Notes on the Boussinesq-Full dispersion systems for internal waves: Numerical solution and solitary waves

by   V. A. Dougalis, et al.

In this paper we study some theoretical and numerical issues of the Boussinesq/Full dispersion system. This is a a three-parameter system of pde's that models the propagation of internal waves along the interface of two-fluid layers with rigid lid condition for the upper layer, and under a Boussinesq regime for the upper layer and a full dispersion regime for the lower layer. We first discretize in space the periodic initial-value problem with a Fourier-Galerkin spectral method and prove error estimates for several ranges of values of the parameters. Solitary waves of the model systems are then studied numerically in several ways. The numerical generation is analyzed by approximating the ode system with periodic boundary conditions for the solitary-wave profiles with a Fourier spectral scheme, implemented in a collocation form, and solving iteratively the corresponding algebraic system in Fourier space with the Petviashvili method accelerated with the minimal polynomial extrapolation technique. Motivated by the numerical results, a new result of existence of solitary waves is proved. In the last part of the paper, the dynamics of these solitary waves is studied computationally, To this end, the semidiscrete systems obtained from the Fourier-Galerkin discretization in space are integrated numerically in time by a Runge-Kutta Composition method of order four. The fully discrete scheme is used to explore numerically the stability of solitary waves, their collisions, and the resolution of other initial conditions into solitary waves.



There are no comments yet.


page 1

page 2

page 3

page 4


Notes on numerical analysis and solitary wave solutions of Boussinesq/Boussinesq systems for internal waves

In this paper a three-parameter family of Boussinesq systems is studied....

Numerical solution of internal-wave systems in the intermediate long wave and the Benjamin-Ono regimes

The paper is concerned with the numerical approximation of the Intermedi...

A conservative fully-discrete numerical method for the regularised shallow water wave equations

The paper proposes a new, conservative fully-discrete scheme for the num...

Lattice Boltzmann Method for wave propagation in elastic solids with a regular lattice: Theoretical analysis and validation

The von Neumann stability analysis along with a Chapman-Enskog analysis ...

Numerical study of the stabilization of 1D locally coupled wave equations

In this paper, we study the numerical stabilization of a 1D system of tw...

User guide on Hopf bifurcation and time periodic orbits with pde2path

We explain the setup for using the pde2path libraries for Hopf bifurcati...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.