Modified Boussinesq-Type Water Wave Model Based on Fourth-Order Runge-Kutta Method

It is very important to adopt reasonable discrete way for Boussinesq-type equation which is often used to simulate offshore wave field. In order to obtain the accurate numerical results, we present the finite different numerical model for the modified Boussinesq equations which are introduced by Beji and Nadaoka. In the numerical model, the difference of first order derivative in space has fourth-order accuracy, that of two order derivative has second-order, and the fourth-order Runge-Kutta method is used for the difference in time. The numerical model is validated by the classical experiment which has been conducted to study the wave propagation on a elliptic type shoal, and the related phenomena in wave propagation has been reproduced, such as light, refraction, diffraction and reflection, etc. The mean square wave height value in the computing domain could be calculated by statistical surface elevation in two period after wave development steady. The numerical wave height agree well with that of the eight sections in the experiment, it is shown that the wave propagation on complex topography could be simulated by this numerical model.