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Research Papers

Numerical Wave Tanks Based on Finite Element and Boundary Element Modeling

[+] Author and Article Information
R. Eatock Taylor1

Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UKr.eatocktaylor@eng.ox.ac.uk

G. X. Wu, Z. Z. Hu

Department of Mechanical Engineering, University College London, Torrington Place, London WC1E 7JE, UK

W. Bai

Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UK

When the BE method is to be coupled with the FE method, the BE domain must also include vertical boundary surfaces adjacent to the FE domains at each end.

1

Corresponding author.

J. Offshore Mech. Arct. Eng 130(3), 031001 (Jul 11, 2008) (8 pages) doi:10.1115/1.2904583 History: Received June 05, 2006; Revised December 11, 2007; Published July 11, 2008

This work forms part of an investigation into the nonlinear interaction between steep (but not overturning) transient waves and flared structures, using a coupled finite element and boundary element model. The use of a coupled approach is based on consideration of the relative strengths and weaknesses of the finite element (FE) and boundary element (BE) methods when implemented separately (e.g., efficiency of computation versus complexity of adaptive mesh generation). A FE model can be used to advantage away from the body, where the domain is regular, and a BE discretization near the body where the moving mesh is complex. This paper describes the aspects of the FE and BE models which have been developed for this analysis, each based on the use of quadratic isoparametric elements implemented in a mixed Eulerian–Lagrangian formulation. Initially, the two approaches have been developed side by side, in order to ensure the use of robust components in the coupled formulation. Results from these methods are obtained for a series of test cases, including the interaction of an impulse wave with a circular cylinder in a circular tank, and nonlinear diffraction by a cylinder in a long tank.

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Copyright © 2008 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Coupled BE/FE mesh regions on free surface for four cylinders in a wave tank

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Figure 2

Spatial profile of propagating wave at ω=2.0: a=0.01(⋯); a=0.043 (—). (a) t=7T; (b) t=15T.

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Figure 3

Time history of horizontal force on cylinder ((—) PSME; (---) BE)

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Figure 4

Free surface contours around cylinder at the center of circular tank, a=0.1: (a) PSME t=15; (b) BE t=15; (c) PSME t=30; and (d) BE t=30

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Figure 5

Time history of elevation at the front of cylinder ((—) PSME; (---) BE)

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Figure 6

BE and FE meshes for cylinder in a rectangular tank

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Figure 7

Time history of force on fixed cylinder in a rectangular tank

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Figure 8

Time history of up-wave run-up

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Figure 9

Time history of down-wave run-up

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