Modelling linear wave transformation induced by dissipative structures-Regular waves

A numerical model of the modified time-independent mild-slope equation for linear waves over a rapidly changing finite porous bed is presented. In this solution the reflection and phase coefficient shift are solved implicitly. Boundaries are assumed to be open, partially reflecting, or fully absorbing through the second-order parabolic approximation. Discretisation of the governing equation and boundary conditions is by means of a second-order accurate central difference scheme. The resulting sparse-banded matrix is solved using an inexpensive banded solver with Gaussian elimination. The model has been validated and the numerical predictions are in excellent agreement with analytical solutions.