Efficient computation of steady solitary gravity waves

TL;DR

This paper introduces a fast and accurate numerical method for computing steady solitary gravity waves using conformal mapping and Fourier spectral techniques, improving efficiency and precision over existing methods.

Contribution

It combines conformal mapping with Fourier pseudo-spectral methods and Petviashvili iteration to efficiently solve the free surface Euler equations for solitary waves.

Findings

The method achieves high accuracy in computing wave profiles.

It effectively handles a large range of wave amplitudes.

Provides detailed integral quantities and velocity fields for solitary waves.

Abstract

An efficient numerical method to compute solitary wave solutions to the free surface Euler equations is reported. It is based on the conformal mapping technique combined with an efficient Fourier pseudo-spectral method. The resulting nonlinear equation is solved via the Petviashvili iterative scheme. The computational results are compared to some existing approaches, such as the Tanaka method and Fenton's high-order asymptotic expansion. Several important integral quantities are numerically computed for a large range of amplitudes. The integral representation of the velocity and acceleration fields in the bulk of the fluid is also provided.