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

Zhi-qiang LUO

doi:10.1631/jzus.C1100313

Your Location：

Home >

Browse articles >

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

计算数学 | Updated：2022-12-09

- Numerical solution of potential flow equations with a predictor-corrector finite difference method
- Numerical solution of potential flow equations with a predictor-corrector finite difference method
- 信息与电子工程前沿（英文） 2012年13卷第5期页码：393-402
- Affiliations：
  
  Department of System Science and Applied Mathematics, School of Science, Kunming University of Science and Technology, Kunming 650083, China
- Author bio：
  
  [ "Zhi-qiang LUO, E-mail: zql1009@126.com" ]
- Funds：
- DOI：10.1631/jzus.C1100313
  中图分类号： O24
- 收稿：2011-10-26，
  
  修回：2012-;4-;9，
  
  纸质出版：2012-05
- Accepted：
Scan QR Code
Numerical solution of potential flow equations with a predictor-corrector finite difference method[J]. 信息与电子工程前沿（英文）, 2012,13(5):393-402.

Zhi-qiang LUO. Numerical solution of potential flow equations with a predictor-corrector finite difference method[J]. Frontiers of Information Technology & Electronic Engineering, 2012, 13(5): 393-402.
Numerical solution of potential flow equations with a predictor-corrector finite difference method[J]. 信息与电子工程前沿（英文）, 2012,13(5):393-402. DOI： 10.1631/jzus.C1100313.

Zhi-qiang LUO. Numerical solution of potential flow equations with a predictor-corrector finite difference method[J]. Frontiers of Information Technology & Electronic Engineering, 2012, 13(5): 393-402. DOI： 10.1631/jzus.C1100313.

摘要

Abstract

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.

关键词

Keywords

references

M. Abbaspour , , , M.G. Hassanabad . . A novel 2D BEM with composed elements to study sloshing phenomenon . . J. Appl. Fluid Mech. , , 2009 . . 2 ( ( 2 ): ): 77 - - 83 . . . .

H.N. Abramson . . The Dynamic Behavior of Liquids in Moving Containers . . Technical Report, SP 106. NASA , , 1966 . . .

C. Chainais-Hillairet , , , Y.J. Peng , , , I. Violet . . Numerical solutions of Euler-Poisson systems for potential flows . . Appl. Numer. Math. , , 2009 . . 59 ( ( 2 ): ): 301 - - 315 . . . .

O.M. Faltinsen . . A nonliner theory of sloshing in retangular tanks . . J. Ship Res. , , 1974 . . 18 ( ( 4 ): ): 224 - - 241 . . . .

O.M. Faltinsen . . A numerical non-linear method of sloshing in tanks with two dimensional flow . . J. Ship Res. , , 1978 . . 18 ( ( 4 ): ): 224 - - 241 . . . .

O.M. Faltinsen , , , A.N. Timokha . . Asymptotic modal approximation of nonlinear resonant sloshing in a rectangular tank with small fluid depth . . J. Fluid Mech. , , 2002 . . 470 319 - - 357 . . DOI: 10.1017/S0022112002002112 http://doi.org/10.1017/S0022112002002112 . .

J.B. Frandsen . . Sloshing motions in excited tanks . . J. Comput. Phys. , , 2004 . . 196 ( ( 1 ): ): 53 - - 87 . . DOI: 10.1016/j.jcp.2003.10.031 http://doi.org/10.1016/j.jcp.2003.10.031 . .

K. Friedrichs . . Über ein minimumproblem für potentialströmungen mit freiem rande . . Math. Ann. , , 1934 . . 109 ( ( 1 ): ): 60 - - 82 . . DOI: 10.1007/BF01449125 http://doi.org/10.1007/BF01449125 . .

T.V. Hromadka , , , R.J. Whitley . . Approximating three-dimensional steady-state potential flow problems using two-dimensional complex polynomials . . Eng. Anal. Bound. Elem. , , 2005 . . 29 ( ( 2 ): ): 190 - - 194 . . DOI: 10.1016/j.enganabound.2004.07.004 http://doi.org/10.1016/j.enganabound.2004.07.004 . .

M. Ikegawa . . Finite Element Analysis of Fluid Motion in a Container, Infinite Element Methods in Flow Problems , , : : Huntsville UAH Press , , 1974 . . .

E. Klaseboer , , , R.M. Derek , , , Y.C. Chan . . BEM simulations of potential flow with viscous effects as applied to a rising bubble . . Eng. Anal. Bound. Elem. , , 2011 . . 35 ( ( 3 ): ): 489 - - 494 . . DOI: 10.1016/j.enganabound.2010.09.005 http://doi.org/10.1016/j.enganabound.2010.09.005 . .

