Treatment of singularities in boundary element method and application in Darcy’s flow through porous media
Email:
anh-tuan.tran@utc.edu.vn
Keywords:
Singularity, boundary element method, potential equation, Darcy’s flow
Abstract
The potential equation such as Poisson and Laplace, describes the behavior of many varied physical situations. The boundary element method has been used successfully to determinate accurate solutions of this potential problem. The basic of this method is the expression of the solution in terms of the boundary values by applying Green’s identity and its fundamental solution. However, one difficulty that arises in the boundary element method is the treatment of kernel singularities appear in integrals. This work presents an improved technique for the evaluation of singular values that appear in the solution of two-dimensional Darcy’s flow through porous media using the boundary element method. In this case study, the singularities are removed by employing a finite difference scheme and an analytical integration scheme. The comparative results of the velocity and pressure fields of Darcy’s flow determined by the present method and the finite element method showed the accuracy as well as efficiency of the proposal approach.References
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[3]. A. Teimoori, Z. Chen, S. S. Rahman, T. Tran, Effective Permeability Calculation Using Boundary Element Method in Naturally Fractured Reservoirs, Petroleum Science and Technology, 23 (2005) 693–709. https://doi.org/10.1081/LFT-200033029
[4]. O. O. Onyejekwe, A Boundary Element-Finite Element Equation Solutions to Flow in Heterogeneous Porous Media, Transport in Porous Media, 31 (1998) 293–312. https://doi.org/10.1023/A:1006529122626.
[5]. J. T. Katsikadelis, Boundary Elements : Theory and Application, First ed., Elsevier Science Ltd, Oxford, 2002.
[6]. L. Gaul, M. Kogl, M. Wagner, Boundary Element Methods for Engineers and Scientists, First ed., Springer-Verlag Berlin, Heidelberg, New York, 2003.
[7]. C. A. Brebbia, J. C. F. Telles, L. C. Wrobel, Boundary Element Techniques : Theory and Application in Engineering, Springer-Verlag, Berlin, Heidelberg, 1984.
[8]. M. Dehghan, H. Hosseinzadeh, Calculation of 2D singular and near singular integrals of boundary elements method based on the complex space C, Applied Mathematical Modelling, 36 (2012) 545–560. https://doi.org/10.1016/j.apm.2011.07.036
[9]. L. Marin, D. Lesnic, V. Mantic, Treatment of singularities in Helmholtz-type equations using the boundary element method, Journal of Sound and Vibration, 278 (2004) 39–62. https://doi.org/10.1016/j.jsv.2003.09.059
[10]. Q. Huang, T. A. Cruse, Some notes on singular integral techniques in boundary element analysis, International journal for numerical methods in engineering, 36 (1993) 2643–2659. https://doi.org/10.1002/nme.1620361509.
[11]. V. Sladek, J. Sladek, Singular integrals and boundary elements, Comput. Methods Appl. Mech. Engrg., 157 (1998) 251 – 266. https://doi.org/10.1016/S0045-7825(97)00239-9
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Received
12/12/2019
Revised
24/03/2020
Accepted
29/03/2020
Published
24/04/2020
Type
Research Article
How to Cite
Trần Anh, T., & Nguyễn Đình, H. (1587661200). Treatment of singularities in boundary element method and application in Darcy’s flow through porous media . Transport and Communications Science Journal, 71(3), 230-240. https://doi.org/10.25073/tcsj.71.3.7
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