Approximation techiques for MHD flows in highly heterogeneous domains

本研究计划的目的是发展求解磁流体力学流动的三维域的解决方法，包括导电区和非导电区以及可变/不连续磁导率。待开发的方法将具有足够的鲁棒性，可以处理高雷诺数和高普朗特数。拉格朗日有限元将被使用，新的数学公式将被开发，使拉格朗日有限元收敛于非光滑域和非光滑界面。要开发的代码将是完全并行的。这些应用的目标是地球动力、海水/油分离和液态金属流动。待开发的解决策略将具有足够的灵活性，以便易于修改以模拟托卡马克几何形状的等离子体流动，从而为正在进行的等离子体磁约束的全球和国际努力做出贡献。本课题的研究重点是提出和分析模拟非均质介质中三维流体与电磁场高速相互作用的新数值策略。一个有趣的现象是所谓的流体发电机效应。发电机现象出现在天体物理学中。它负责在有液体内核的恒星和行星周围观察到的磁场。这种现象也出现在旨在重现发电机效应的实验装置中。这些流体可能是恒星和托卡马克中的等离子体，行星中的熔融铁，或实验装置中的液态镓或钠。发电机效应可能对快中子增殖反应堆的抽热过程产生意想不到的后果。这项研究也将为进一步发展托卡马克几何结构中的等离子体流奠定基础。该研究项目将涉及大规模并行计算，并将产生新的数值策略来模拟与磁场相互作用的高速流动。

The objective of this research program is to develop solution methods forsolving magneto-hydrodynamics flows in three-dimensional domains comprising conductingand nonconducting regions and variable/discontinuous magneticpermeability. The method to be developed will be robust enough tohandle High Reynolds flows and high Prandtl numbers. Lagrange finite elements will be used and novel mathematical formulations will be developedto make Lagrange finite elements to convergein non-smooth domains and with non-smooth interfaces. The code to be developed will be fully parallel.The applications targetedare the geodynamo, sea-water/oil separation and liquid metal flows.The solution strategy to be developed will beflexible enough so as to be easily modifiable to simulate plasma flowsin Tokamak geometries and thus to contribute to the ongoing globalinternational effort on magnetic confinement of plasmas.The focus of the research program is to propose and analyze newnumerical strategies for simulating three-dimensional fluid flowsinteracting with electromagnetic fields in heterogeneous media at highspeed. One phenomenon of interest is the so-called fluid dynamoeffect. The dynamo phenomenon arises in astrophysics. It isresponsible for the magnetic fields that are observed around stars andplanets with liquid cores. This phenomenon arises also in experimentalsetups aiming at reproducing the dynamo effect. The fluid may beplasma in stars and in tokamaks, molten iron in planets, or liquidgallium or sodium in experimental setups. The dynamo effect may haveundesired consequence on heat extraction processes from fast breederreactors. This research will also prepare the ground for furtherdevelopments on plasma flows in Tokamak geometries. This researchproject will involve large scale parallel computing and will lead to newnumerical strategies to simulate high speed flows interacting withmagnetic fields.