This study is concerned with the development of a high-order numerical model to solve incompressible water wave motion based on improved nonlinear dispersive Boussinesq equations. A third-order Adams-Bashforth and a fourth-order Adams-Mouton predictor-corrector scheme was selected in an attempt to eliminate the truncation error terms that would be of the same form as the dispersive terms in the Boussinesq equations with second order schemes as in many other studies.
Eddy viscosity type momentum correction term was added into the Boussinesq equation to simulate the energy loss due to wave breaking and to extend the model application to surf zone wave transformation. The location of the breaking point was determined through a wave breaking criterion using the ratio of horizontal water particle velocity to wave celerity.
A moving boundary technique utilizing linear extrapolation is developed to investigate wave runup and rundown. Wave absorption at an open boundary was simulated by solving the Sommerfeld radiation and introducing sponge layer into the model.
Breaking regular wave runup propagation on a sloping beach is simulated. It would seem that inclusion of an accurate dissipation term becomes increasingly important with increasing degree of wave breaking. In regard to breaking regular wave runup simulation, additional dissipation term acted as bottom friction was required for long term stability in surf zone area. The validity of the model was confirmed by comparing computations with analytical solutions and measured data.