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Solution of Two-Dimensional Stokes Flow Problems Using Improved Singular Boundary Method

  • Wenzhen Qu (a1) and Wen Chen (a1)
Abstract
Abstract

In this paper, an improved singular boundary method (SBM), viewed as one kind of modified method of fundamental solution (MFS), is firstly applied for the numerical analysis of two-dimensional (2D) Stokes flow problems. The key issue of the SBM is the determination of the origin intensity factor used to remove the singularity of the fundamental solution and its derivatives. The new contribution of this study is that the origin intensity factors for the velocity, traction and pressure are derived, and based on that, the SBM formulations for 2D Stokes flow problems are presented. Several examples are provided to verify the correctness and robustness of the presented method. The numerical results clearly demonstrate the potentials of the present SBM for solving 2D Stokes flow problems.

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Corresponding author
*Email:chenwen@hhu.edu.cn(W. Chen)
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[1] M. Li , T. Tang and B. Fornberg , A compact fourth-order finite difference scheme for the steady incompressible Navier-Stokes equations, Int. J. Numer. Methods Fluids, 20 (1995), pp. 11371151.

[2] C. Taylor and P. Hood , A numerical solution of the Navier-Stokes equations using the finite element technique, Comput. Fluids, 1 (1973), pp. 73100.

[5] H. Ogata , A fundamental solution method for three-dimensional Stokes flow problems with obstacles in a planar periodic array, J. Comput. Appl. Math., 189 (2006), pp. 622634.

[6] C. J. S. Alves and A. Silvestre , Density results using Stokeslets and a method of fundamental solutions for the Stokes equations, Eng. Anal. Boundary Elements, 28 (2004), pp. 12451252.

[7] G. Fairweather and A. Karageorghis , The method of fundamental solutions for elliptic boundary value problems, Adv. Comput. Math., 9 (1998), pp. 6995.

[9] Y. Liu , A new boundary meshfree method with distributed sources, Eng. Anal. Boundary Elements, 34 (2010), pp. 914919.

[10] W. Chen and F. Z. Wang , A method of fundamental solutions without fictitious boundary, Eng. Anal. Boundary Elements, 34 (2010), pp. 530532.

[11] Y. Gu , W. Chen and C. Z. Zhang , Singular boundary method for solving plane strain elasto-static problems, Int. J. Solids Structures, 48 (2011), pp. 25492556.

[13] D. Young , S. Jane , C. Fan , K. Murugesan and C. Tsai , The method of fundamental solutions for 2D and 3D Stokes problems, J. Comput. Phys., 211 (2006), pp. 18.

[14] D. Young , C. Chen , C. Fan , K. Murugesan and C. Tsai , The method of fundamental solutions for Stokes flow in a rectangular cavity with cylinders, Euro. J. Mech. B Fluids, 24 (2005), pp. 703716.

[15] W. Chen and Z. J. Fu , A novel numerical method for infinite domain potential problems, Chinese Science Bulletin, 55 (2010), pp. 15981603.

[16] M. Tanaka , V. Sladek and J. Sladek , Regularization techniques applied to boundary element methods, Appl. Mech. Rev., 47 (1994), pp. 457.

[17] D. L. Young , K. H. Chen and C. W. Lee , Novel meshless method for solving the potential problems with arbitrary domain, J. Comput. Phys., 209 (2005), pp. 290321.

[18] Y. Gu , W. Chen and J. Zhang , Investigation on near-boundary solutions by singular boundary method, Eng. Anal. Boundary Elements, 36 (2012), pp. 11731182.

[19] Y. Liu , A new fast multipole boundary element method for solving 2-D Stokes flow problems based on a dual BIE formulation, Engineering Anal. Boundary Elements, 32 (2008), pp. 139151.

[21] D. L. Young , S. C. Jane , C. Y. Lin , C. L. Chiu and K. C. Chen , Solutions of 2D and 3D Stokes laws using multiquadrics method, Engineering Anal. Boundary Elements, 28 (2004), pp. 12331243. ˇ

[22] B. Šarler , Solution of potential flow problems by the modified method of fundamental solutions: formulations with the single layer and the double layer fundamental solutions, Engineering Anal. Boundary Elements, (2009), pp. 13741382.

[24] C. Pozrikidis , Boundary Integral and Singularity Methods for Linearized Viscous Flow, Cambridge University Press, 1992.

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Advances in Applied Mathematics and Mechanics
  • ISSN: 2070-0733
  • EISSN: 2075-1354
  • URL: /core/journals/advances-in-applied-mathematics-and-mechanics
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