We systematically validate the static local mesh refinement capabilities of a recently proposed IMEX-DG scheme implemented in the framework of the deal.II library. Non-conforming meshes are employed in atmospheric flow simulations to increase the resolution around complex orography. The proposed approach is fully mass and energy conservative and allows local mesh refinement in the vertical and horizontal direction without relaxation at the internal coarse/fine mesh boundaries. A number of numerical experiments based on classical benchmarks with idealized as well as more realistic orography profiles demonstrate that simulations with the locally refined mesh are stable for long lead times and that no spurious effects arise at the interfaces of mesh regions with different resolutions. Moreover, correct values of the momentum flux are retrieved and the correct large-scale orographic response is reproduced. Hence, large-scale orography-driven flow features can be simulated without loss of accuracy using a much lower total amount of degrees of freedom.