UNDA is a fully nonlinear solver for potential flow around marine constructions. Particular attention has been made to multi-cylinder platforms with or without pontoons. It was originally developed for surface-piercing columns or fully submerged bodies. Recently we have also shown how it can be generalized to describe green water, for which an originally surface-piercing body is inundated by a large wave. Some typical situations are shown in these snapshots:

Long-crested waves hitting a four-legged platform

Click on the image to the left to see a video animation of the simulation.

The water depth is 345 m. The cylindrical legs have radius 15.5 m, with 80 m spacing between their centers. In the simulation, the legs extend from 77 m below to 23 m above the mean water level, while the animation only shows the legs extending from 23 m below the mean water level. The simulation was done in a domain extending from 1000 m in front to 1000 m behind the platform center, and extending 300 m to each side. The animation shows a limited region extending from 180 m in front to 125 m behind the platform center, and extending 89 m to each side. The vertical scale has been exaggerated 2.5 times in comparison with the horizontal scale.

The incoming wave has period 12 s and nominal amplitude 7 m. That gives a nominal steepness of ka = 0.2, which may be unrealistically high for waves in the ocean. The simulation starts from rest at time 0 s when waves begin to enter through one of the short sides of the simulation domain. The simulation stops at time 200 s in order to avoid contamination by waves reflected from the side walls.

Waves pasing a single cylinder

Sample animations of one-legged and four-legged platforms.

Publications

1. Trulsen, K. and Teigen, P.   2002   Wave scattering around a vertical cylinder: Fully nonlinear potential flow calculations compared with low order perturbation results and experiment.   In Proceedings of OMAE'02, Paper OMAE2002-28173, pp. 1-9.
2. Trulsen, K., Spjelkavik B. and Mehlum, E. Green water computed with a spline-based collocation method for potential flow. International Journal of Applied Mechanics in Engineering, 7(1):107-123, 2002.
3. Teigen, P. and Trulsen, K.   2001   Numerical investigation of nonlinear wave effects around multiple cylinders.   In Proceedings of ISOPE 2001, Vol. 3, pp. 369-378.
4. Mehlum, E. Splines and ocean wave modelling. In "Numerical Methods and Software Tools in Industrial Mathematics", Eds., M. Dæhlen and A. Tveito, pp. 235-253, Birkhäuser, 1997.
5. Cai, X. and Mehlum, E. Two fragments of a method for fully nonlinear simulations of water waves. In "Waves and Nonlinear Processes in Hydrodynamics". Eds., J. Grue, B. Gjevik and J. E. Weber, pp. 37-50, Kluwer Academic Publishers, 1996.

UNDA development has been funded by Statoil, Norsk Hydro, Norske Conoco, Saga Petroleum, SINTEF Applied Mathematics and Norske Shell.