Moving meshes for global atmospheric modelling

用于全球大气建模的移动网格

• 批准号: NE/M013634/1
• 负责人: Colin Cotter
• 金额: $ 12.77万
• 依托单位: Imperial College London
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2015
• 资助国家: 英国
• 起止时间: 2015 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=NE%2FM013634%2F1
• 关键词: Moving; meshes; global; atmospheric; modelling

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.

这个项目是关于使用移动网格--r-adaptivity--来提高大气流动模拟的预测能力。大气流动模拟用于数值天气预报和气候建模领域。当在计算机上模拟大气时，这是通过将球体分成网格排列的单元来完成的。在对精度的需求（需要更小（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：对于给定的精度，我需要多大的单元？答案可以用数学方法给出，但这取决于大气模拟中实际发生的情况。在较小尺度特征的区域中需要小得多的单元，例如大气锋、旋风、喷流、对流单体等。因此，即使在不存在这些特征的区域中，在整个地球仪上选择相同的单元尺寸似乎是浪费。一个有吸引力的想法是尝试拉伸、变形和移动网格，使得较小的单元用于小尺度特征的区域，而较大的单元用于其它地方。这意味着可以在准确性和计算效率之间做出更好的妥协，从而提高相同资源的预测能力。这个想法已经成功地应用于许多工程应用中，本项目的目标是将这项技术应用于大气模拟，供气象学家和气候科学家使用，以推动他们的科学发展。然而，还有一些具有挑战性的方面。高效的网格移动算法以前没有开发的球形几何形状，这是全球大气模拟所需要的。问题是如何检测网格应该移动到哪里。这也是一种情况，它是非常具有挑战性的设计稳定和准确的数值算法模拟大气，这些必须适应网格移动下保持稳定和准确。所有这些问题都将在本项目中得到解决。

项目成果

A new implementation of the geometric method for solving the Eady slice equations

求解Eady切片方程的几何方法的新实现

• DOI: 10.1016/j.jcp.2022.111542
• 发表时间: 2022
• 期刊: Journal of Computational Physics
• 影响因子: 4.1
• 作者: Egan C

Embedded discontinuous Galerkin transport schemes with localised limiters

具有局部限制器的嵌入式不连续伽辽金输运方案

• DOI: 10.1016/j.jcp.2016.02.021
• 发表时间: 2016
• 期刊: J. Comput. Phys.
• 作者: C.J. Cotter;D. Kuzmin
• 通讯作者: D. Kuzmin

Compatible Finite Element Methods for Geophysical Flows - Automation and Implementation Using Firedrake

地球物理流的兼容有限元方法 - 使用 Firedrake 进行自动化和实现

• DOI: 10.1007/978-3-030-23957-2
• 发表时间: 2019
• 作者: Gibson T

Mixed finite elements for global tide models.

• DOI: 10.1007/s00211-015-0748-z
• 发表时间: 2016
• 期刊: Numerische mathematik
• 影响因子: 2.1
• 作者: Cotter CJ;Kirby RC
• 通讯作者: Kirby RC

Energy-enstrophy conserving compatible finite element schemes for the rotating shallow water equations with slip boundary conditions

具有滑移边界条件的旋转浅水方程能量熵守恒兼容有限元格式

• DOI: 10.1016/j.jcp.2018.06.071
• 发表时间: 2018
• 期刊: Journal of Computational Physics
• 影响因子: 4.1
• 作者: Bauer W