Recent advances in Serre–Green Naghdi modelling for wave transformation, breaking and runup processes

To describe the strongly nonlinear dynamics of waves propagating in the final stages of shoaling and in the surf and swash zones, fully nonlinear models are required. The ability of the Serre or Green Naghdi (S–GN) equations to reproduce this nonlinear processes is reviewed. Two high-order methods for solving S–GN equations, based on Finite Volume approaches, are presented. The first one is based on a quasi-conservative form of the S–GN equations, and the second on a hybrid Finite Volume/Finite Difference method. We show the ability of these two approaches to accurately simulate nonlinear shoaling, breaking and runup processes.