J.C. Luke . . A variational principle for a fluid with a free surface . . J. Fluid Mech. , , 1967 . . 27 ( ( 2 ): ): 395 - - 397 . . DOI: 10.1017/S0022112067000412 http://doi.org/10.1017/S0022112067000412 . .

J.W. Miles . . On Hamilton's principle for surface waves . . J. Fluid Mech. , , 1977 . . 83 ( ( 1 ): ): 153 - - 158 . . DOI: 10.1017/S0022112077001104 http://doi.org/10.1017/S0022112077001104 . .

N.N. Moiseyev . . On the theory of nonlinear vibrations of a liquid of finite volume . . Appl. Math. Mech. , , 1958 . . 22 ( ( 5 ): ): 224 - - 241 . . . .

T. Nakayama , , , K. Washizu . . The boundary element method applied to the analysis of two dimensional nonlinear sloshing problems . . Int. J. Numer. Method Eng. , , 1981 . . 17 ( ( 11 ): ): 1631 - - 1646 . . DOI: 10.1002/nme.1620171105 http://doi.org/10.1002/nme.1620171105 . .

W.G. Penney , , , A.T. Price . . Finite periodic stationary gravity waves in a perfect liquid . . Phil. Trans. R. Soc. Lond. A , , 1952 . . 224 ( ( 882 ): ): 254 - - 284 . . DOI: 10.1098/rsta.1952.0004 http://doi.org/10.1098/rsta.1952.0004 . .

N.A. Phillips . . A coordinate system having some special advantages for numerical forecasting . . J. Meteorol. , , 1957 . . 14 ( ( 2 ): ): 184 - - 185 . . DOI: 10.1175/1520-0469(1957)014<0184:ACSHSS>2.0.CO;2 http://doi.org/10.1175/1520-0469(1957)014<0184:ACSHSS>2.0.CO;2 . .

M.L. Rocca , , , P. Mele , , , V. Armenio . . Variational approach to the problem of sloshing in a moving container . . J. Theoret. Appl. Fluid Mech. , , 1997 . . 1 ( ( 4 ): ): 280 - - 310 . . . .

B. Šarler . . Solution of potential flow problems by the modified method of fundamental solutions: formulations with the single layer and the double layer fundamental solutions . . Eng. Anal. Bound. Elem. , , 2009 . . 33 ( ( 12 ): ): 1374 - - 1382 . . DOI: 10.1016/j.enganabound.2009.06.008 http://doi.org/10.1016/j.enganabound.2009.06.008 . .

M.S. Tarafder , , , K. Suzuki . . Numerical calculation of free surface potential flow around a ship using the modified Rankine source panel method . . Ocean Eng. , , 2008 . . 35 ( ( 5-6 ): ): 536 - - 544 . . DOI: 10.1016/j.oceaneng.2007.11.004 http://doi.org/10.1016/j.oceaneng.2007.11.004 . .

H. Wang , , , H. Zhang . . Boundary element method for simulating the coupled motion of a fluid and a three-dimensional body . . Appl. Math. Comput. , , 2007 . . 190 ( ( 2 ): ): 1328 - - 1343 . . DOI: 10.1016/j.amc.2007.02.053 http://doi.org/10.1016/j.amc.2007.02.053 . .

G.B. Whitham . . A general approach to linear and non-linear dispersive waves using a Lagrangian . . J. Fluid Mech. , , 1965 . . 22 ( ( 2 ): ): 273 - - 283 . . DOI: 10.1017/S0022112065000745 http://doi.org/10.1017/S0022112065000745 . .

C.H. Wu , , , B.F. Chen . . Sloshing waves and resonance modes of fluid in a 3D tank by a time independent finite difference method . . Ocean Eng. , , 2009 . . 36 ( ( 6-7 ): ): 500 - - 510 . . DOI: 10.1016/j.oceaneng.2009.01.020 http://doi.org/10.1016/j.oceaneng.2009.01.020 . .

G.X. Wu . . Second order resonance of sloshing in a tank . . Ocean Eng. , , 2007 . . 34 ( ( 17-18 ): ): 2345 - - 2349 . . DOI: 10.1016/j.oceaneng.2007.05.004 http://doi.org/10.1016/j.oceaneng.2007.05.004 . .

V.E. Zakharov . . Stability of periodic waves of finite amplitude on the surface of a deep fluid . . Zh. Prokl. Mekh. Tekh. Fiz. , , 1968 . . 9 ( ( 2 ): ): 190 - - 194 . . . .

浏览量

Downloads

CSCD

文章被引用时，请邮件提醒。

Submit

工具集

关联资源

暂无数据