This PhD project is about the development of structure preserving (e.g. mass and total energy) finite element discretizations of flow models in Geophy

该博士项目是关于地球物理学中流动模型的结构保持（例如质量和总能量）有限元离散化的发展

• 批准号: 2753929
• 金额: --
• 依托单位: University of Surrey
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2022
• 资助国家: 英国
• 起止时间: 2022 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2753929
• 关键词: PhD; project; about; development; structure

. It intends to develop in a systematic manner by combining compatible finiteelement (exterior calculus) with variational methods and by developing new basis functions that are constructed via the method of subdivision adaptive structure preserving schemes. As such, the topic is of high interest particularly in the GFD community, because there is a constant need of improving both accuracy and efficiency of fluid solvers. Here, mesh adaptivity plays a crucial role as it permits to more accurately resolve local features of interest while keeping the resolution course elsewhere, keeping the computational cost affordable. While mesh adaptivity has been successfully implemented in various flavours, there is still a lack of adaptivity methods that preserve important structures of the underlying dynamicalsystem. This is important to improve the reliability and accuracy of the numerical simulations that are the essence of weather and climate predictions.

。它打算通过将兼容的有限元（外微积分）与变分方法相结合，并开发通过细分自适应结构保持方案的方法构造的新基函数，以系统的方式进行开发。因此，该主题在 GFD 社区中尤其受到高度关注，因为不断需要提高流体求解器的准确性和效率。在这里，网格自适应性起着至关重要的作用，因为它允许更准确地解析感兴趣的局部特征，同时在其他地方保持解析过程，从而保持计算成本可承受。虽然网格自适应性已在各种风格中成功实现，但仍然缺乏保留底层动力系统重要结构的自适应方法。这对于提高数值模拟的可靠性和准确性非常重要，而数值模拟是天气和气候预测的本质。