Simulation of nonlinear free surface dispersive shallow water waves

The two-dimensional time domain simulation of nonlinear waves has received considerable attention in the recent years, in which a mixed Eulerian and Lagrangian method (MEL) shows potential application. In this paper, the finite element method is used in the domain for the estimation of the velocity potential, while, a cubic spline approximation is used to recover the velocity. The present methodology has been compared with the laboratory simulation of a Cnoidal wave over a long time far away from the wave making boundary. The present numerical model is further extended to investigate the interactions with the submerged obstacles. This reveals that by using the present methodology, the dispersive characteristics are not predicted well, compared, to the experimental measurements for very steep waves. Further modification is carried out for the velocity recovery by using least square method to overcome the difficulties in the simulation of steep waves. Smoothing or regridding is not applied in the simulation unlike in most of the existing simulation.