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Journal of Applied Mathematics
Volume 2012, Article ID 340640, 20 pages
Research Article

A Boundary Element Investigation of Liquid Sloshing in Coupled Horizontal and Vertical Excitation

1State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, China
2Key Laboratory of Renewable Energy and Gas Hydrate, Chinese Academy of Sciences, Guangzhou 510640, China

Received 24 January 2012; Revised 22 April 2012; Accepted 2 May 2012

Academic Editor: Armin Troesch

Copyright © 2012 De-Zhi Ning et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Sloshing flows in a two-dimensional rigid rectangular tank under specified excitations in the coupled horizontal and vertical modes are simulated by using a higher-order boundary element method (BEM). The liquid sloshing is formulated as an initial-boundary-value problem based on the fully nonlinear potential flow theory. And a semi-mixed Eulerian-Lagrangian technique combined with the 4th-order Runge-Kutta scheme is employed to advance the solutions in the time marching process. A smoothing technique is applied to the free surface at every several time steps to avoid the possible numerical instabilities. Numerical results obtained are compared with the available solutions to validate the developed model. The parametric studies are carried out to show the liquid sloshing effects in terms of the slosh frequencies and excitation amplitudes in horizontal and vertical modes, the second-order resonance frequency, a bottom-mounted vertical rigid baffle, free surface displacement, and hydrodynamic forces acting on the tank.