  We present a novel hyperbolic reformulation of the Serre-Green-Naghdi (SGN)
model for the description of dispersive water waves. Contrarily to the
classical Boussinesq-type models, it contains only first order derivatives,
thus allowing to overcome the numerical difficulties and the severe time step
restrictions arising from higher order terms. The proposed model reduces to the
original SGN model when an artificial sound speed tends to infinity. Moreover,
it is endowed with an energy conservation law from which the energy
conservation law associated with the original SGN model is retrieved when the
artificial sound speed goes to infinity. The governing partial differential
equations are then solved at the aid of high order ADER discontinuous Galerkin
finite element schemes. The new model has been successfully validated against
numerical and experimental results, for both flat and non-flat bottom. For
bottom topographies with large variations, the new model proposed in this paper
provides more accurate results with respect to the hyperbolic reformulation of
the SGN model with the mild bottom approximation recently proposed in "C.
Escalante, M. Dumbser and M.J. Castro. An efficient hyperbolic relaxation
system for dispersive non-hydrostatic water waves and its solution with high
order discontinuous Galerkin schemes, Journal of Computational Physics 2018".
