Method of fundamental solutions for multidimensional Stokes equations by the dual-potential formulation

European Journal of Mechanics, B/Fluids

Volumn 25, Issue 6, 2006, Pages 877-893

  Young, D L ^a   Chiu, C L ^a   Fan, C M ^a   Tsai, C C ^b   Lin, Y C ^a  

^a NATIONAL TAIWAN UNIVERSITY   (Taiwan)

^b TOKO UNIVERSITY   (Taiwan)

Author keywords

2D and 3D Stokes flows; Bi harmonic equation; Dual potential formulation; Laplace equation; Method of fundamental solutions; Velocity potential and stream function vector

Indexed keywords

FINITE ELEMENT METHOD; FUNCTION EVALUATION; LAPLACE TRANSFORMS; NUMERICAL METHODS; VECTORS; VELOCITY MEASUREMENT;

2D AND 3D STOKES FLOWS; BI-HARMONIC EQUATION; DUAL-POTENTIAL FORMULATION; METHOD OF FUNDAMENTAL SOLUTIONS; VELOCITY POTENTIAL AND STREAM FUNCTION VECTOR;

NAVIER STOKES EQUATIONS;

EID: 33750103091     PISSN: 09977546     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.euromechflu.2006.02.004     Document Type: Article

References (40)

1. Abousleiman Y., and Cheng A.H.-D. Boundary element solution for steady and unsteady Stokes flow. Comput. Methods Appl. Mech. Engrg. 117 (1994) 1-13
2. Zeb A., Elliott L., Ingham D.B., and Lesnic D. The boundary element method for the solution of Stokes equations in two-dimensional domain. Eng. Anal. Bound. Elem. 22 (1998) 317-327
3. Alves C.J.S., and Silvestre A.L. Density results using Stokeslets and a method of fundamental solutions for the Stokes equations. Eng. Anal. Bound. Elem. 28 (2004) 1245-1252
4. Young D.L., Chen C.W., Fan C.M., Murugesan K., and Tsai C.C. Method of fundamental solutions for Stokes flows in a rectangular cavity with cylinders. Eur. J. Mech. B Fluids 24 (2005) 703-716
5. Young D.L., Jane S.J., Fan C.M., Murugesan K., and Tsai C.C. The method of fundamental solutions for 2D and 3D Stokes problems, J. Comput. Phys. 211 (2006) 1-8
6. Chen C.W., Young D.L., Tsai C.C., and Murugesan K. The method of fundamental solutions for inverse 2D Stokes problems, Comput. Mech. 37 (2005) 2-14
7. Tsai C.C., Young D.L., Lo D.C., and Wong T.K. Method of fundamental solutions for three-dimensional Stokes flow in exterior field. J. Engrg. Mech. ASCE 132 (2006) 317-326
8. Fan C.M., and Young D.L. Analysis of the 2D Stokes flows by the non-singular boundary integral equation method. Int. Math. J. 2 (2002) 1199-1215
9. Young D.L., Jane S.C., Lin C.Y., Chiu C.L., and Chen K.C. Solutions of 2D and 3D Stokes laws using multiquadrics method. Eng. Anal. Bound. Elem. 28 (2004) 1233-1243
10. Tsai C.C., Young D.L., and Cheng A.H.-D. Meshless BEM for three-dimensional Stokes flows. CMES 3 (2002) 117-128
11. Karageorghis A., and Fairweather G. The method of fundamental solutions for the numerical solution of the biharmonic equation. J. Comput. Phys. 69 (1987) 434-459
12. Karageorghis A., and Fairweather G. The Almansi method of fundamental solutions for solving biharmonic problems. Int. J. Numer. Methods Engrg. 26 (1988) 1668-1682
13. Smyrlis Y.S., and Karageorghis A. Some aspects of the method of fundamental solutions for certain biharmonic problems. CMES 4 (2003) 535-550
14. Elshabka A.M., and Chung T.J. Numerical solution of three-dimensional stream function vector components of vorticity transport equations. Comput. Methods Appl. Mech. Engrg. 170 (1999) 131-153
15. Pozrikidis C. Boundary Integral and Singularity Methods for Linearized Viscous Flow (1992), Cambridge University Press, New York
16. Hirasaki G.J., and Hellums J.D. Boundary conditions on the vector and scalar potentials in viscous three-dimensional hydrodynamics. Quart. Appl. Math. 28 (1970) 293-296
