Numerical modeling for wave propagation by solving the shallow water equations using finite difference method

Abstract

The shallow water theory has been widely used to model the wave propagation. In this thesis, the 1D wave propagation is modeled using the shallow water equations and the Preissmann implicit scheme is used to discretize the equations due to its simplicity and stability that can be maintained over the large value of time step. The concept of shallow water is based on the smallness of the ratio between water depth and wavelength, and the model is fundamentally developed for the shallow water condition. However, to test the accuracy of the numerical model comprehensively, three different types of wave are simulated in this thesis: (1) tidal wave, (2) roll wave, and (3) solitary wave. For the tidal wave case, the numerical model is proven to be accurate indicated by the relatively-small errors for both water level and velocity. For the roll wave case, the numerical model is fairly accurate to capture the periodic permanent roll waves despite showing a higher water level than the one measured caused by the neglect of the turbulence terms. Finally, for the solitary case, as expected, the numerical model shows significant errors compared with the analytical result due to the neglect of the dispersion term.