Solution of a two-dimensional bubble shape in potential flow by the method of fundamental solutions

Engineering Analysis with Boundary Elements

Volumn 30, Issue 3, 2006, Pages 227-235

  Sarler B ^a  

^a UNIVERSITY OF NOVA GORICA   (Slovenia)

Author keywords

Bernoulli equation; Bubble shape; Free boundary problem; Method of fundamental solutions; Potential flow; Two dimensional Cartesian co ordinates

Indexed keywords

BOUNDARY VALUE PROBLEMS; BUBBLES (IN FLUIDS); PARAMETER ESTIMATION; POLYNOMIALS; RADIAL BASIS FUNCTION NETWORKS; STEADY FLOW;

BERNOULLI EQUATION; BUBBLE SHAPE; FREE BOUNDARY PROBLEM; METHOD OF FUNDAMENTAL SOLUTIONS; TWO-DIMENSIONAL CARTESIAN CO-ORDINATES;

POTENTIAL FLOW;

EID: 32544444605     PISSN: 09557997     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.enganabound.2005.09.007     Document Type: Article

References (26)

1. W. Shyy, H.S. Udaykumar, M.M. Rao, and R.W. Smith Computational fluid dynamics with moving boundaries 1996 Taylor & Francis London
2. G. Kaptay Modelling interfacial energies in metallic systems Mater Sci Forum 473-474 2005 1 10
3. B. Šarler C.A. Brebbia Computational modelling of moving and free boundary problems VI 2001 Wit Press Southampton
4. M.A. Golberg, and C.S. Chen Discrete projection methods for integral equations 1997 Computational Mechanics Pubications Southampton
5. L.C. Wrobel The boundary element method, volume I: applications in termo-fluids and acoustics 2002 Wiley London
6. M.H. Aliabady The boundary element method, volume II: applications in solids and structures 2002 Wiley London
7. G. Fairweather, and A. Karageorghis The method of fundamental solutions for elliptic boundary value problems Adv Comput Math 9 1998 69 95
8. K. Balakrishnan, and P.A. Ramachadran The method of fundamental solutions for linear diffusion-reaction equations Math Comput Model 31 2000 221 237
9. T.Y. Hou, J.S. Lowengrub, and M.J. Shelley Boundary integral methods for multicomponent fluids and multiphase materials J Comput Phys 169 2001 302 326
10. R.L. Johnston, and G. Fairweather The method of fundamental solutions for problems in potential flow Appl Math Model 8 1984 265 270
11. A. Bogomolny Fundamental solutions method for elliptic boundary value problems SIAM J Numer Anal 22 1985 644 669
12. A. Poullikkas, A. Karageorghis, and G. Georgiou The method of fundamental solutions for signorini problems IMA J Numer Anal 18 1998 273 285
13. A. Karageorghis The method of fundamental solutions for the solution of steady-state free boundary problems J Comput Phys 98 1992 119 128
14. J.R. Blake, J.M. Boulton-Stone, and R.P. Tong Boundary integral methods for rising, bursting and collapsing bubbles H. Power Boundary element applications in fluid mechanics, advances in fluid mechanics vol. 4 1995 Computational Mechanics Publications Southampton 31 71
15. J.M. Boulton-Stone A comparison of boundary integral methods for studying the motion of a two-dimensional bubble in an infinite fluid Comput Methods Appl Mech Eng 102 1993 213 234
16. Z. Rek Determination of velocity at the gas-liquid interface by BEM using potential flow B. Šarler C.A. Brebbia H. Power Moving boundaries V 1999 Computational Mechanics Publications Southampton 139 148
17. Y.L. Zhang, K.S. Yeo, B.C. Khoo, and W.K. Chong Simulation of three-dimensional bubbles using desingularized boundary integral method Int J Numer Methods Fluids 31 1999 1311 1320
18. Y. Cao, W.W. Schultz, and R.F. Beck Three dimensional desingularized boundary integral methods for potential problems Int J Numer Methods Fluids 12 1991 185 803
19. B. Šarler, R. Vertnik, M. Savič, and C.S. Chen A meshless approach to hollow-brick temperature field S.N. Atluri D.W. Pepper Advances in computational engineering & sciences, ICCES'02 2002 Tech Science Press Encinio [CD rom, 6 pages]
20. M.S. Longuet-Higgins, and E.D. Cokelet The deformation of steep surface waves on water: I. A numerical method of computation Proc R Soc London 350 1976 1 26
21. K. Balakrishnan, and P.A. Ramachadran A particular solution trefftz method for non-linear poisson problems in heat and mass transfer J Comput Phys 150 1999 239 267
22. M.A. Golberg, and C.S. Chen The method of fundamental solutions for potential, helmholtz and diffusion problems M.A. Golberg Boundary integral methods - numerical and mathematical aspects 1998 Computational Mechanics Publications Southampton 103 176
23. A. Karageorghis, and G. Fairweather The method of fundamental solutions for axisymmetric potential problems Int J Numer Methods Eng 44 1999 1653 1669
24. B. Šarler Towards a mesh-free computation of transport phenomena Eng Anal Bound Elem 26 2002 731 738
25. M.D. Buhmann Radial basis function: theory and implementations 2003 Cambridge University Press Cambridge, MA
26. Šarler B, Jelićc N, Kovačević I, Lakner M, Perko J. Axisymmetric Multiquadrics, Engineering Analysis with Boundary Elements, 2006, in press.