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Numerical Simulation of Sloshing Motion in a Rectangular Tank using Differential Quadrature Method

  • Water Resources and Hydrologic Engineering
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Abstract

The numerical simulation of sloshing waves for Laplace equation with nonlinear free surface boundary condition in a two-dimensional (2D) rectangular tank is performed using the Differential Quadrature Method (DQM). Application of the DQM to the Laplace equation and the nonlinear free surface boundary condition gives two sets of Ordinary Differential Equations (ODEs) in time. These two sets of ODEs are coupled with each other and can be expressed as a system of nonlinear ODEs which can be further discretized in time using various time integration schemes. The resultant system of nonlinear algebraic equations can then be solved using various iterative methods. In this study, the backward difference time integration scheme (of order six) in conjunction with the Newton-Raphson method is used to solve the resultant system of nonlinear ODEs. The fast rate of convergence of the method is demonstrated and to verify its accuracy, comparison study with the available solutions in the literature is performed. Numerical results reveal that the DQM can be used as an effective tool for handling nonlinear sloshing problems.

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  1. Young Researchers and Elite Club, Karaj Branch, Islamic Azad University, Karaj, Iran

    S. A. Eftekhari

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Eftekhari, S.A. Numerical Simulation of Sloshing Motion in a Rectangular Tank using Differential Quadrature Method. KSCE J Civ Eng 22, 4657–4667 (2018). https://doi.org/10.1007/s12205-015-0672-x

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