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Journal of Numerical Mathematics

Editor-in-Chief: Hoppe, Ronald H. W. / Kuznetsov, Yuri

Managing Editor: Olshanskii, Maxim

Editorial Board: Benzi, Michele / Brenner, Susanne C. / Carstensen, Carsten / Dryja, M. / Feistauer, Miloslav / Glowinski, R. / Lazarov, Raytcho / Nataf, Frédéric / Neittaanmaki, P. / Bonito, Andrea / Quarteroni, Alfio / Guzman, Johnny / Rannacher, Rolf / Repin, Sergey I. / Shi, Zhong-ci / Tyrtyshnikov, Eugene E. / Zou, Jun / Simoncini, Valeria / Reusken, Arnold

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Online
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1569-3953
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Volume 20, Issue 3-4

Issues

Solution of 2D Boussinesq systems with freefem++: the flat bottom case

G. Sadaka
Published Online: 2013-03-30 | DOI: https://doi.org/10.1515/jnum-2012-0016

Abstract

-We consider here different family of Boussinesq systems in two space dimensions. These systems approximate the three-dimensional Euler equations and consist of three coupled nonlinear dispersive wave equations that describe propagation of long surface waves of small amplitude in ideal fluids over a horizontal bottom and which was studied in [7,9,10].We present here a freefem++ code aimed at solving numerically these systems where a discretization using P1 finite element for these systems was taken in space and a second order Runge-Kutta scheme in time.We give the detail of our code where we use a mesh adaptation technique. An optimization of the used algorithm is done and a comparison of the solution for different Boussinesq family is done too. The results we obtained agree with those of the literature.

Keywords: Boussinesq systems; KdV-KdV; BBM-BBM; Bona-Smith; adaptmesh; finite element method; freefem++

About the article

Published Online: 2013-03-30

Published in Print: 2012-12-01


Citation Information: Journal of Numerical Mathematics, Volume 20, Issue 3-4, Pages 303–324, ISSN (Online) 1569-3953, ISSN (Print) 1570-2820, DOI: https://doi.org/10.1515/jnum-2012-0016.

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