Continuation of travelling-wave solutions of the Navier-Stokes equations

An efficient way of obtaining travelling waves in a periodic fluid system is described and tested. We search for steady states in a reference frame travelling at the wave phase velocity using a first-order pseudospectral semi-implicit time scheme adapted to carry out the Newton's iterations. The method is compared to a standard Newton-Raphson solver and is shown to be highly efficient in performing this task, even when high-resolution grids are used. This method is well suited to three-dimensional calculations in cylindrical or spherical geometries. Copyright (c) 2006 John Wiley & Sons, Ltd.