The calculation of wave shoaling and breaking is essential in coastal applications like risk analysis. Due to the high cost of 3D models 2D vertically averaged models are normally used. For the propagation and shoaling, higher order models are needed to describe the dispersion of waves with enough accuracy. For breaking some dissipation mechanism is normally introduced, of which the simple switch from the dispersive high order models to the first order Saint-Venant equations has been very popular for two reasons: the non parametric dissipation of energy of shock waves and its simple implementation. However, it has been shown that this model becomes unstable as the resolution is increased. In this work we show how domain decomposition methods can propose a different way to "switch off" the dispersion by exchanging the information through boundary conditions and overlapping zones, obtaining different performances.