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AbstractWe describe in this work a discontinuous-Galerkin Finite-Element method to approximate the solutions of a new family of 1d Green-Naghdi models. These new models are shown to be more computationally efficient, while being asymptotically equivalent to the initial formulation with regard to the shallowness parameter. Using the free surface instead of the water height as a conservative variable, the models are recasted under apre-balancedformulation and discretized using a nodal expansiondoi:10.4208/cicp.150414.101014a fatcat:lfnw3v5luzgrbkouj2nvgpstme