The Serre-Green-Naghdi (SGN) equations, also known as the fully nonlinear Boussinesq wave equations, are known to accurately describe a wide range of waves and in particular shoaling waves for which dispersive effects cannot be neglected. I will show how this model can be solved in a simple way using the combination of a robust, well-balanced existing Saint-Venant solver with the multigrid solution of the SGN equations. Using the Basilisk framework (http://basilisk.fr) this simple implementation automatically generalises to adaptive quadtree grids which allows efficient large-scale simulation of, for example, dispersive tsunami waves.