Impact of curved elements for flows over orography with a Discontinuous Galerkin scheme

Giuseppe Orlando (1) , Tommaso Benacchio (2) , Luca Bonaventura (3)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 DMI - Danish Meteorological Institute
3 POLIMI - Dipartimento di Matematica [Politecnico Milano]

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.

Keywords: Numerical Weather Prediction; Discontinuous Galerkin methods; High-order mapping; Flows over orography; Curved boundary

Domains: Atmospheric and Oceanic Physics [physics.ao-ph]; Numerical Analysis [math.NA]

Giuseppe Orlando, Tommaso Benacchio, Luca Bonaventura. Impact of curved elements for flows over orography with a Discontinuous Galerkin scheme. 2024. ⟨hal-04547681⟩