Finite Difference Method of Transient Nonlinear Free Surface Wave Problems

Lu Yu-lin; Li Bao-yuan

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 1985 > 6(2): 145-152

Lu Yu-lin, Li Bao-yuan. Finite Difference Method of Transient Nonlinear Free Surface Wave Problems[J]. Applied Mathematics and Mechanics, 1985, 6(2): 145-152.

Citation:

Lu Yu-lin, Li Bao-yuan. Finite Difference Method of Transient Nonlinear Free Surface Wave Problems[J]. Applied Mathematics and Mechanics, 1985, 6(2): 145-152.

Citation:

Lu Yu-lin, Li Bao-yuan. Finite Difference Method of Transient Nonlinear Free Surface Wave Problems[J]. Applied Mathematics and Mechanics, 1985, 6(2): 145-152.

PDF( 518 KB)

Finite Difference Method of Transient Nonlinear Free Surface Wave Problems

Research Institute of Engineering Mechanics, Dalian Institute of Technology, Dalian

Received Date: 1983-12-16
Publish Date: 1985-02-15

Abstract

Abstract

A finite difference method is developed for computing the two-dimensional transient potential flow generated by an impulse on the free surface. Both the dynamic and kinematic free surface conditions are considered in nonlinear version, the primary features of the present paper include the use of special coordinates transformations so that the geometry of the flow field is transformed into a time-invariant region, presents an iteration process, by which the velocity potential is computed as the solution of a Poisson equation, the application of fast Fourier transform (FFT) technique results in a tri-diagonal system of equations which can be readily solved by the Thomas algorithm, the computing time is significantly reduced. Thus an efficient technique for handling the transient potential problems is well justified. The feasibility of the present method is verified by two examples involving different initial disturbances.

FullText(HTML)

References(14)

References

[1]	Harlow, F. H. and J. E. Welch, Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface, Physics of Fluids,8,12,Dec.(1965).
[2]	Horlow. F. H. and J. E. Welch, Numerical study of large-amplitude free-surface motions.Physics of Fluids.9,5. May(1966).
[3]	Nichols, B. D. and C. W. Hirt. Improved free surface boundary conditions for numerical incompressible flow calculations, Journal of Computational Physics,8. 3,Dec.(1971).
[4]	Nichols, B. D. and C. W. Hirt. Calculating three-dimensional free surface flows in the vicinity of submerged and exposed structures. Journal of Computational Physics.12. 2. June(1973).
[5]	Chan, R. K-C. and R. L. Street. A computer study of finite amplitude water waves. Journal of Computational Physics.6,1. Aug.(1970).
[6]	Chan, R. K.-C.,R.L. Street and J. E. Fromn. The digital simulation of water waves:An evolution of SUMMAS, Lecture Note in Physics.8. Springer-Verlag.Berlin.(1970).
[7]	Taylor, C. J., P. W. France, and O. C. Zienkiewicz. Some free surface transient flow problems of seepage and irrotational flow, The Mathematics of Finite Elements and Applications.Academic Press. New York,(1973).
[8]	Visser, W. and M. van der Wilt. A numerical approach to the study of irregular ship motions.Finite Element Method in Flow Problems.UAH Press, Alabama,(1974).
[9]	Nickell, R. E., R. I. Tanner, and B. Caswell,The solution of viscous incompressible jet and free surface flows using finite-element methods. Journal of Fluid Mechanics. 65. Pt.1. (1974).
[10]	Bai, K. J., A localized finite element method for the uniform flow problems with a free surface.First International Conference on Numerical Ship Hydrodynamics, Gaithersburg, Maryland.U.S. A.,Oct.(1975).
[11]	Bai, K. J. and R. W. Yeung, Numerical solutions to free-surface flow problems, Proceedings of The Tenth ONR Symposium on Naval Hydrodynamics, Cambridge, Mass., U.S.A. June(1974).
[12]	Yen, S. M. and K. D. Lee, application of finite element method to potential flow problems.Proceedings of the Second International Sympesium on Finite Element Methods in Flow Problems, Rapallo.Italy. June (1976).
[13]	Haussling, H. J. and R. T. Van Eseltine, A combined spectral finite-difference method for linear and nonlinear water wave problems. Naral Ship R & D Center Report 4580. Nov.(1974).
[14]	Haussling, H. J. and R. T. Van Eseltine, Finite difference methods for transient potential flows with free surfaces. First International Conference on Numerical Ship Hydrodynamics.Gaithersburg. Maryland U.S.A. Oct.(1975).