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

基本信息

项目摘要

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.
这项为期三个月的联合项目提案的主要目的是建立一个数值方案,不仅在准确性、稳定性和一致性方面产生数学上可靠的结果,而且在物理上也产生可靠的解决方案。关键思想是利用嘉当的移动标架方法([29,30,31,32]),最终目标是增强线性化二维磁流体动力学浅水微分方程的现有数值方案,作为迈向更复杂应用的第一步。与其他方法相比,不变的数值方案必须从一开始就构建,移动框架的方法创造了使现有的数值方案不变的可能性,继承了基础微分方程所需的相同对称性。后者的离散化模型将使用移动标架的方法来定义,最后,新的数值方案模型将在现有的开源数值代码中实现,并与标准离散化方案在稳定性和守恒性方面进行比较。

项目成果

期刊论文数量(1)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
A new class of discontinuous solar wind solutions
  • DOI:
    10.1093/mnras/staa1396
  • 发表时间:
    2020-05
  • 期刊:
  • 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
  • 通讯作者:
    B. Shergelashvili;V. Melnik;G. Dididze;H. Fichtner;G. Brenn;S. Poedts;H. Foysi;M. Khodachenko;T. V. Zaqarashvili
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Professor Dr.-Ing. Holger Foysi其他文献

Professor Dr.-Ing. Holger Foysi的其他文献

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{{ truncateString('Professor Dr.-Ing. Holger Foysi', 18)}}的其他基金

The nature of turbulence in compressible homentropic constant shear flows: its vortex and wave contents and self-sustenance.
可压缩垂直恒定剪切流中湍流的本质:其涡流和波内容以及自维持。
  • 批准号:
    438287556
  • 财政年份:
    2020
  • 资助金额:
    --
  • 项目类别:
    Research Grants
Identification of the Linear Sound Sources in Turbulent free Shear Flows:Non-modal Analysis and Direct Numerical Simulation Study
湍流自由剪切流中线性声源的识别:非模态分析和直接数值模拟研究
  • 批准号:
    261830592
  • 财政年份:
    2015
  • 资助金额:
    --
  • 项目类别:
    Research Grants
Unsteady optimal control of shear flows based on the discrete and continuous adjoint Navier-Stokes equations.
基于离散和连续伴随纳维-斯托克斯方程的剪切流非定常最优控制。
  • 批准号:
    235772517
  • 财政年份:
    2013
  • 资助金额:
    --
  • 项目类别:
    Research Grants
Kombinierte experimentelle und numerische Analyse der Fluid-Struktur Interaktion und Wandschubspannung in elastischen Gefäßen bei instationärer Durchströmung
非定常流动过程中弹性容器流固相互作用和壁面剪应力的实验与数值联合分析
  • 批准号:
    203317824
  • 财政年份:
    2011
  • 资助金额:
    --
  • 项目类别:
    Research Grants
Turbulente Mischung und Verbrennung in kompressiblen Scherschichten - Simulation und Beeinflussung
可压缩剪切层中的湍流混合和燃烧 - 模拟和操纵
  • 批准号:
    57812851
  • 财政年份:
    2008
  • 资助金额:
    --
  • 项目类别:
    Independent Junior Research Groups
ColtBig: Compressible and thermal lattice Boltzmann methods on interpolation-based grids
ColtBig:基于插值网格的可压缩和热晶格玻尔兹曼方法
  • 批准号:
    439383920
  • 财政年份:
  • 资助金额:
    --
  • 项目类别:
    Research Grants

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偏线性分位数样本截取和选择模型的估计与应用—基于非参数筛分法(Sieve Method)
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