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To describe the strongly nonlinear dynamics of waves propagating in the finalstages of shoaling and in the surf and swash zones, fully nonlinear models arerequired. The ability of the Serre or Green Naghdi (S-GN) equations toreproduce this nonlinear processes is reviewed. Two high-order methods forsolving S-GN equations, based on Finite Volume approaches, are presented. Thefirst one is based on a quasi-conservative form of the S-GN equations, and thesecond on a hybrid Finite Volume/Finite Difference method. We show the abilityof these two approaches to accurately simulate nonlinear shoaling, breaking andrunup processes.

Fully nonlinear weakly dispersive modelling of wave transformation, breaking and runup