We present and discuss discontinuous Galerkin (DG) schemes for dry and moist atmospheric flows in the mesoscale. We derive terrain-following coordinates on the sphere in strong-conservation form, which makes it possible to perform the computation on a Cartesian grid and yet conserves the momentum density on an f -plane. A new DG model, i.e. DG-COSMO, is compared to the operational model COSMO of the Deutscher Wetterdienst (DWD). A simplified version of the suggested terrain-following

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... is implemented in DG-COSMO and is compared against the DG dynamical core implemented within the DUNE framework, which uses unstructured grids to capture orography. Finally, a few idealised test cases, including 3d and moisture, are used for validation. In addition an estimate of efficiency for locally adaptive grids is derived for locally and non-locally occurring phenomena.