To assess the generation, propagation, deformation and breaking of the solitary wave on a mild slope, a numerical simulation of the wave making problem by a boundary element method is developed in this paper The numerical scheme involved is based on Lagrangian description together with a finite difference approximation of the time derivatives. The simulation of this study concerns of solitary wave propagating from constant depth and over a mild slope. The time history of the solitary wave propagation is shown and the numerical results of mass, potential energy and kinetic energy of the fluid are presented to confirm its accuracy. Introduction When water waves reach coastal regions. it is observed that an increase in wave height and a decrease in wavelength occurs due to the reduction of water depth. This phenomenon makes wave steeper towards the shore and leads to wave instability and breaking. For the sediment transport by coastal current, shaping of beaches, and design of coastal structures used for beach protection. knowledge of the crest height or location of breaking wave is Important in coastal engineering. Numerical studies of solitary wave in shallow water have been developed by many researchers. The first discussion in detail for the propagation of solitary wave on a slope was made by Madsen and Mel (1969) Based on a set of approximate equations for long wave, the numerical results in that study were compared with experimental date and a reasonable agreement was obtained. To describe the development of solitary wave moving onto a shelf, numerical solutions of a variable-coefficient Korteweg-de Vries equation was derived by Johnson (1972). Nakayama (1983) discussed the transformation of solitary wave and the running up against a vertical wall by means of a boundary element method. Using the nonlinear initial boundary condition and the velocity potential,

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