On the accurate simulation of nearshore and dam break problems involving dispersive breaking waves

The ability of numerical models to deal with wave breaking processes and dry areas is of paramount importance for applications in coastal zones and dam breaks. The mathematical models commonly used in such real problems are usually based on Boussinesq-type equations and, to a small extend, on Serre equations. However, these standard models are weakly dispersive and must be appropriately modified to deal with breaking waves and dry areas. Indeed, nearshore and dam break problems involve complex wave dynamics and highly dispersive wave processes can easily arise. In those cases, it is well known that weakly dispersive models like the ones based on classical Boussinesq or Serre equations are unreliable for an accurate simulation of the phenomena involved. In this work we extend the applicability of an improved Serre model, herein denoted by Serre(alpha,beta), to include the wave breaking process, the broken waves propagation, and dry areas. We provide a comprehensive set of numerical examples involving wave propagation over exposed and submerged structures, as well as dam break problems. The numerical experiments show the accuracy and robustness of the proposed model. Particular attention is given to bottom friction modeling, where the standard Manning's assumption is compared with a more realistic formulation. Also noteworthy is the simulation of wave breaking problems with highly dispersive effects. The advantages of the Serre(alpha,beta) model over the standard Serre model for these challenging cases are clear. (C) 2018 Elsevier B.V. All rights reserved.