A more effective numerical model using the dual reciprocity boundary element method (DRBEM) is presented to study the combined effects of wave refraction-diffraction and currents. The mild-slope equation with current effects is reformulated to an inhomogeneous Helmholtz equation. Applying the conventional boundary element method to this inhomogeneous equation, the inhomogeneous part will result in a domain integral which makes the computation· complicated and messy. To improve this drawback, the DRBEM is adopted to transform the domain integral to boundary integral. To verify the validity of this model, the relative amplitude around a circular island without current effects was calculated, and compared with analytical solutions of Homma (1950). The agreement is fairly satisfactory. The combined effects of wave refraction- diffraction and currents around a circular island over a seabed with a variable depth are calculated by this model. The results show that the model has a great potential to be used to solve the problem of combined wave refraction-diffraction and currents.
The study of the combined effects of wave refraction-diffraction and currents becomes an important topic on ocean engineering nowadays. It has drawn attention of researchers to do the relate investigation. Homma(l950) used shallow water equation to investigate wave refraction and diffraction around a circular island. Berkhoff(1972), and later Vanstano and Reid(1975) derived the well known mild-slope equation to describe wave refraction and diffraction. Booij(l981), Liu(1983) and Kifby(1984) extended the mild-slope equation to include the effects of current. Based on the equation derived by Kirby(l984), a m6del using finite boundary element method was proposed by Lin et al.(1994) to study the effects of wave refraction-diffraction together with a current. The model needs to place with a large number of finite elements in a variable seabed domain. Thus, the computer storage and time are formidable.