Denys DUTYKH's Blog of an applied mathematician

Fast and accurate computation of cnoidal waves

There are many points to mention and describe briefly today.

First of all, together with my collaborator Didier Clamond, we submitted a manuscript, which describes a new method for the computation of cnoidal waves in the full Euler equations with free surface:

These solutions can be used to validate and check the accuracy of various dynamic solvers for the full water wave problem. Moreover, the Matlab code is freely available at this URL:

This Matlab code computes irrotational 2D periodic steady surface pure gravity waves of arbitrary length in arbitrary depth. The formulation is based on the so-called Babenko equation and pseudo-spectral discretization in the conformal domain. The resulting equation is solved using Petviashvili iteration method.

In the continuation of our previous short publication on peaked solitary capillary-gravity waves, we submitted the full manuscript, which investigates this system of equations (capillary-gravity Serre model) in more details:

In the last manuscript we focus more on the dynamics and properties of smooth solitary wave solutions in various regimes with respect to the Bond number.

Finally, the following week I am going to spend at Al-Farabi Kazakh National University