17. Chwang A.T., and Wu T.Y.-T. Hydromechanics of low-Reynolds-number flow. Part. 2. Singularity method for Stokes flow. J. Fluid Mech. 67 (1975) 787-815
18. Dabros T. A singularity method for calculating hydrodynamic forces and particle velocities in low-Reynolds-number flows. J. Fluid Mech. 156 (1985) 1-21
19. Kupradze V.D., and Aleksidze M.A. The method of functional equations for the approximate solution of certain boundary value problem. USSR Comput. Math. Math. Phys. 4 (1964) 82-126
20. Golberg M.A. The method of fundamental solutions for Poisson's equations. Eng. Anal. Bound. Elem. 16 (1995) 205-213
21. Balakrishnan K., and Ramachandran P.A. Osculatory interpolation in the method of fundamental solutions for nonlinear Poisson problems. J. Comput. Phys. 172 (2001) 1-18
22. Chen C.S., Golberg M.A., and Hon Y.C. The method of fundamental solutions and quasi-Monte Carlo method for diffusion equations. Int. J. Numer. Methods Engrg. 43 (1998) 1421-1436
23. Young D.L., Tsai C.C., Murugesan K., Fan C.M., and Chen C.W. Time-dependent fundamental solutions for homogeneous diffusion problems. Eng. Anal. Bound. Elem. 28 (2004) 1463-1473
24. Karageorghis A. The method of fundamental solutions for the calculation of the eigenvalues of the Helmholtz equation. Appl. Math. Lett. 14 (2001) 837-842
25. Young D.L., Hu S.P., Chen C.W., Fan C.M., and Murugesan K. Analysis of elliptical waveguides by the method of fundamental solutions. Micro. Opt. Tech. Lett. 44 (2005) 552-558
26. Katsurada M., and Okamoto H. A mathematical study of the charge simulation method. I. J. Fac. Sci. Univ. Tokyo Sect. IA Math. 35 (1988) 507-518
27. Kitagawa T. Asymptotic stability of the fundamental solution method. J. Comput. Appl. Math. 38 (1991) 263-269
28. Smyrlis Y.S., and Karageorghis A. Numerical analysis of the MFS for certain harmonic problems. Math. Model. Numer. Anal. 28 (2004) 495-517
29. Fairweather G., and Karageorghis A. The method of fundamental solutions for elliptic boundary value problems. Adv. Comput. Math. 9 (1998) 69-95
30. Golberg M.A., and Chen C.S. The method of fundamental solutions for potential, Helmholtz and diffusion problems. In: Golberg M.A. (Ed). Boundary Integral Methods: Numerical and Mathematical Aspects (1999), WIT Press/Computational Mechanics Publications, Boston 103
31. Cho H.A., Golberg M.A., Muleshkov A.S., and Li X. Trefftz method for time dependent partial differential equations. Comput. Mat. Cont. 1 (2004) 1-37
32. Chen C.W., Fan C.M., Young D.L., Murugesan K., and Tsai C.C. Eigenanalysis for membranes with stringers using the methods of fundamental solutions and domain decomposition. CMES 8 (2005) 29-44
33. Ames W.F. Numerical Methods for Partial Differential Equations. third ed. (1992), Academic Press, Boston
34. Arfken G. Mathematical Methods for Physicists. third ed. (1985), Academic Press, Orlando
35. Tannehill J.C., Pletcher R.H., and Anderson D.A. Computational Fluid Mechanics and Heat Transfer. second ed. (1997), Taylor & Francis Press, Philadelphia
36. Weinan E., and Liu J.G. Finite difference methods for 3D viscous incompressible flows in the vorticity-vector potential formulation on nonstaggered grids. J. Comput. Phys. 138 (1997) 57-82
37. Hwu T.Y., Young D.L., and Chen Y.Y. Chaotic advections for Stokes flow in a circular cavity. J. Engrg. Mech. ASCE 123 (1997) 774-782
38. Tritton D.J. Physical Fluid Dynamics (1988), Oxford University Press, New York
39. Guyon E., Hulin J.P., Petit L., and Mitescu C.D. Physical Hydrodynamics (2001), Oxford University Press, Oxford
40. Ballal B.Y., and Rivlin R.S. Flow of a Newtonian fluid between eccentric rotating cylinders: inertial effects. Arch. Rational Mech. Anal. 62 (1976) 237-294