A grid-free, nonlinear shallow-water model with moving boundary

Engineering Analysis with Boundary Elements

Volumn 28, Issue 8, 2004, Pages 967-973

  Zhou, X ^a   Hon, Y C ^a   Cheung, K F ^b  

^a CITY UNIVERSITY OF HONG KONG   (Hong Kong)

^b UNIVERSITY OF HAWAII   (United States)

Author keywords

Lagrangian Eulerian scheme; Meshless; Moving boundary; Radial basis functions; Shallow water equations

Indexed keywords

APPROXIMATION THEORY; BOUNDARY VALUE PROBLEMS; FINITE DIFFERENCE METHOD; FLOW OF WATER; HYDROSTATIC PRESSURE; INTEGRAL EQUATIONS; POISSON EQUATION;

LAGRANGIAN-EULERIAN SCHEME; MESHLESS; MOVING BOUNDARY; RADIAL BASIS FUNCTION; SHALLOW-WATER EQUATIONS;

BOUNDARY ELEMENT METHOD;

EID: 2942542888     PISSN: 09557997     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0955-7997(03)00124-3     Document Type: Article

References (26)

1. Titov V.V., Synolakis C.E. Numerical modeling of tidal wave runup. J Water Port Coastal Ocean Engng. 124:1998;157-171.
2. Liu P.L.-F., Cho Y.-S., Briggs M.J., Kanoglu U., Synolakis C.E. Runup of solitary waves on a circular island. J Fluid Mech. 302:1995;259-285.
3. Zelt J.A., Raichlen F. Overland flow from solitary waves. J Water Port Coastal Ocean Engng. 117:1991;247-263.
4. Bellos C.V., Sakkas J.G. 1-D dam-break flood-wave propagation on dry bed. J Hydraulic Engng. 113:1987;1510-1524.
5. Zhang J.E., Wu T.Y., Hou T.Y. Coastal hydrodynamics of ocean waves on beach. Adv Appl Mech. 37:2001;89-165.
6. Powell M.J.D. Radial basis functions for multivariable interpolation: a review. Griffiths D.F., Watson G.A. Numerical analysis. 1987;223-241 Longman, Harlow.
7. Wu Z.M. Hermite-Bikhoff interpolation of scattered data by radial basis function. Approx Theory Appl. 8:1992;1-10.
8. Kansa E.J. Multiquadrics: a scattered data approximation scheme with applications to computational fluid dynamics. II. Solution to parabolic, hyperbolic and elliptic partial differential equations. Comput Math Appl. 19:1990;147-161.
9. Golberg M.A., Chen C.S. The theory of radial basis functions applied to the BEM for inhomogeneous partial differential equations. Bound Elem Commun. 5:1994;57-61.
10. Golberg M.A., Chen C.S. Discrete projection methods for integral equations. 1997;Computational Mechanics Publications, Boston, MA.
11. Hon Y.C., Mao X.Z. A multiquadric interpolation method for solving initial value problems. Sci Comput. 12:1997;51-55.
12. Hon Y.C., Mao X.Z. An efficient numerical scheme for Burgers equation. Appl Math Comput. 95:1998;37-50.
13. Hon Y.C., Cheung K.F., Mao X.Z., Kansa E.J. A multiquadric solution for shallow water equation. ASCE J Hydraulic Engng. 125:1999;524-533.
14. Hon Y.C., Mao X.Z. A radial basis function method for solving options pricing model. J Financial Engng. 8:1999;31-49.
15. Hon Y.C., Zhou X. A comparison on using various radial basis functions for options pricing. Int J Appl Sci Comput. 7:2000;29-47.
16. Atluri S.N., Zhu T. New concepts in meshless methods. Int J Numer Meth Engng. 47:2000;537-556.
17. Hon Y.C., Chen W. Boundary knot method for 2D and 3D Helmholtz and convection-diffusion problems under complicated geometry. Int J Numer Meth Engng. 56:2003;1931-1948.
18. Golberg M.A., Chen C.S. The method of fundamental solutions for potential Helmholtz and diffusion problems. Golberg M.A. Boundary integral methods: numerical and mathematical aspects. 1998;103-176 Computational Mechanics Publications, Southampton.
19. Micchelli C.A. Interpolation of scattered data: distance matrices and conditionally positive definite functions. Constr Approx. 2:1986;11-22.
20. Powell M.J.D. The uniform convergence of thin plate spline interpolation in two dimensions. Numer Math. 68:1994;107-128.
21. Madych W.R., Nelson S.A. Multivariate interpolation and conditionally positive definite functions. Approx Theory Appl. 4:1988;77-89.
22. Wu Z. Solving PDE with radial basis functions. Chen Z., Li Y., Micchelli C.A., Xu Y., Dekker M., Zhou G. Advances in computational mathematics. Lecture notes on pure and applied mathematics. vol. 202:1998.
23. Franke C., Schaback R. Solving partial differential equations by collocation using radial basis functions. Appl Math Comput. 93:1998;73-82.
24. Wendland H. Meshless Galerkin methods using radial basis functions. Math Comput. 119:2001;177-186.
25. Stoker J.J. Water waves. 1992;Wiley, New York.
26. Zhou X., Hon Y.C., Li J. Overlapping domain decomposition method by radial basis functions. Appl Numer Math. 44:(1/2):2003;243-257.