×

zbMATH — the first resource for mathematics

The method of fundamental solutions for 2D and 3D Stokes problems. (English) Zbl 1160.76332
Summary: A numerical scheme based on the method of fundamental solutions (MFS) is proposed for the solution of 2D and 3D Stokes equations. The fundamental solutions of the Stokes equations, Stokeslets, are adopted as the sources to obtain flow field solutions. The present method is validated through other numerical schemes for lid-driven flows in a square cavity and a cubic cavity. Test results obtained for a rectangular cavity with wave-shaped bottom indicate that the MFS is computationally efficient than the finite element method (FEM) in dealing with irregular shaped domain. The paper also discusses the effects of number of source points and their locations on the numerical accuracy.

MSC:
76D07 Stokes and related (Oseen, etc.) flows
76M25 Other numerical methods (fluid mechanics) (MSC2010)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Fairweather, G.; Karageorghis, A., The method of fundamental solutions for elliptic boundary value problems, Adv. comput. math., 9, 69, (1998) · Zbl 0922.65074
[2] Golberg, M.A.; Chen, C.S., The method of fundamental solutions for potential, Helmholtz and diffusion problems, (), 103 · Zbl 0945.65130
[3] Kupradze, V.D.; Aleksidze, M.A., The method of functional equations for the approximate solution of certain boundary value problem, Zh. vych. mat., 4, 4, 683, (1964)
[4] Smyrlis, Y.S.; Karageorghis, A., Some aspects of the method of fundamental solutions for certain biharmonic problems, Cmes, 4, 535, (2003) · Zbl 1051.65110
[5] Tsai, C.C.; Young, D.L.; Cheng, A.H.-D., Meshless BEM for three-dimensional Stokes flows, Cmes, 3, 117, (2002) · Zbl 1147.76595
[6] Pozrikidis, C., Boundary integral and singularity methods for linearized viscous flow, (1992), Cambridge University Press New York · Zbl 0772.76005
[7] Alves, C.J.S.; Silvestre, A.L., Density results using stokeslets and a method of fundamental solutions for the Stokes equations, Eng. anal. bound. elem., 28, 1245, (2004) · Zbl 1079.76058
[8] D.L. Young, C.W. Chen, C.M. Fan, K. Murugesan, C.C. Tsai, Method of fundamental solutions for Stokes flows in a rectangular cavity with cylinders, Euro. J. Mech. B/F (in press). · Zbl 1103.76319
[9] C.W. Chen, D.L. Young, C.C. Tsai, K. Murugesan, The method of fundamental solutions for inverse 2D Stokes problems, Comput. Mech. (in press). · Zbl 1158.76392
[10] Fan, C.M.; Young, D.L., Analysis of the 2D Stokes flows by the non-singular boundary integral equation method, Int. math. J., 2, 1199, (2002) · Zbl 1221.76065
[11] Young, D.L.; Jane, S.C.; Lin, C.Y.; Chiu, C.L.; Chen, K.C., Solutions of 2D and 3D Stokes laws using multiquadrics method, Eng. anal. bound. elem., 28, 1233, (2004) · Zbl 1178.76290
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.