In this paper, Fluidity-Atmosphere, representative of a three-dimensional (3D) non-hydrostatic Galerkin compressible atmospheric dynamic framework, is generated to resolve large-scale and small-scale phenomena simultaneously. This achievement is facilitated by the use of non-hydrostatic 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 non-hydrostatic 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.

在本文中，生成了代表三维 (3D) 非静压伽辽金可压缩大气动力学框架的流动性-大气层，以同时解决大尺度和小尺度现象。通过使用非流体静力方程和采用灵活的 3D 动态自适应网格促进了这一成就，其中网格在变量解梯度较高的区域更密集，在域的其余部分相对稀疏，同时保持有希望的准确性并减少计算资源需求。动态核心是基于水平和垂直方向的各向异性四面体网格制定的。通过模拟非静水山波的形成和传播来评估自适应网格技术在流动性-大气中的性能。二维各向异性自适应网格表明数值解与解析解吻合良好。水平和垂直分辨率的变化对结果的平滑度有很大影响，即使在高分辨率下也能保持收敛。当模拟扩展到 3D 时，Fluidity-Atmosphere 在基准测试用例中显示出稳定且对称的结果。钟形山上的水流得到了相当顺利的解决。对于陡峭的山脉，Fluidity-Atmosphere 表现得非常好，这显示了在大气建模中使用 3D 自适应网格的潜力。最后，作为 Fluidity-Atmosphere 中的替代切割单元网格，各向异性自适应网格与 Galerkin 方法相结合，提供了地形诱导流动的替代准确表示。