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

Journal of Zhejiang University-Science C(Computers and Electronics) 2012年第5期13卷 393-402页

作者： Zhi-qiang LUO Department of System Science and Applied Mathematics School of ScienceKunming University of Science and TechnologyKunming 650083China

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) *** 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 *** finite difference method with a predictor-corrector scheme is applied to discretize the nonlinear dynamic boundary condition and nonlinear kinematic boundary *** 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 *** beating period and the nonlinear phenomenon are very *** numerical solutions agree well with the analytical solutions and previously published results.

关键词： Predictor-corrector method Nonlinear potential flow equations Finite difference method Staggered grid nested iterative method

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

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Applied Mathematics and Mechanics(English Edition) 2013年第8期34卷 931-944页

作者：罗志强陈志敏 Department of System Science and Applied Mathematics School of Science Kunming University of Science and Technology School of Engineering Sciences University of Southampton

A three-dimensional （3D） predictor-corrector finite difference method for standing wave is developed. It is applied to solve the 3D nonlinear potential flow equa- tions 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 equa- tions 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.

关键词： three-dimensional (3D) nonlinear potential flow equation predictor-corrector finite difference method staggered grid nested iterative method 3D sloshing

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