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ISSN 2083-6473
ISSN 2083-6481 (electronic version)
 

 

 

Editor-in-Chief

Associate Editor
Tomasz Neumann
 

Published by
TransNav, Faculty of Navigation
Gdynia Maritime University
3, John Paul II Avenue
81-345 Gdynia, POLAND
www http://www.transnav.eu
e-mail transnav@am.gdynia.pl
Numerical Simulation of Nonlinear Water Wave Problems
1 National Kaohsiung Marine University, Kaohsiung, Taiwan
ABSTRACT: The main purpose of present paper aims at the establishment of a numerical model for solving the nonlinear water wave problems. The model is based on the Navier-Stokes equations with the consideration of a free-surface through the streamfunction-vorticity formulation. The main advantage of the streamfunction-vorticity formulation is that pressure field can be eliminated from the Navier-Stokes equations. To demonstrate the model feasibility, the present studies are first concentrated on problems including the collision of two solitary waves with different amplitudes, and the overtaking collision of two solitary waves. Then, the model is also applied to a solitary wave passes over the submerged obstacle in a viscous fluid. Finally, the application of present study is also to simulate the generation of solitary waves by underwater moving object. All examples give very promising results, those applications reveal that present formulation is a very powerful approach to simulate the fully nonlinear water wave problems.
REFERENCES
Y. Cao and R.F. Beck, Numerical computations of two- dimensional solitary waves generated by moving disturbances, Int. J. Numer. Meth. Fluids, 17 (1993) 905-920.
D. Ambrosi and L. Quartapelle, A Taylor-Galerkin method for simulating nonlinear dispersive water waves, J. Comput. Phys., 146 (1998) 546-569.
Lo, D.C., and Young, D. L. (2004). “Arbitrary Lagrangian--Eulerian finite element analysis of free surface flow using a velocity-vorticity formulation.” J. Comput. Phys., 195, 175-201.
C.W. Hirt, A.A. Amsden and J.L. Cook, An arbitrary Lagrangian Eulerian computing method for all flow speeds, J. Comput. Phys., 14 (1974) 227-253.
R. Grimshaw, The solitary wave in water of variable depth, part 1. J. Fluid Mech. 46 (1971) 611-622.
C.H. Su and R.M. Mirie, On head-on collision between two solitary waves, J. Fluid Mech. 98 (1980) 509-529.
R.M. Mirie and C. H. Su, Collisions between two solitary waves, Part 2: A Numerical Study, J. Fluid Mech. 115 (1982.
Citation note:
Lo D.C., Hu J.S., Lin I.F.: Numerical Simulation of Nonlinear Water Wave Problems. TransNav, the International Journal on Marine Navigation and Safety of Sea Transportation, Vol. 2, No. 2, pp. 137-142, 2008

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