A FINITE DIFFERENCE METHOD FOR THE ONE-DIMENSIONAL VARIATIONAL BOUSSINESQ EQUATIONS

A. Suryanto; E. van Groesen

doi:10.22342/jims.14.1.57.1-11

A. Suryanto ⁽¹⁾ , E. van Groesen ⁽²⁾

(1) Jurusan Matematika, Fakultas MIPA, Universitas Brawijaya, Jl Veteran Malang 65145, Indonesia., Indonesia,

(2) Applied Analysis and Mathematical Physics, Dept. of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands.Applied Analysis and Mathematical Physics, Dept. of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands., Netherlands

https://doi.org/10.22342/jims.14.1.57.1-11

Issue
Volume 14 Number 1 (April 2008)

Submitted
May 17, 2012

Accepted
June 3, 2012

Published
June 3, 2012

Keywords:

Finite difference method, Boussinesq equations

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Abstract

The variational Boussinesq equations derived by Klopman et. al. (2005) con-verse mass, momentum and positive-definite energy. Moreover, they were shown to have significantly improved frequency dispersion characteristics, making it suitable for wave simulation from relatively deep to shallow water. In this paper we develop a numerica lcode for the variational Boussinesq equations. This code uses a fourth-order predictor-corrector method for time derivatives and fourth-order finite difference method for the first-order spatial derivatives. The numerical method is validated against experimen-tal data for one-dimensional nonlinear wave transformation problems. Furthermore, the method is used to illustrate the dispersive effects on tsunami-type of wave propagation.

DOI : http://dx.doi.org/10.22342/jims.14.1.57.1-11

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Authors

A. Suryanto

Jurusan Matematika, Fakultas MIPA, Universitas Brawijaya, Jl Veteran Malang 65145, Indonesia.

penulis@jims-a.org (Primary Contact)

E. van Groesen

Applied Analysis and Mathematical Physics, Dept. of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands.Applied Analysis and Mathematical Physics, Dept. of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands.

Suryanto, A., & Groesen, E. van. (2012). A FINITE DIFFERENCE METHOD FOR THE ONE-DIMENSIONAL VARIATIONAL BOUSSINESQ EQUATIONS. Journal of the Indonesian Mathematical Society, 14(1), 1–11. https://doi.org/10.22342/jims.14.1.57.1-11