A new approach to modelling an unsteady free surface in boundary integral methods with application to bubble-structure interactions

Mathematics and Computers in Simulation

Volumn 44, Issue 4, 1997, Pages 415-426

  Tong, R P ^a  

^a UNIVERSITY OF BIRMINGHAM   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; BOUNDARY CONDITIONS; BUBBLES (IN FLUIDS); BUOYANCY; FLUID STRUCTURE INTERACTION; FUNCTIONS; INTEGRAL EQUATIONS; POLYNOMIALS; SURFACES; THREE DIMENSIONAL; VELOCITY;

BJERKNES EFFECT; BOUNDARY INTEGRAL METHODS; RADIAL BASIS FUNCTION; TRANSIENT CAVITIES; UNSTEADY FREE SURFACE;

MATHEMATICAL MODELS;

EID: 0031271453     PISSN: 03784754     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0378-4754(97)00067-0     Document Type: Article

References (19)

1. G. Beer, J.O. Watson, Introduction to Finite and Boundary Element Methods for Engineers (John Wiley and Sons, Chichester, 1992).
2. J.P. Best, A. Kucera, A numerical investigation of non-spherical rebounding bubbles, J. Fluid Mech. 245 (1992) 137-154.
3. J.R. Blake, J.M. Boulton-Stone, R.P. Tong, Boundary integral methods for rising, bursting and collapsing bubbles, in: H. Power (Ed.), BE Applications in Fluid Mechanics, (Computational Mechanics Publications, 1995), pp.31-72.
4. J.R. Blake, B.B. Taib, G. Doherty, Transient cavities near boundaries, Part 1, Rigid boundary, J. Fluid Mech. 170 (1986) 479-497.
5. G.L. Chahine, T.O. Perdue, Simulation of the three-dimensional behavior of an unsteady large bubble near a structure, 3rd International Colloquium on Bubble and Drops, Monterey, 1988.
6. C. de Boor, A. Rom, Computational aspects of polynomial interpolation in several variables, Math. Comp. 198 (1992) 705-727.
7. J.W. Dold, An efficient surface-integral algorithm applied to unsteady gravity waves, J. Comput. Phys. 103 (1992) 103-115.
8. M. Eck, MQ-curves are curves in tension, in: T. Lyche, L.L Schumaker (Eds.), Mathematical Methods in Computer Aided Design, Vol. II (1992), pp.217-228.
9. R. Franke, Scattered data interpolation: Test of some methods, Math. Comp. 38 (1982) 151-200.
10. P.J. Harris, A numerical model for determining the motion of a bubble close to a fixed rigid structure in a fluid, Int. J. Math. Eng. 33 (1992) 1813-1822.
11. M.S. Longuet-Higgins, E.D. Cokelet, The deformation of step surface waves on water: I. A numerical method of computation, Proc. R. Soc. Lond. A 350 (1976) 1-26.
12. K. Nabors, F.T. Korsmeyer, F.T. Leighton, J. White, Preconditioned, adaptive, multipole-accelerated iterative methods for three-dimensional first-kind integral equations of potential theory, SIAM J. Sci. Comput. 15 (1994) 713-735.
13. H. Pottmann, M. Eck, Modified multiquadric methods for scattered data interpolation over a sphere, Comp. Aid. Geom. Des. 7 (1990) 313-321.
14. M.J.D. Powell, The theory of radial basis function approximation in 1990, in: W. Light (Ed.), Advances in Numerical Analysis, Vol. 2 (Oxford Science Publications, 1992).
15. Y. Saad, M.H. Schultz, GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM J. Sci. Stat. Comput. 7 (1986) 856-869.
16. C. Schwab, H.L. Wendland, On numerical cubatures of singular surface integral in boundary element methods, Num. Math. 62 (1992) 343-369.
17. S.E. Stead, Estimation of gradients from scattered data, Rocky. Mtn. J. Math. 14 (1984) 265-279.
18. A.H. Stroud, Approximate Calculation of Multiple Integrals (Prentice-Hall, New Jersey, 1971).
19. Z.-M. Wu, R. Schaback, Local error estimates for radial basis function interpolation of scattered data, IMA J. Num. Anal. 13 (1993) 13-27.