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This study investigates a numerical simulation of two-dimensional wave makingproblem by means of boundary element method. The numerical scheme is based on the Lagrangian description together with finite differencing to the time derivative. An algorithm to generate waves with any prescribed form was also implanted in the scheme, as the pseudo boundary is assumed to represent a wave generating device. In this study, a piston wave generator is selected for simplicity, although it is clear that paddle of any desire type can be simulated.
The numerical model was first verified by studying the case of solitary wave impinging against a vertical wall. Time histories of the evolution of both solitary waves and periodical waves running up on a sloping beach with arbitrary topography and submerged obstacle are then presented. Besides, the present paper also treats the scattering problem due to solitary wave propagating from a constant water depth, over a slope and on to a shelf. Also, the distribution of velocity field within the fluid region for the case of periodical waves are shown as well.
Laboratory experiments were carried out respectively in our wave flume to testify the numerical solutions, image processing technology and facilities has being used as an way to study the deformation of the water elevations. The numerical model was confirmed with the existing laboratory experiments and theoretical solutions obtained by many researchers. When simulating, it was found that the numerical instability of the present scheme appears for some cases where the slope is mild. However, numerical simulations of the generations and deformations of waves using the present scheme indicate favorable agreement.
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