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On-line Access: 2012-05-03

Received: 2011-10-26

Revision Accepted: 2012-02-09

Crosschecked: 2012-04-09

Cited: 3

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Journal of Zhejiang University SCIENCE C 2012 Vol.13 No.5 P.393-402


Numerical solution of potential flow equations with a predictor-corrector finite difference method

Author(s):  Zhi-qiang Luo

Affiliation(s):  Department of System Science and Applied Mathematics, School of Science, Kunming University of Science and Technology, Kunming 650083, China

Corresponding email(s):   zql1009@126.com

Key Words:  Predictor-corrector method, Nonlinear potential flow equations, Finite difference method, Staggered grid, Nested iterative method

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Zhi-qiang Luo. Numerical solution of potential flow equations with a predictor-corrector finite difference method[J]. Journal of Zhejiang University Science C, 2012, 13(5): 393-402.

@article{title="Numerical solution of potential flow equations with a predictor-corrector finite difference method",
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publisher="Zhejiang University Press & Springer",

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%T Numerical solution of potential flow equations with a predictor-corrector finite difference method
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%J Journal of Zhejiang University SCIENCE C
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%P 393-402
%@ 1869-1951
%D 2012
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.C1100313

T1 - Numerical solution of potential flow equations with a predictor-corrector finite difference method
A1 - Zhi-qiang Luo
J0 - Journal of Zhejiang University Science C
VL - 13
IS - 5
SP - 393
EP - 402
%@ 1869-1951
Y1 - 2012
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.C1100313

We develop a numerical solution algorithm of the nonlinear potential flow equations with the nonlinear free surface boundary condition. A finite difference method with a predictor-corrector method is applied to solve the nonlinear potential flow equations in a two-dimensional (2D) tank. The irregular tank is mapped onto a fixed square domain with rectangular cells through a proper mapping function. A staggered mesh system is adopted in a 2D tank to capture the wave elevation of the transient fluid. The finite difference method with a predictor-corrector scheme is applied to discretize the nonlinear dynamic boundary condition and nonlinear kinematic boundary condition. We present the numerical results of wave elevations from small to large amplitude waves with free oscillation motion, and the numerical solutions of wave elevation with horizontal excited motion. The beating period and the nonlinear phenomenon are very clear. The numerical solutions agree well with the analytical solutions and previously published results.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


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