  We present a quantitative assessment of the impact of high-order mappings on
the simulation of flows over complex orography. Curved boundaries were not used
in earlier numerical methods, whereas they are employed nowadays to an
increasing extent in combination with high-order methods, such as the Finite
Element Method (FEM) and the Spectral Element Method (SEM). We consider here a
specific Discontinuous Galerkin (DG) method implemented in the framework of the
deal.II library, which natively supports high-order mappings. A number of
numerical experiments based on classical benchmarks over idealized orographic
profiles demonstrate the positive impact of curved boundaries on the accuracy
of the results. These findings are also supported by results of the application
of this approach to non-smooth and realistic orographic profiles.
