SOLUTION OF 2D BOUSSINESQ SYSTEMS WITH FREEFEM++: THE FLAT BOTTOM CASE

Georges Sadaka (1)

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée

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. 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.

Mots clés: Boussinesq systems; KdV-KdV; BBM-BBM; Bona-Smith; adaptmesh; finite element method; FreeFem++.; FreeFem++

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Georges Sadaka. SOLUTION OF 2D BOUSSINESQ SYSTEMS WITH FREEFEM++: THE FLAT BOTTOM CASE. 2012. ⟨hal-00697129v3⟩