A Comparison of Dirichlet and Neumann Wavemakers for the Numerical Generation and Propagation of Nonlinear Long-Crested Surface Waves

R. E. Baddour; W. Parsons

doi:10.1115/1.1835987

Journal of Offshore Mechanics and Arctic Engineering | Volume 126 | Issue 4 | TECHNICAL PAPERS

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TECHNICAL PAPERS

A Comparison of Dirichlet and Neumann Wavemakers for the Numerical Generation and Propagation of Nonlinear Long-Crested Surface Waves

R. E. Baddour and W. Parsons

[+] Author and Article Information

R. E. Baddour

National Research Council—Canada, Institute for Ocean Technology, Arctic Avenue, P.O. Box 12093, A1B 3T5 St John’s, NL, Canada

W. Parsons

College of the North Atlantic, Ridge Road, P.O. Box 1150, A1C 6L8, St John’s, NL, Canada

J. Offshore Mech. Arct. Eng 126(4), 287-296 (Mar 07, 2005) (10 pages) doi:10.1115/1.1835987 History: Received March 01, 2003; Revised March 01, 2004; Online March 07, 2005

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References

Parsons, W., and Baddour, R. E., 2002, “The Generation and Propagation of Transient Long-Crested Surface Waves Using a Waveform Relaxation Method,” Proceedings Advances in Fluid Mechanics 2002, Wessex Institute of Technology Press.

Tsai, W., and Yue, D. K., 1996, “Computation of Nonlinear Free-Surface Flows,” Annual Review of Fluid Mechanic’s, Vol. 28, Annual Reviews Inc., CA.

Debnath, L., 1994, Nonlinear Water Waves, Academic Press, New York.

Wehausen, J. V., and Laitone, E. V., 1960, Encyclopedia of Physics, Vol. IX, Fluid Dynamics III, Springer-Verlag, Berlin.

Dimas, A. A., and Triantafyllou, G. S., 1994, “Nonlinear Interaction of Shear Flow With a Free Surface,” J. Fluid Mech., 260, pp. 91–115.

Kaplan, W., 1993, Advanced Calculus, 4th ed., Addison-Wesley, Reading, MA.

Durran, D. R., 1999, Numerical Methods for Wave Equations in Geophysical Fluid Dynamics, Springer-Verlag, New York.

Boyd, J. P., 2001, Chebyshev and Fourier Spectral Methods, 2nd ed., Dover, New York.

The MathWorks Inc., 1996, MATLAB 5.2 User’s Guide, Natick, MA.

Parsons, W., 1999, “Waveform Relaxation Methods For Volterra Integro-Differential Equations,” Ph.D. thesis, MUN, St. John’s NF.

Parsons, W., and Baddour, R. E., 2003, “A Numerical Wave Tank for the Generation and Propagation of Bi-Chromatic Nonlinear Long-Crested Surface Waves,” Proceedings Fluid Structure Interaction 2003, Wessex Institute of Technology Press.

Figures

Free surface elevation of the filtered wave of steepness S=2A/λ=0.05, after 50 periods of simulation. The Stokes third order wave is also plotted.

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Free surface elevation of the transient filtered wave of steepness S=2A/λ=0.05, after 10 periods

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Free surface elevation of the filtered wave of steepness S=2A/λ=0.08, after 30 periods

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Coordinate system configuration

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Free surface coordinate system

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Flow chart of the time integration algorithm

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Curvilinear coordinate system for the Laplace Solver Test Problem

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The computed and exact z derivative of the free surface potential for the Laplace Solver Test Problem

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Baddour RE, Parsons WW. A Comparison of Dirichlet and Neumann Wavemakers for the Numerical Generation and Propagation of Nonlinear Long-Crested Surface Waves. ASME. J. Offshore Mech. Arct. Eng. 2005;126(4):287-296. doi:10.1115/1.1835987.

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A Comparison of Dirichlet and Neumann Wavemakers for the Numerical Generation and Propagation of Nonlinear Long-Crested Surface Waves

References

Figures

Free surface elevation of the unfiltered wave of steepness S=2A/λ=0.01

Spectrum of unfiltered wave of steepness=0.01, after 50 periods of simulation

Spectrum of the unfiltered wave of steepness=0.05

Spectrum of the filtered wave of steepness=0.05 after 50 periods of simulation

Free surface elevation of the filtered wave of steepness S=2A/λ=0.05, after 50 periods of simulation. The Stokes third order wave is also plotted.

Free surface elevation of the transient filtered wave of steepness S=2A/λ=0.05, after 10 periods

Free surface elevation of the filtered wave of steepness S=2A/λ=0.08, after 30 periods

Coordinate system configuration

Free surface coordinate system

Flow chart of the time integration algorithm

Curvilinear coordinate system for the Laplace Solver Test Problem

The computed and exact z derivative of the free surface potential for the Laplace Solver Test Problem

Tables

Errata

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