Simulations of Non-hydrostatic Flows by an Efficient and Accurate p-Adaptive DG Method

We review recent results in the development of a class of accurate, efficient, high order, dynamically p-adaptive Discontinuous Galerkin methods for geophysical flows. The proposed methods are able to capture phenomena at very different spatial scales, while minimizing the computational cost by means of a dynamical degree adaptation procedure and of a novel, fully second order, semi-implicit semi-Lagrangian time discretization. We then present novel results of the application of this technique to high resolution simulations of idealized non-hydrostatic flows.