A time-domain numerical model is established with a higher-order boundary element method to study the problem of wave-current interaction with structures. Using regular perturbation with two small parameters ε and δ associated with wave slope and current velocity, respectively, the boundary value problem is decomposed into a steady double-body-flow problem at O(δ) and an unsteady wave problem at O(εδ) and O(ε). A 4th-order Runge-Kutta method is applied for the time marching. An artificial damping layer is adopted to dissipate the scattering waves. Validations of the numerical model on wave-current force and run-up on a bottom-mounted vertical cylinder and a complex bridge pier are carried out.
The problem of wave-current interaction with bodies has been widely studied in the frequency domain (Grue and Palm, 1985; Wu and Eatock Taylor, 1987; Matsui et al, 1991; Zhao and Faltinsen, 1988; Nossen et al, 1991; Teng and Eatock Taylor, 1993; Teng and Eatock Taylor, 1995; Teng et al, 2001). Although the frequency-domain analysis has been presented for a long time, it is in general mathematically complicated and cannot be easily extended to nonlinear problems. Isaacson and Cheung (1992) employed an alternative time-domain analysis to solve the same problem by a constant panel method. However, accurate computation of the second-order spatial derivatives of the velocity potential on the integral surface is very difficult. A time domain analysis based on a higher-order boundary element method is then developed. Using regular perturbation expansion with wave steepness ε to the mean position of the non-stationary boundaries, a solution of time-domain higher-order boundary element method (THOBEM) for 3D wave radiation and diffraction in a current was proposed (Buchmann et al, 1998). They presented the results of the diffractive run-up of wave-current interaction with a structure in a flume.