A 2D numerical scheme for modelling non-hydrostatic flows

In the present work, a fully implicit finite element scheme for modelling two-dimensional (2D) non-hydrostatic flows is presented. The model solves the 2D Vertically Averaged and Moment (VAM) equations, which overcome the classical shallow water hypotheses by incorporating polynomial profiles to describe the horizontal and vertical velocity and the pressure field along the water column. The proposed numerical scheme combines a Discontinuous Galerkin (DG) discretization with a local Taylor-based reconstruction of the non- conservative terms, allowing all governing equations to be advanced simultaneously in time without any operator splitting or iterative solvers. The model is successfully validated against experimental benchmarks.