A fast algorithm for modeling multiple bubbles dynamics

Journal of Computational Physics

Volumn 216, Issue 2, 2006, Pages 430-453

  Bui, T T ^a   Ong, E T ^b   Khoo, B C ^a,c   Klaseboer, E ^b   Hung, K C ^b  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^b INSTITUTE OF HIGH PERFORMANCE COMPUTING   (Singapore)

^c SINGAPORE MIT ALLIANCE   (Singapore)

Author keywords

Boundary integral method; Bubble dynamics; Fast Fourier transform on multipoles; Multipole approximations

Indexed keywords

APPROXIMATION ALGORITHMS; BOUNDARY INTEGRAL EQUATIONS; DYNAMICS; EFFICIENCY; FAST FOURIER TRANSFORMS; NUMERICAL METHODS; SAILING VESSELS;

BOUNDARY INTEGRAL METHODS; BOUNDARY-ELEMENT METHODS; BUBBLE DYNAMICS; CLUSTERINGS; FAST ALGORITHMS; FAST FOURIER TRANSFORM ON MULTIPOLE; MULTIPOLE APPROXIMATION; MULTIPOLE METHODS; MULTIPOLES;

BOUNDARY ELEMENT METHOD;

EID: 33747029355     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2005.12.009     Document Type: Article

References (33)

1. Blake J.R., and Gibson D.C. Growth and collapse of a vapour cavity near a free surface. J. Fluid Mech. 111 (1981) 123-140
2. Blake J.R., and Gibson D.C. Cavitation bubbles near boundaries. Annu. Rev. Fluid Mech. 19 (1987) 99-123
3. Blake J.R., Keen G.S., Tong R.P., and Wilson M. Acoustics cavitations: the fluid dynamics of non-spherical bubbles. Phil. Trans. Roy. Soc. A 375 (1999) 251-267
4. S.A. Wilkerson, A boundary integral approach to three-dimensional underwater explosion bubble dynamics, Ph.D dissertation, Johns Hopkins University, 1992.
5. Cole R.H. Underwater Explosions (1948), Princeton University Press, Princeton, NJ
6. Brennen C.E. Cavitation and Bubble Dynamics (1995), Oxford University Press, New York
7. L. Guerri, G. Lucca, A. Prosperetti, A numerical method for dynamics of non-spherical cavitation bubbles, in: Proceedings of the 2nd International Colloquium on Drops And Bubbles, 1981, pp. 175-181.
8. Wang Q.X., Yeo K.S., Khoo B.C., and Lam K.Y. Strong interaction between a buoyancy bubble and a free surface. Theor. Comput. Fluid Dyn. 8 (1996) 73-88
9. Wang Q.X., Yeo K.S., Khoo B.C., and Lam K.Y. Nonlinear interaction between gas bubble and free surface. Comput. Fluids 25 (1996) 607-628
10. Zhang Y.L., Yeo K.S., Khoo B.C., and Wang C. 3D jet impact and toroidal bubbles. J. Comput. Phys. 166 (2001) 336-360
11. Wang Q.X. The evolution of a gas bubble near an inclined wall. Theoret. Comput. Fluid Dyn. 12 (1998) 29-51
12. Rungsiyaphornrat S., Klaseboer E., Khoo B.C., and Yeo K.S. The merging of two gaseous bubbles with an application to underwater explosion. Comput. Fluids 32 (2003) 1049-1074
13. Best J.P., and Kucera A. A numerical investigation of nonspherical rebounding bubbles. J. Fluid Mech. 245 (1992) 137-154
14. Kelley C.T. Iterative Methods for Linear and Nonlinear Equations (1995), SIAM Frontiers in Applied Mathematics, SIAM Philadelphia
15. Saad Y. Iterative Methods for Sparse Linear Systems (1996), PWS, Boston
16. Appel A.W. An efficient program for many-body simulations. SIAM J. Sci. Statist. Comput. 6 (1985) 85-103
17. Barnes J., and Hut P. A hierarchical O(N log N) force calculation algorithm. Nature 324 (1986) 446-449
18. Greengard L., and Rokhlin V. A fast algorithm for particle simulations. J. Comput. Phys. 73 (1987) 325-348
19. Greengard L., and Rokhlin V. A new version of the fast multipole method for the Laplace equation in three dimensions. Acta Numer. 6 (1997) 229-269
20. Nabors K., Korsmeyer F.T., Leighton F.T., and White J. Preconditioned, adaptive, multipole-accelerated iterative methods for three-dimensional first-kind integral equations of potential theory. SIAM J. Sci. Statist. Comput. 15 (1994) 713-735
21. Luty B.A., and Gunstersun W.F. Calculating electrostatics interactions using particle-particle-particle-mesh method with non-periodic long-range interactions. J. Chem. Phys. 100 (1996) 2581-2587
22. Phillips J.R., and White J. A precorrected-FFT method for electrostatics analysis of complicated 3-D structures. IEEE Trans. Comput. Aided Design 16 (1997) 1059-1072
23. Ong E.T., Lim K.M., and Lee H.P. A parallel fast Fourier transform on multipoles (FFTM) algorithm for electrostatics analysis of three-dimensional structure. IEEE Trans. Comput. Aided Design 23 (2004) 1063-1072
24. Ong E.T., Lim K.M., Lee K.H., and Lee H.P. A fast algorithm for three-dimensional potential fields calculation: fast Fourier transform on multipoles (FFTM). J. Comput. Phys. 192 (2003) 244-261
25. Brigham E.O. The Fast Fourier Transform and its Applications (1988), Prentice-Hall, Englewood Cliffs, NJ
26. Kapur S., and Long D.E. IES3: Efficient electrostatic and electromagnetic simulation. IEEE Comput. Sci. Eng. 5 (1998) 60-67
27. Levin P.L., Spasojevic M., and Schneider R. Creation of sparse boundary element matrices for 2-D and axis-symmetric electrostatics problems using the bi-orthogonal Haar wavelet. IEEE Trans. Dielectric Elect. Insulat. 5 (1998) 469-484
28. Brandt A., Spasojevic M., and Schneider R. Multilevel matrix multiplication and fast solution of integral equations. J. Comput. Phys. 90 (1990) 348-370
29. Epton M., and Dembart B. Multipole translation theory for the three-dimensional Laplace and Helmholtz equations. SIAM J. Sci. Comput. 16 (1995) 865-897
30. Appel A.W. Handbook of Mathematical Functions (1974), Dover Publications, New York
31. M. Frigo, S.G. Johnson, FFTW, C subroutines library for computing discrete Fourier transform (DFT) [Online]. Available from: .
32. T.T. Bui, A fast algorithm for modeling multiple bubbles dynamics, MEng Dissertation, National University of Singapore, 2005.
33. Chahine G.L. Strong interactions bubble/bubble and bubble/flow. In: Blake J.R., et al. (Ed). Bubble Dynamics and Interface Phenomena (1994), Kluwer Academic Publishers, Netherlands 195-206