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Continuation of travelling‐wave solutions of the Navier–Stokes equations
Author(s) -
Mercader Isabel,
Batiste Oriol,
Alonso Arantxa
Publication year - 2006
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1196
Subject(s) - solver , continuation , computational fluid dynamics , newton's method , mathematics , pseudo spectral method , navier–stokes equations , mathematical analysis , reference frame , computer science , frame (networking) , physics , mechanics , mathematical optimization , nonlinear system , fourier analysis , fourier transform , compressibility , programming language , telecommunications , quantum mechanics
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 © 2006 John Wiley & Sons, Ltd.