Demonstration of a three-dimensional dynamically adaptive atmospheric dynamic framework for the simulation of mountain waves

Abstract

In this paper, Fluidity-Atmosphere, representative of a three-dimensional (3D) nonhydrostatic Galerkin compressible atmospheric dynamic framework, is generated to resolve large-scale and small-scale phenomena simultaneously. This achievement is facilitated by the use of nonhydrostatic equations and the adoption of a flexible 3D dynamically adaptive mesh where the mesh is denser in areas with higher gradients of variable solutions and relatively sparser in the rest of the domain while maintaining promising accuracy and reducing computational resource requirements. The dynamic core is formulated based on anisotropic tetrahedral meshes in both the horizontal and vertical directions. The performance of the adaptive mesh techniques in Fluidity-Atmosphere is evaluated by simulating the formation and propagation of a nonhydrostatic mountain wave. The 2D anisotropic adaptive mesh shows that the numerical solution is in good agreement with the analytic solution. The variation in the horizontal and vertical resolutions has a strong impact on the smoothness of the results and maintains convergence even at high resolutions. When the simulation is extended to 3D, Fluidity-Atmosphere shows stable and symmetric results in the benchmark test cases. The flows over a bell-shaped mountain are resolved quite smoothly. For steep mountains, Fluidity-Atmosphere performs very well, which shows the potential of using 3D adaptive meshes in atmospheric modeling. Finally, as an alternative cut-cell mesh in Fluidity-Atmosphere, the anisotropic adaptive mesh coupled with the Galerkin method provides an alternative accurate representation of terrain-induced flow.

A Non‐Column Based, Fully Unstructured Implementation of Kessler's Microphysics With Warm Rain Using Continuous and Discontinuous Spectral Elements

“…(2015) extending the latter to unstructured tetrahedral grids in 2015, as also recently done by Li et al. (2021). Large numerical errors when using structured grids to represent steep topography are a well known problem (see, e.g., Baldauf (2021) and Schar et al.…”

“…The first two atmospheric research models to adopt unstructured grids in the vertical direction were presented by Aubry et al (2010) and Smolarkiewicz et al (2013), with Szmelter et al (2015) extending the latter to unstructured tetrahedral grids in 2015, as also recently done by Li et al (2021). Large numerical errors when using structured grids to represent steep topography are a well known problem (see, e.g., Baldauf (2021) and Schar et al (2002)).…”

A non column based fully unstructured implementation of Kessler s microphysics with warm rain using continuous and discontinuous spectral elements

“…The first two atmospheric research models to adopt unstructured grids in the vertical direction were presented by [17] and [18], with [19] extending the latter to unstructured tetrahedral grids in 2015. At the time of writing this article, the latest in this series of efforts was published by [20]. All of them demonstrate that the use of unstructured grids combined with adaptive mesh refinement reduces the numerical errors for dry mountain waves problems with steep orography, even at high resolutions.…”