Robust solutions of the Mild Slope Equations using a discontinuous DRBEM

The original Mild Slope Equation (MSE) was derived by Berkhoff (1972), assuming that the linear, constant depth potential flow solution is locally valid, and integrating over the depth. The result is a two-dimensional elliptic equation describing linear wave scattering over moderately varying bathymetry, which is widely used to estimate wave transformation from the deep ocean to coastal regions. In the present paper, the MSE is solved using the well-known Dual Reciprocity Boundary Element Method (DRBEM). The new contribution of this work is an implementation which exploits discontinuous, high-order elements within the context of a boundary element method. A nearly optimal position is suggested for the location of the collocation points. Convergence of the solution with resolution is demonstrated, in particular for several cases where solutions based on continuous elements are found to diverge. The ability of the proposed method to treat practical engineering applications, e.g. modeling refraction/diffraction around islands and in the vicinity of offshore reef breakwaters is also demonstrated.