Application of the "Method of Moving Frames" to the magnetohydrodynamic shallow water equations - Conservation Properties and Robustness

“移动框架法”在磁流体动力学浅水方程中的应用——守恒性和鲁棒性

• 批准号: 374462528
• 负责人: Professor Dr.-Ing. Holger Foysi
• 金额: --
• 依托单位: Institut für Weltraumforschung
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2017
• 资助国家: 德国
• 起止时间: 2016-12-31 至 2020-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/374462528?language=en
• 关键词: Application; Method; Moving; Frames; magnetohydrodynamic

The main aim of the proposal for a three-month joint project is to construct a numerical scheme which not only produces mathematically reliable results regarding accuracy, stability and consistency, but also physically reliable solutions. The key idea is to make use of Cartan's method of moving frames ([29, 30, 31, 32]) with the final goal of enhancing existing numerical schemes for the linearized two-dimensional magnetohydrodynamic shallow water differential equations, as a first step towards more complex applications. In contrast to other methods where invariant numerical schemes have to be constructed from the outset, the method of moving frames creates the possibility to invariantize already existing numerical schemes, to inherit the same symmetries as required by the underlying differential equations. A discretization model for the latter will be de- veloped using the method of moving frames, and finally, the new model of numerical scheme will be implemented in an existing open-source numerical code and compared to a standard discretization schemes with respect to stability and conservation properties.

为期三个月的联合项目的提案的主要目的是构建一个数值方案，该方案不仅在准确性，稳定性和一致性上产生数学上可靠的结果，而且还产生了物理上可靠的解决方案。关键思想是利用卡坦的移动框架（[29、30、31、32]）的方法，其最终目标是增强线性化的二维磁性水力学浅水水分方程的现有数值方案，这是迈向更复杂应用的第一步。与必须从一开始构建不变的数值方案的其他方法相反，移动帧的方法创造了使已经存在的数值方案不变的可能性，以继承基础微分方程所要求的相同的对称性。后者的离散模型将使用移动框架的方法进行解析，最后，数值方案的新模型将在现有的开源数值代码中实现，并将其与稳定性和保护属性的标准离散方案进行了比较。

项目成果

A new class of discontinuous solar wind solutions

• DOI: 10.1093/mnras/staa1396
• 发表时间: 2020-05
• 期刊: Monthly Notices of the Royal Astronomical Society
• 影响因子: 4.8
• 作者: B. Shergelashvili;V. Melnik;G. Dididze;H. Fichtner;G. Brenn;S. Poedts;H. Foysi;M. Khodachenko;T. V. Zaqarashvili