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Fig 12 Runup on surface of the cylinder (— · — · — t=15; — — — t=20; ———— t=25)

Fig 13 Horizontal force acting on cylinder

CONCLUSIONS

This paper has shown how the domain decomposition method may be extended to a three-dimensional finite element analysis of non-linear water waves interacting with bodies. A scheme of overlapping adjacent domains is found to be more effective than an earlier scheme used by the authors for the two-dimensional problem, and a study has been conducted into the optimum amount of overlap and the optimum relaxation coefficient in the iterative scheme. Preliminary results have been obtained for the case of a vertical cylinder in a wave tank. The method requires extensive computer run times when implemented on a workstation, and further work is required to improve the methodology. This includes the development of a procedure for combining the domain decomposition method with wave absorbing techniques to allow the imposition of appropriate radiation conditions close to the body.

The results shown are for the case of a fixed cylinder. For a floating structure, body motions need to be taken into account, and it is intended to achieve this by using the method described by Wu and Eatock Taylor [7].

ACKNOWLEDGEMENT

This work forms part of the research programme “Uncertainties in Loads on Offshore Structures” sponsored by EPSRC through MTD Ltd and jointly funded with: Amoco (UK) Exploration Company, BP Exploration Operating Co Ltd, Brown & Root, Exxon Production Research Company, Health and Safety Executive, Norwegian Contractors a.s., Shell UK Exploration and Production, Den Norske Stats Oljeselskap a.s., Texaco Britain Ltd.

REFERENCES

1. Cointe, R., Geyer, P., King, B., Molin, B. and Tanoni, M., 1990, “Nonlinear and linear motions of a rectangle barge in a perfect fluid, ” 18th Symp. on naval hydrody., Univ. of Michigan, Ann Arbor, pp. 85–98.

2. Glowinski, R., Dinh, Q.V. & Periaux, J., 1984, “Domain decomposition for elliptic problems”, in Finite Element Methods, John Wiley and Sons, Chichester, Vol. 5, pp. 45–106.

3. Longuet-Higgins, M.S. & Cokelet, E.D., 1976, “The deformation of steep surface waves on water: I. a numerical method of computation” , Proc. R. Soc. London, A Vol. 350, pp.1–26.

4. Romate, J.E., 1992, “Absorbing boundary conditions for free surface waves”, J. Comp. Physics. Vol. 99, pp. 135–145.

5. Wu, G.X. and Eatock Taylor, R., 1995, “Time stepping solutions of the two dimensional



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