Numerical Simulation of Nonlinear Surface Gravity Waves Transformation under Shallow-Water Conditions

Iftikhar B Abbasov

doi:10.4236/am.2012.32021

Abstract

This work considers the problems of numerical simulation of non-linear surface gravity waves transformation under shallow bay conditions. The discrete model is built from non-linear shallow-water equations. Are resulted boundary and initial conditions. The method of splitting into physical processes receives system from three equations. Then we define the approximation order and investigate stability conditions of the discrete model. The sweep method was used to calculate the system of equations. This work presents surface gravity wave profiles for different propagation phases.

Highlights

The research of surface gravity waves under shallow water conditions has a long history
This work considers the problems of numerical simulation of non-linear surface gravity waves transformation under shallow bay conditions
The discrete model is built from non-linear shallow-water equations

Summary

Introduction

The research of surface gravity waves under shallow water conditions has a long history. Non-linear surface gravity waves under shallow water conditions are described with shallow-water equations. The first four harmonics influence on surface wave profile with its propagation on shallow water was studied in laboratory experiments and using numerical simulation. Paper [4] considers numerical simulation and experimental observations of non-linear interaction, reflection and attenuation effects influencing the beach propagation of surface gravity waves. Shallow water non-linear dispersion model is viewed considering the topography and fluid viscosity They carry out a calculation comparison between free surface plane disturbance transformation and experimental data. Article [7] describes surface wave non-linear dispersion under shallow water conditions within Boussinesq model. Work [8] offers a stochastic model of surface wave propagation under shallow water conditions with regard to the bottom topography In the beginning it describes determined spectral model based on wave spectrum decomposition. Vertical intensity of liquid particle velocity is assumed to be equal to zero:

Discrete Model Construction

Analysis and the Result Comparison