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

A pseudospectral matrix-element method is proposed for the analysis of 2-D nonlinear time-domain free-surface flow problems. The Chebyshev expansion t echnique established by Ku & Hatziavramidis has been used to discretize the sigma-transformed governing equations including nonlinear boundary conditi ons. Simulations of nonoverturning transient waves in fixed and base-excite d tanks are presented. The results are compared with first- and second-orde r analytical solutions for sloshing and standing waves, respectively. Excel lent agreement is achieved at low values of wave steepness, with the high a ccuracy due to the close coupling between points. As the wave steepness inc reases, the influence of higher-order nonlinear components becomes signific ant, 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 Aca demic Press.