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conservation is satisfied within an relative accuracy of about 10 –3. Similar figures are obtained regarding energy conservation.

CONCLUSION

Significant results of two different version of the three dimensional Rankine panel code ANSWAVE have been presented. Both version solve fully nonlinear free surface problems under the assumptions of potential flow.

The first version is based on a semi Lagrangian representation of free-surface motions, with markers fixed horizontally, and is formulated in terms of a perturbation flow defined as the difference between the incident and the total flow. This splitting is possible here with fully nonlinear free surface conditions because of the characteristics of the incident wave model based on a stream function theory. We first discuss with more details original results on the nonlinear diffraction of long waves by a bottom-mounted vertical cylinder, already presented at the 11th WWWFB in Hamburg (Ferrant 1996). The capacity of the model to capture stable higher order components of the diffracted flow is attested, although it seems to be difficult to find a common range of applicability of fully nonlinear simulation and of higher order perturbation analysis. This point will motivate further reseach in order to improve the accuracy of the model at low amplitudes, as well as its stability for larger ones. This first model has been extended to the problem of the free motions of a floating body in regular incoming waves. The behaviour of the model in such a configuration is illustrated by the stable simulation of the nonlinear vertical motion of a floating cylinder, over 10 wave periods.

The secund version is based on a fully Lagrangian formulation. It is applied here to the computation of large amplitude standing waves in a three dimensional tank. Strongly nonlinear effects are observed, while the accuracy of the simulation is attested by mass and energy conservation. The Lagrangian representation of the free surface is potentially more adapted to the simulation of steep waves interfering with moving boundaries, a problem on which we concentrate our present research efforts.

Acknowledgments

The development of the code ANSWAVE was supported by the French Ministry of Defense, under contract DRET/SIREHNA 94/360. The application to nonlinear diffraction problems was part of a CLAROM project on “ high frequency resonance of offshore structures”, with BUREAU VERITAS, DORIS ENGINEERING, IFP, IFREMER, PRINCIPIA and SIREHNA as partners.

References

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