A PSEUDOSPECTRAL σ -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 technique established by Ku & Hatziavramidis has been used to discretize the σ-transformed governing equations including nonlinear boundary conditi...

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Bibliographic Details
Published in:Journal of fluids and structures 1999-07, Vol.13 (5), p.607-630
Main Authors: CHERN, M.J., BORTHWICK, A.G.L., TAYLOR, R.EATOCK
Format: Article
Language:English
Subjects:
Computational methods in fluid dynamics
Exact sciences and technology
Fluid dynamics
Fundamental areas of phenomenology (including applications)
Hydrodynamic waves
Physics
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Summary: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 σ-transformed governing equations including nonlinear boundary conditions. Simulations of non overturning 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 solution is extremely stable, with the σ-transformation exactly fitting the free-surface boundary, unlike other schemes which have to use free-surface smoothing.
ISSN:0889-9746
1095-8622
DOI:10.1006/jfls.1999.0221