Numerical Simulation of Solition Propagation with Variable Depth

Abstract

The numerical simulation of long wave propagation is extendedly studied in the literature. The effects on the shape, speed and amount of energy carried by this type of waves have an important significance in many scientific and technological applications. In particular the propagation of solitons, this turned on the eye of the scientific community due to the events of the past ten years.
When a soliton travels in the middle of the sea, the bottom is disregarded in order to understand the propagatory behavior mechanisms.
In this work we show what happens when a soliton reaches the beach, when the depth of the sea becomes lower. Many other configurations of the bottom had been studied to understand how to design efficient coastal defenses to avoid the destructive effects of the Tsunamis.
To carry out with the studies, a high resolution numerical scheme based upon spectral methods has been designed and implemented to solve the Korteweg and de Vries equation with variable depth.
The results constitute a remarkable contribution in the field of the numerical simulation of fluid mechanics, and show a few applications in other fields like bioengineering and communication with optic fibers.