The paper presents the calculation of wave run-up on a floating body in current by a higher order boundary element method. The method is based on the perturbation expansion of velocity potential and Green's function in terms. of current velocity. Novel integral equation are employed, which improve the calculation of some of the Cauchy principal value integrations. In order to save computer time and storage, the numerical scheme has been designed to accept two, one or no planes of symmetry of the body geometry.
Many researchers have developed efficient algorithms to evaluate the action on structure by waves and current individually. However, at as a common phenomenon in nature that waves and current co-exist, or bodies move in waves. When a current and waves coexist, the free surface boundary condition wall be changed. Accordingly, the diffraction and the radiation of waves from a body will be changed, and wave forces and wave run-up on structures will also be modified. The wave run-up is a dominant factor in the determination of the deck elevation of an offshore platform. An under-estimated elevation will not assure the safe normal operation of the platform, and an overestimated elevation will increase the cost and decrease the stability of the platform. In the calculation of wave diffraction and radiation around bodies, the integral equation method is widely used. For the wave and current problem, by using a Green's function (Wehausen and Laitone 1960) which satisfies the free water surface and far field conditions, the integration domain can be limited to the body surface and a small area on the free water surface. Unfortunately, the calculation of the Green's function is time consuming, so efficiency of this method is greatly reduced as compared with the case without a current.
