Robust and accurate simulations of flows over orography using non-conforming variable resolution meshes

Atmospheric flows display phenomena on a very wide range of spatial scales that interact with each other. Many strongly localized features, such as complex orography, can only be modelled correctly if a very high spatial resolution is employed, especially in the lower troposphere, while larger scale features such as high/low pressure systems and stratospheric flows can be adequately resolved on much coarser meshes. The insufficient resolution of orographic features is compensated in numerical weather predictions (NWP) and climate models by subgrid-scale orographic drag parameterizations, which are essential for an accurate description of atmospheric flows with models using feasible resolutions. The interplay between resolved and parameterized orographic effects is critical, since many operational models employ resolutions in the so-called 'grey zone', for which some orographic effects are well resolved while others still require parameterization. Global simulations without drag parameterization have shown that the increase in forecast skill for increasing atmospheric resolution was mainly due to the improved representation of the orography. 

Because of these considerations, NWP is an apparently ideal framework for adaptive numerical approaches. However, mesh adaptation strategies have only slowly found their way into the NWP literature, due to limitations of earlier numerical methods, concerns about the accuracy of the representation of atmospheric wave phenomena for variable resolution meshes, and the complexity of an efficient parallel implementation for non-uniform or adaptive meshes. We present a quantitative assessment of the static local mesh refinement capabilities of a recently proposed IMEX-DG method [1] to a number of benchmarks for atmospheric flows over both idealized and real orography. We show that simulations with adaptive meshes around orography can increase the accuracy of the local flow description without affecting the larger scales, thereby significantly reducing the overall number of degrees of freedom compared to uniform mesh simulations [2, 3]. Importantly, no spurious reflections arise at internal boundaries separating mesh regions with different resolution and correct values for the momentum flux are retrieved. Both on idealised benchmarks and on test cases over real orographic profiles, simulations using non-conforming meshes correctly reproduce the larger scale, far-field response with meshes that are relatively coarse over most of the domain. This supports the idea that locally refined meshes can be an effective tool to reduce the dependence of NWP on parametrizations of orographic effects.

[1] G. Orlando, T. Benacchio, and L. Bonaventura. “An IMEX-DG solver for atmospheric dynamics simulations with adaptive mesh refinement”. Journal of Computational and Applied Mathematics 427 (2023), p. 115124.

[2] G. Orlando, T. Benacchio, and L. Bonaventura. "Robust and accurate simulations of flows over orography using non-conforming meshes". 2024. arXiv:2402.07759.

[3] G. Orlando, T. Benacchio, and L. Bonaventura. "Impact of curved elements for flows over orography with a Discontinuous Galerkin scheme". 2024. arXiv: 2404.09319.