A pseudospectral sigma-transformation model of 2-D nonlinear waves

MJ Chern*, AGL Borthwick, RE Taylor

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


A pseudospectral matrix-element method is proposed for the analysis of 2-D nonlinear time-domain free-surface flow problems. The Chebyshev expansion technique established by Ku & Hatziavramidis has been used to discretize the sigma-transformed governing equations including nonlinear boundary conditions. Simulations of nonoverturning transient waves in fixed and base-excited tanks are presented. The results are compared with first- and second-order analytical solutions for sloshing and standing waves, respectively. Excellent agreement is achieved at low values of wave steepness, with the high accuracy due to the close coupling between points. As the wave steepness increases, the influence of higher-order nonlinear components becomes significant, and is modelled by the present scheme. The solutionis extremely stable, with the sigma-transformation exactly fitting the free-surface boundary, unlike other schemes which have to use free-surface smoothing. (C) 1999 Academic Press.

Original languageEnglish
Pages (from-to)607-630
Number of pages24
JournalJournal of fluids and structures
Issue number5
Publication statusPublished - Jul 1999


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