Using a time-domain higher-order boundary element method to simulate wave and current diffraction from a 3-D body

Abstract

To study wave-current actions on 3-D bodies a time-domain numerical model was established using a higher-order boundary element method (HOBEM). By assuming small flow velocities, the velocity potential could be expressed for linear and higher order components by perturbation expansion. A 4th-order Runge-Kutta method was applied for time marching. An artificial damping layer was adopted at the outer zone of the free surface mesh to dissipate scattering waves. Validation of the numerical method was carried out on run-up, wave exciting forces, and mean drift forces for wave-currents acting on a bottom-mounted vertical cylinder. The results were in close agreement with the results of a frequency-domain method and a published time-domain method. The model was then applied to compute wave-current forces and run-up on a Seastar mini tension-leg platform.

Keywords

wave-current diffraction / time-domain simulation / drift force / higher-order boundary element method (HOBEM)

References

[1] Buchmann B., Skourup J., Cheung K.F. Run-up on a structure due to second-order waves and current in a numerical wave tank. Applied Ocean Research, 1998, 20: 297-308

[2] Ferrant P. Three-dimensional unsteady wave-body interactions by a Rankine boundary element method. Ship Technology Research, 1993, 40: 165-175

[3] Grue J., Palm E. Wave radiation and wave diffraction from a submerged body in a uniform current. Journal of Fluid Mechanics, 1985, 151: 257-278

[4] Isaacson M, Cheung KF (1992). Wave-current interaction with a large structure. Proceedings of International Conference on Civil Engineering in Oceans, Texas.

[5] Kim DJ, Kim MH (1997). Wave-Current-Body interaction by a time-domain high-order boundary element method. International offshore and polar engineering conference, Hawaii, 25–30.

[6] Matsui T., Lee S.Y., Sano K. Hydrodynamic forces on a vertical cylinder in current and waves. Journal of the Society of Naval Architects of Japan, 1991, 170: 277-287

[7] Ning D.Z., Teng B. Numerical simulation of fully nonlinear irregular wave tank in three-dimension. International Journal for Numerical Methods in Fluids, 2007, 53(12): 1847-1862

[8] Nossen J., Grue J., Plam E. Wave forces on three dimensional floating bodies with small forward speed. Journal of Fluid Mechanics, 1991, 227: 135-160

[9] Teng B, Eaock Taylor R (1993). The effect of corners on diffraction/radiation forces and wave drift damping. Proceedings of Offshore Technology Conference, OTC7187, London.

[10] Teng B., Eatock Taylor R. Application of a higher order BEM in the calculation of wave run-up on bodies in a weak current. International Journal of Offshore and Polar Engineering, 1995, 5: 219-224

[11] Teng B., Zhao M., Bai W. Wave diffraction in a current over a local shoal. Coastal Engineering, 2001, 42: 163-172

[12] Wu GX, Eatock Taylor R (1987). Hydrodynamic forces on submerged oscillating cylinders at forward speed. Proceedings of the Royal Society of London, Series A, London, 149–170.

[13] Zhao R., Faltinsen O.M. Interaction between waves and current on a two-dimensional body in the free surface. Applied Ocean Research, 1988, 10(2): 87-99