Moving meshes for Global Atmospheric Modelling

这个项目是关于使用移动网格-r-自适应-来提高大气流动模拟的预测能力，用于数值天气预报和气候模拟领域。当在计算机上模拟大气时，这是通过将球体划分成排列成网格的单元来完成的。精度的需要与计算效率之间存在冲突，前者需要更小的单元(因此需要更多的单元)，后者随着单元的数量增加而增加。一个合理的问题是：对于给定的准确度，我需要多大的单元格？答案可以从数学上提供，但这取决于大气模拟中实际发生的情况。在小尺度特征的区域，如大气锋面、气旋、急流、对流单体等，需要小得多的单元格。因此，即使在没有这些特征的地区，在全球范围内选择相同的单元格大小似乎是一种浪费。一个吸引人的想法是尝试拉伸、变形和移动网格，以便在小尺度特征区域使用小单元格，而在其他地方使用大单元格。这将意味着可以在准确性和计算效率之间做出更好的折衷，从而提高对相同资源的预测能力。这一想法已经成功地应用于许多工程应用中，该项目的目标是将这项技术传输到大气模拟中，供气象学家和气候学家使用，以促进他们的科学发展。然而，也有一些具有挑战性的方面。对于全球大气模拟所需的球面几何形状，以前还没有开发出有效的网格移动算法。有一个问题是如何检测网格应该移动到哪里。同样，设计稳定和精确的数值算法来模拟大气也是非常具有挑战性的，而这些算法必须在网格移动的情况下保持稳定和准确。所有这些问题和问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.