A flexible and efficient DG discretization for Numerical Weather Prediction

As a first step towards construction of a DG based dynamical core for high resolution atmospheric modelling, a semi-implicit and semi-Lagrangian discontinuous Galerkin method for the SWE on the sphere and for nonhydrostatic vertical slice equations is proposed and analysed. The method is equipped with a simple p-adaptivity criterion, that allows to adjust dynamically the number of degrees of freedom employed. Numerical results in the framework of standard idealized test cases prove the accuracy and effectiveness of the method even at high Courant numbers.