Numerical Model of Breaking Regular Wave Runup Propagation by Using 1D Boussinesq Equation

Boussinesq Equation main figure
Yuliarko Sukardi

B.E. Ocean Engineering
Institute Technology of Bandung

M. Eng. Coastal Engineering
University of Tokyo



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Numerical Model of Breaking Regular Wave Runup Propagation by Using 1D Boussinesq Equation
This study is concerned with the development of a high-order numerical model to solve incompressible water wave motion based on improved nonlinear dispersive Boussinesq equations. A third-order Adams-Bashforth and a fourth-order Adams-Mouton predictor-corrector scheme was selected in an attempt to eliminate the truncation error terms that would be of the same form as the dispersive terms in the Boussinesq equations with second order schemes as in many other studies.
www.boussinesq-equation.blogspot.com

Wave Propagation Modeling


Numerical experiments are developed and performed to evaluate the ability of the Boussinesq model to simulate the propagation of regular waves on a constant depth and on a sloping beach. The computations start from the still water condition.

Given a beach bathymetry with a constant depth or a mildly sloping bottom, the elevation of a grid was defined as the vertical distance from the still water line. Grids located above the still water line have positive elevations while those located below have negative value.


Numerical codes have been succesfully developed include:

Simulation of Non-breaking Regular Wave Propagation on a Constant Depth

Simulation of Non-breaking Regular Wave Propagation on a Sloping Beach up to Breaking Location

Simulation of Breaking Regular Wave Propagation on a Sloping Beach up to Very Shallow Water Depth

Simulation of Non-breaking Regular Wave Runup Propagation on a Sloping Beach

Simulation of Breaking Regular Wave Runup Propagation on a Sloping Beach


References can be found here.


BOUSSINESQ EQUATION's CONTENT


Abstract

Introduction

Boussinesq-type Equation

Wave Breaking Model

Wave Runup Model

Numerical Methodology

Wave Propagation Modeling

- Simulation of Non-breaking Regular Wave Propagation on a Constant Depth

- Simulation of Non-breaking Regular Wave Propagation on a Sloping Beach up to Breaking Location

- Simulation of Breaking Regular Wave Propagation on a Sloping Beach up to Very Shallow Water Depth

- Simulation of Non-breaking Regular Wave Runup Propagation on a Sloping Beach

- Simulation of Breaking Regular Wave Runup Propagation on a Sloping Beach


Conclusions and Recommendations

References



Joseph Valentin Boussinesq
He (born March 13, 1842 in Saint-André-de-Sangonis (Hérault département), died February 19, 1929 in Paris) was a French mathematician and physicist who made significant contributions to the theory of hydrodynamics, vibration, light, and heat.

Master Research
This study was supported by the Asian Development Bank-Japan Scholarship Program.
Numerical Model of Breaking Regular Wave Runup Propagation by Using 1D Boussinesq Equation



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