An operator expansion method for computing nonlinear surface waves on a ferrofluid jet

We present a new numerical method to simulate the time evolution of axisymmetric nonlinear waves on the surface of a ferrofluid jet. It is based on the reduction of this problem to a lower-dimensional computation involving surface variables alone. To do so, we describe the associated Dirichlet-Neumann operator in terms of a Taylor series expansion where each term can be efficiently computed by a pseudo-spectral scheme using the fast Fourier transform. We show detailed numerical tests on the convergence of this operator and, to illustrate the performance of our method, we simulate the longtime propagation and pairwise collisions of axisymmetric solitary waves. Both depression and elevation waves are examined by varying the magnetic field. Comparisons with weakly nonlinear predictions are also provided. (C) 2016 Elsevier Inc. All rights reserved.