Wave-current-body interaction by a time-domain high-order boundary element method

The effects of uniform steady currents (or small forward velocity) on the interaction of a large three-dimensional body with waves are investigated by a time-domain higher order boundary element method (THOBEM). Using regular perturbation with two small parameters epsilon and delta associated with wave slope and current velocity, respectively, the boundary value problem is decomposed into the zeroth-order steady double-body-how problem at O(delta) with a rigid-wall free-surface condition and the first-order unsteady wave problem with the modified free-surface and body-boundary conditions expanded up to O(epsilon delta). Higher-order boundary integral equation methods are then used to solve the respective problems with the Rankine sources distributed over the entire boundary. The free surface is integrated at each time step. The Sommerfeld/Orlanski radiation condition is numerically implemented to absorb all the wave energy at the open boundary. Using the developed numerical method, wave forces, wave field and run-up, mean drift forces and wave drift damping are calculated.