Efficient computation of steady solitary gravity 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.

21 pages, 12 figures, 66 references. Other authors papers can be downloaded at http://www.denys-dutykh.com/

References in corpus (4)

• A generalized Petviashvili iteration method for scalar and vector Hamiltonian equations with arbitrary form of nonlinearity
• Fast accurate computation of the fully nonlinear solitary surface gravity waves
• Special solutions to a compact equation for deep-water gravity waves
• Hamiltonian form and solitary waves of the spatial Dysthe equations

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