Numerical study of the solitary wave shoaling phenomena using KdV Equation

Abstract

In this paper, we use a mathematical model to study the amplification of solitary wave height as water depth decreases. When considering solitary waves, it is necessary to incorporate nonlinear and dispersive effects into the model. As a consequence, we consider Korteweg–De Vries (KdV) to accurately examine this shoaling solitary wave phenomenon. The challenge in solving KdV equations is numerical approximation due to the presence of higher order derivative terms. In this section, we define a fourth-order forward time-centered space numerical scheme. Additionally, we compare our numerical results to the analytical solution. The shallower the water, the greater the wave height amplification. This research may be used to forecast wave heights along the shoreline, which may aid in the design of coastal management.

Keywords

• KdV
• Shoaling
• Solitary waves
• 4th-order FTCS