Instytut Budownictwa Wodnego
Polskiej Akademii Nauk

Essay #9110 details

database id9110
titleImproving performance of a semi-analytical model for nonlinear water waves
authorsPaprota M.1, Sulisz W.1
pages38 — 49
keywordsGravity waves, Nonlinear waves, Numerical modeling, Spectral method, Parallel computing
abstractsAn efficient semi-analytical solution to the problem of nonlinear water waves propagating at a constant depth is derived using parallel computing techniques. The approach is based on the assumptions of an irrotational flow of an inviscid and incompressible fluid. Velocity potential and free-surface displacement functions are represented in a form based on Fourier series satisfying a formulated initial boundary-value problem by a proper selection of time-dependent coefficients. The eigenfunction expansions are resolved by means of a Fast Fourier Transform technique and a higher-order time-stepping procedure to provide an efficient spectral collocation method of computation of wave-induced free-surface flows. The application of the Fourier transform qualifies the semi-analytical algorithm for efficient parallelization. Hence, the numerical model performance is improved using the computing capabilities of a GPU. The derived semi-analytical approach is easy to implement and may be straightforwardly extended to cover the generation of waves in a flume or a basin. The ability of the model to reproduce nonlinear phenomena is demonstrated in simulations of two- and three-dimensional instabilities of a modulated Stokes wave. The model can be used to solve standard as well as complex wave problems in large computational domains considerably faster than its CPU-based counterpart.
attributes [reviewed] [scientific]
database id9109
seriesJournal of Hydro-environment Research


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