Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-27T18:43:03.678Z Has data issue: false hasContentIssue false
  • English
  • Français

Non-singular boundary integral methods for fluid mechanics applications

Published online by Cambridge University Press:  07 March 2012

Evert Klaseboer ,
Qiang Sun  and
Derek Y. C. Chan
Evert Klaseboer*
Affiliation:
Institute of High Performance Computing, 1 Fusionopolis Way, 138632, Singapore
Qiang Sun*
Affiliation:
Department of Mechanical Engineering, National University of Singapore, 10 Kent Ridge Crescent, 119260, Singapore
Derek Y. C. Chan
Affiliation:
Department of Mathematics and Statistics, The University of Melbourne, Parkville 3010 VIC, Australia Faculty Life and Social Sciences, Swinburne University of Technology, Hawthorn 3122 VIC, Australia
*
†Email addresses for correspondence: [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

A formulation of the boundary integral method for solving partial differential equations has been developed whereby the usual weakly singular integral and the Cauchy principal value integral can be removed analytically. The broad applicability of the approach is illustrated with a number of problems of practical interest to fluid and continuum mechanics including the solution of the Laplace equation for potential flow, the Helmholtz equation as well as the equations for Stokes flow and linear elasticity.

JFM classification

Low-Reynolds-number flows: Boundary integral methods
Type
Papers
Information
Journal of Fluid Mechanics , Volume 696 , 10 April 2012 , pp. 468 - 478
Copyright
Copyright © Cambridge University Press 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Bazhlekov, I. B., Anderson, P. D. & Meijer, H. E. H. 2004 Nonsingular boundary integral method for deformable drops in viscous flows. Phys. Fluids 16, 106–1081.CrossRefGoogle Scholar
2. Becker, A. A. 1992 The Boundary Element Method in Engineering: A Complete Course. McGraw-Hill International (UK) Limited.Google Scholar
3. Blake, J. R., Taib, B. B. & Gibson, D. C. 1986 Transient cavities near boundaries. Part 1. Rigid boundary. J. Fluid Mech. 170, 479–497.CrossRefGoogle Scholar
4. Cheng, A. H. D. & Cheng, D. T. 2005 Heritage and early history of the boundary element method. Engng Anal. Bound. Elem. 29, 268–302.CrossRefGoogle Scholar
5. Fong, S. W., Adhikari, D., Klaseboer, E. & Khoo, B. C. 2009 Interactions of multiple spark-generated bubbles with phase differences. Exp. Fluids 46, 705–724.CrossRefGoogle Scholar
6. Gonzalez-Avila, S. R., Klaseboer, E., Khoo, B. C. & Ohl, C. D. 2011 Cavitation bubble dynamics in a liquid gap of variable height. J. Fluid Mech. 682, 241–260.CrossRefGoogle Scholar
7. Klaseboer, E., Rosales-Fernandez, C. & Khoo, B. C. 2009 A note on true desingularization of boundary element methods for three-dimensional potential problems. Engng Anal. Bound. Elem. 33, 796–801.CrossRefGoogle Scholar
8. Lean, M. H. & Wexler, A. 1985 Accurate numerical integration of singular boundary element kernels over boundaries with curvature. Intl J. Numer. Meth. Engng 21, 211–228.CrossRefGoogle Scholar
9. Liu, Y. J. & Rudolphi, T. J. 1991 Some identities for fundamental solutions and their applications to weakly-singular boundary element formulations. Engng Anal. Bound. Elem. 8, 301–311.CrossRefGoogle Scholar
10. Liu, Y. J. & Rudolphi, T. J. 1999 New identities for fundamental solutions and their applications to non-singular boundary element formulations. Comput. Mech. 24, 286–292.CrossRefGoogle Scholar
11. Lorentz, H. A. 1907 Abhandlungen Über Theoretische Physik. B. G. Teubner.Google Scholar
12. Pigeonneau, F. & Sellier, A. 2011 Low-Reynolds-number gravity-driven migration and deformation of bubbles near a free surface. Phys. Fluids 23, 2102–2116.CrossRefGoogle Scholar
13. Pozrikidis, C. 1992 Boundary Integral and Singularity Methods for Linearized Viscous Flow. Cambridge University Press.CrossRefGoogle Scholar
14. Symm, G. T. 1963 Integral equation methods in potential theory. ii. Proc. R. Soc. Lond. Ser. A Math. Phys. Sci. 275, 33–46.Google Scholar
15. Wang, Q. X. 1998 The evolution of a gas bubble near an inclined wall. Theor. Comput. Fluid Dyn. 12, 29–51.CrossRefGoogle Scholar
16. Wrobel, L. C. 2002 The Boundary Element Method, Vol. 1, Applications in Thermo-Fluids and Acoustics. Wiley.Google Scholar
17. Zhang, Y. L., Yeo, K. S., Khoo, B. C. & Wang, C. 2001 3D jet impact and toroidal bubbles. J. Comput. Phys. 166, 336–360.CrossRefGoogle Scholar