Moving meshes for Global Atmospheric Modelling

这个项目是关于使用移动网格- r- adaptive -来提高大气流动模拟的预测能力，这在数值天气预报和气候建模领域中使用。当在计算机上模拟大气时，这是通过将球体划分成网格排列的单元来完成的。在对准确性的需求（需要更小的（因此更多的）单元）和计算效率（随着单元数量的增加而增加）之间存在冲突。一个合理的问题是：对于给定的精确度，我需要多大大小的单元格？答案可以在数学上给出，但这取决于大气模拟中实际发生的情况。在具有较小尺度特征的区域，如大气锋、气旋、射流、对流单体等，则需要更小的单体。因此，在全球范围内选择相同的细胞大小似乎是一种浪费，即使在没有这些特征的地区也是如此。一个有吸引力的想法是尝试拉伸、变形和移动网格，以便在小尺度特征的区域使用较小的单元，而在其他地方使用较大的单元。这意味着可以在准确性和计算效率之间做出更好的妥协，从而提高对相同资源的预测能力。这个想法已经在许多工程应用中得到了成功的应用，这个项目的目标是将这项技术应用到大气模拟中，在那里它可以被气象学家和气候科学家用来推动他们的科学发展。然而，有许多具有挑战性的方面。有效的网格运动算法以前还没有开发出用于全局大气模拟所需的球体几何。有一个问题是如何检测网格应该移动到哪里。此外，设计稳定和精确的模拟大气的数值算法也是非常具有挑战性的，这些算法必须适应在网格运动下保持稳定和精确。所有这些问题和议题都将在这个项目中得到解决。

This project is about using moving meshes - r-adaptivity - to improve the predictive power of atmospheric flow simulations, which are used in the fields of numerical weather prediction and climate modelling.When the atmosphere is simulated on a computer, this is done by dividing the sphere into cells which are arranged in a mesh. There is a conflict between the need for accuracy, which requires smaller (and hence more) cells, and computational efficiency, which increases with the number of cells. A reasonable question to ask is: for a given amount of accuracy, what size of cells do I need? The answer can be provided mathematically, but it depends on what is actually happening in the atmosphere simulation. Much smaller cells are required in the regions of smaller scale features such as atmospheric fronts, cyclones, jets, convective cells etc. It then seems like a waste to choose the same cell size all over the globe even in regions where these features are absent.An attractive idea is to try to stretch, deform and move the mesh around so that smaller cells are used in the regions of small scale features, and larger cells are used elsewhere. This would mean that a better compromise can be made between accuracy and computational efficiency, thus improving predictive power for the same resource. This idea has been used successfully in many engineering applications, and the goal of this project is to transmit this technology to atmosphere simulation, where it can be used by meteorologists and climate scientists to take their science forward.There are, however, a number of challenging aspects. Efficient mesh movement algorithms have not previously been developed for the sphere geometry which is needed for global atmosphere simulations. There is the question of how to detect where the mesh should be moved to. It is also the case that it is very challenging to design stable and accurate numerical algorithms for simulating the atmosphere, and these must be adapted to remain stable and accurate under mesh movement. All of these questions and issues will be addressed in this project.