High-order schemes in boundary element methods for transient non-linear free surface problems

International Journal for Numerical Methods in Fluids

Volumn 24, Issue 10, 1997, Pages 1049-1072

  Machane, R ^a   Canot, E ^a  

^a Institut de Mecanique de Grenoble   (France)

Author keywords

Boundary element method; Free surface flow; Lagrangian derivative; Symbolic computation; Taylor series expansion

Indexed keywords

CODES (SYMBOLS); COMPUTER SOFTWARE; DIFFERENTIAL EQUATIONS; FLOW OF FLUIDS; INTEGRATION; LAGRANGE MULTIPLIERS;

FREE SURFACE FLOW; HIGH ORDER TIME STEPPING; LAGRANGIAN DERIVATIVE; RUNGE-KUTTA TECHNIQUE; TAYLOR SERIES EXPANSION;

BOUNDARY ELEMENT METHOD;

EID: 0031139121     PISSN: 02712091     EISSN: None     Source Type: Journal    
DOI: 10.1002/(sici)1097-0363(19970530)24:10<1049::aid-fld531>3.0.co;2-4     Document Type: Article

References (22)

1. M. S. Longuet-Higgins and E. D. Cokelet, 'The deformation of steep surface waves on water. Part I. A numerical method of computation', Proc. R. Soc. Lond. A, 350, 1-26 (1976).
2. J. W. Dold and D. H. Peregrine, 'Steep unsteady water waves: an efficient computational scheme', Proc. 19th Int. Conf. on Coastal Engineering, Houston, TX, 1984, pp. 955-967.
3. J. W. Dold and D. H. Peregrine, 'An efficient boundary-integral method for steep unsteady water waves', in K. W. Morton and M. J. Baines (eds), Numerical Methods for Fluid Dynamics II, Oxford University Press, Oxford, 1986, pp. 671-679.
4. I. Stakgold, Green's Functions and Boundary Value Problems, Wiley, 1979.
5. M. A. Jawson and G. T. Symm, Integral Equation Methods in Potential Theory, Academic, New York, 1977.
6. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, 9th printing, Dover, New York, 1970.
7. C. A. Brebbia, J. C. F. Telles and L. C. Wrobel, Boundary Element Techniques Theory and Applications in Engineering, Springer, New York, 1984.
8. L. C. Wrobel, 'Numerical solutions of axisymmetric cavity flows using the boundary element method', Int. j. numer. methods fluids, 16, 845-854 (1993).
9. R. Ans, Vectors, Tensors and Basic Equations of Fluid Mechanics, Prentice-Hall, Englewood Cliffs, NJ, 1962.
10. R. M. Bowen and C. C. Wang, Introduction to Vectors and Tensors, 1. Linear and multilinear Algebra, 2. Vector and Tensor Analysis, Plenum, New York, 1976.
11. S. T. Grilli, J. Skourup and I. A. Svendsen, 'An efficient boundary element method for nonlinear water waves', Eng. Anal. Bound. Elem., 6, 97-107 (1989).
12. T. Nakayama, 'A computational method for simulating transient motions of an incompressible inviscid fluid with a free surface', Int. j. numer. methods fluids, 10, 683-695 (1990).
13. A. F. Teles da Silva and D. H. Peregrine, 'Nonlinear perturbations on a free surface induced by a submerged body: a boundary integral approach', Eng. Anal. Bound. Elem., 7, 214-222 (1990).
14. P. L. F. Liu, H. W. Hsu and M. H. Lean, 'Applications of boundary integral equation methods for two-dimensional non-linear water wave problems', Int. J. numer. methods fluids, 15, 1119-1141 (1992).
15. V. G. Levich, Physiochemical Hydrodynamics, Prentice-Hall, Englewood Cliffs, NJ, 1962.
16. J. Vignes, 'A stochastic arithmetic for reliable scientific computation', Math. Comput. Simul., 35, 233-261 (1993).
17. H. Lamb, Hydrodynamics, 6th edn, Cambridge University Press, Cambridge, 1932.
18. C. C. Mei, The Applied Dynamics of Ocean Surface Waves, Wiley, New York, 1983.
19. D. G. Dommermuth and D. K. P. Yue, 'Numerical simulations of nonlinear axisymmetric flows with a free surface', J. Fluid Mech., 178, 195-219 (1987).
20. T. S. Lundgren and N. N. Mansour, 'Oscillations of drops in zero gravity with weak viscous effects', J. Fluid Mech., 194, 479- -510 (1988).
21. G. Marchouk, Méthodes de Calcul Numériques, Mir, Moscow, 1980.
22. J. J. S. P. Cabral, L. C. Wrobel and C. A. Brebbia, 'A BEM formulation using B-splines: I - Uniform blending functions', Eng. Anal. Bound. Elem., 7, 136-144 (1990).