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.
Liu, Z., Teng, B., Ning, D. Z., & Sun, L. (2010). Using a time-domain higher-order boundary element method to simulate wave and current diffraction from a 3-D body. Journal of Marine Science and Application, 9(2), 156-162. https://doi.org/10.1007/s11804-010-9011-2