, Lassaad
    ABSTRACT AND APPLIED ANALYSIS, 2014,
  • [27] Aspects about treating integrals of singular kernels when applying BEM to solve 3D problems of fluid flow
    Luminita, Grecu
    Valentin, Grecu
    PROCEEDINGS OF THE 4TH IASME/WSEAS INTERNATIONAL CONFERENCE ON CONTINUUM MECHANICS, 2009, : 46 - 49
  • [28] 3D acoustic wave simulation using BEM formulations: Closed form integration of singular and hypersingular integrals
    Tadeu, A.
    Antonio, J.
    ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 2012, 36 (09) : 1389 - 1396
  • [29] An efficient scheme of calculating nearly singular integrals for the 3D BEM modeling of thin media
    Shiah, Y. C.
    Zhan, Jin-Jia
    Hematiyan, M. R.
    ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 2024, 169
  • [30] Closed Form Integration of Singular and Hypersingular Integrals in 3D BEM Formulations for Heat Conduction
    Tadeu, A.
    Prata, J.
    Simoes, N.
    MATHEMATICAL PROBLEMS IN ENGINEERING, 2012, 2012
12345