Downloads

Matlab codes:

• BabenkoCG.m: his function computes the steady irrotational surface solitary (classical and generalized) capillary-gravity wave solutions of the full Euler equations (homogeneous, incompressible and perfect fluids). The full Euler system is recasted under the form of the Babenko equation using the conformal mapping technique. The wave is defined by its initial Froude and Bond numbers (Fr, Bo) and the result is about twelve digits accurate. The method works for all but the highest waves.

• run_Euler.m: Fourier-type pseudo-spectral solver of the full Euler equations with the free surface on a fluid layer of infinite depth. The time-dependent fluid domain is transformed into a strip using the conformal mapping technique. Time discretization is done using the embedded Cash-Karp method of the order 5(4). The time integration is improved using the integrating factor technique (i.e. exact integration of linear terms). The solver is initialized to simulate the celebrated Peregrine breather evolution in the full Euler.

• SerreGravityWave.m: This Matlab script is a pseudo-spectral solver for the Serre-Green-Naghdi equations which model the propagation of long gravity waves. Here, for the sake of simplicity, we restrict our attention to the case of the flat bottom. The numerical scheme is described in the following publication:
  • D. Dutykh, D. Clamond, P. Milewski & D. Mitsotakis. Finite volume and pseudo-spectral schemes for the fully nonlinear 1D Serre equations, European Journal of Applied Mathematics, 24(5), 761-787, 2013
     
• SolitaryWave.m: this script computes in ultra-fast way and potentially to the arbitrary accuracy the solitary waves to the full free-surface Euler equations. The method is based on the conformal map technique and the Petviashvili iteration. Some more technical details and numerical results can be found in the following preprints:
  • D. Clamond, D. Dutykh. Fast accurate computation of the fully nonlinear solitary surface gravity waves. Comp. & Fluids, 84, 35-38, 2013
     
• OkadaSol.m: this script computes co-seismic displacements according to the classical Okada solution. For more details you can have a look at the original Okada (1985) paper or this freely available my publication:
  • D. Dutykh, F. Dias, Water waves generated by a moving bottom. In Book:"Tsunami and Nonlinear Waves", Kundu, A. (Editor), Springer Verlag 2007, Approx. 325 p., 170 illus., Hardcover, ISBN: 978-3-540-71255-8

FreeFem++ codes:

• sine-Gordon solver: This script allows to solve numerically the sine-Gordon equation in a Y-junction geometry using the Finite Element Method (FEM). The scheme is of 2nd order in space and time. The implixit-explicit time stepping method is of the Crank-Nicolson type and it possesses excellent energy conservation properties. More details can be found in this publication:
  • J.-G. Caputo, D. Dutykh. Nonlinear waves in networks: a simple approach using the sine-Gordon equation. Phys. Rev. E, 90, 022912, 2014

In this section you will find useful pieces of codes and some other information:

• biblio.bib: my BibTeX file containing 1400+ bibliographical items that I use in my publications. JabRef helps me a lot to manage this database.
• All my presentations are prepared using Beamer package in LaTeX. The corresponding styles that I use can be downloaded here: beamerthemeKiev.sty and beamerthemeDnepropetrovsk.sty. To use theme, just put the command "\usetheme{Dnepropetrovsk}" or"\usetheme{Kiev}" in the beginning of your Beamer document.