三维切割单元建模用于高分辨率大气模拟
3D cut-cell modelling for high-resolution atmospheric simulations
AI总结：
本文提出一种三维笛卡尔坐标非静力大气模型，结合切割单元地形表示与单元合并方法，实现高分辨率地形模拟，验证了模型在陡峭地形上流体模拟的准确性与可扩展性。
摘要：
由于计算机技术的快速发展，大气数值模型的分辨率已显著提高。利用下一代超计算机，使用水平网格间隔为O(100) m或更小的大气模拟将变得流行。在高分辨率下，山脉地形中的陡峭梯度将被更好地解析，这可能导致使用地形跟随坐标的模型出现较大的截断误差。本文开发了一种新的三维笛卡尔坐标非静力大气模型。基于有限体积离散化的地形切割单元表示与单元合并方法相结合，在垂直或水平方向上将小切割单元与相邻单元合并。此外，引入了块结构网格细化技术，以在模型网格上实现可变分辨率，最细的分辨率发生在地形表面附近。该模型成功重现了流经三维钟形山的流动，与线性理论预测的流动具有良好的一致性。通过使用半球形山，展示了模型在陡峭地形上模拟流动的能力，其中最大坡度角被解析至71度。此外，使用半球形山展示了在三维山周围局部细化网格、在地形表面具有切割单元的优势。该模型在不同网格分辨率下重现了平滑的山脉波，而不会引入与网格分辨率变化相关的较大误差。同时，该模型在使用OpenMP时在局部细化网格上表现出良好的可扩展性。
英文摘要：
Owing to the recent, rapid development of computer technology, the resolution of atmospheric numerical models has increased substantially. With the use of next-generation supercomputers, atmospheric simulations using horizontal grid intervals of O(100) m or less will gain popularity. At such high resolution more of the steep gradients in mountainous terrain will be resolved, which may result in large truncation errors in those models using terrain-following coordinates. In this study, a new 3D Cartesian coordinate non-hydrostatic atmospheric model is developed. A cut-cell representation of topography based on finite-volume discretization is combined with a cell-merging approach, in which small cut-cells are merged with neighboring cells either vertically or horizontally. In addition, a block-structured mesh-refinement technique is introduced to achieve a variable resolution on the model grid with the finest resolution occurring close to the terrain surface. The model successfully reproduces a flow over a 3D bell-shaped hill that shows a good agreement with the flow predicted by the linear theory. The ability of the model to simulate flows over steep terrain is demonstrated using a hemisphere-shaped hill where the maximum slope angle is resolved at 71 degrees. The advantage of a locally refined grid around a 3D hill, with cut-cells at the terrain surface, is also demonstrated using the hemisphere-shaped hill. The model reproduces smooth mountain waves propagating over varying grid resolution without introducing large errors associated with the change of mesh resolution. At the same time, the model shows a good scalability on a locally refined grid with the use of OpenMP.
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