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Numerical simulation of standing wave with 3D predictor-corrector finite difference method for potential flow equations

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  • 1. Department of System Science and Applied Mathematics, School of Science, Kunming University of Science and Technology, Kunming 650083,
    P. R. China;
    2. School of Engineering Sciences, University of Southampton, Southampton SO17 1BJ, UK

Online published: 2013-07-15

Abstract

A three-dimensional (3D) predictor-corrector finite difference method for standing wave is developed. It is applied to solve the 3D nonlinear potential flow equations with a free surface. The 3D irregular tank is mapped onto a fixed cubic tank through the proper coordinate transform schemes. The cubic tank is distributed by the staggered meshgrid, and the staggered meshgrid is used to denote the variables of the flow field. The predictor-corrector finite difference method is given to develop the difference equations of the dynamic boundary equation and kinematic boundary equation. Experimental results show that, using the finite difference method of the predictor-corrector scheme, the numerical solutions agree well with the published results. The wave profiles of the standing wave with different amplitudes and wave lengths are studied. The numerical solutions are also analyzed and presented graphically.

Cite this article

Zhi-qiang LUO;Zhi-min CHEN . Numerical simulation of standing wave with 3D predictor-corrector finite difference method for potential flow equations[J]. Applied Mathematics and Mechanics, 2013 , 34(8) : 931 -944 . DOI: 10.1007/s10483-013-1718-7

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