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

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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.

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Authors and Affiliations

  1. Department of System Science and Applied Mathematics, School of Science, Kunming University of Science and Technology, Kunming, 650083, P. R. China

    Zhi-qiang Luo  (罗志强)

  2. School of Engineering Sciences, University of Southampton, Southampton, SO17 1BJ, UK

    Zhi-min Chen  (陈志敏)

Authors
  1. Zhi-qiang Luo  (罗志强)
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  2. Zhi-min Chen  (陈志敏)
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Corresponding author

Correspondence to Zhi-qiang Luo  (罗志强).

Additional information

Project supported by the Yunnan Provincial Applied Basic Research Program of China (No. KKSY201207019)

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Luo, Zq., Chen, Zm. Numerical simulation of standing wave with 3D predictor-corrector finite difference method for potential flow equations. Appl. Math. Mech.-Engl. Ed. 34, 931–944 (2013). https://doi.org/10.1007/s10483-013-1718-7

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  • DOI: https://doi.org/10.1007/s10483-013-1718-7

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Chinese Library Classification

2010 Mathematics Subject Classification

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