Approximation techiques for MHD flows in highly heterogeneous domains

本研究计划的目标是发展求解三维域中磁流体力学流动的求解方法，该三维域包括导电和非导电区域以及可变/不连续磁导率。 所发展的方法将是强大的，足以处理高雷诺数和高普朗特数。本文将采用拉格朗日元，并发展新的数学公式，使拉格朗日元在非光滑区域和非光滑界面上收敛。将要开发的代码将是完全并行的。目标应用程序是地球发电机，海水/油分离和液态金属流动。要开发的解决方案策略将是足够灵活的，以便易于修改，以模拟托卡马克几何结构中的等离子体流动，从而为正在进行的全球国际等离子体磁约束努力做出贡献。研究计划的重点是提出和分析新的数值策略，模拟高速非均匀介质中与电磁场相互作用的三维流体流动。一个有趣的现象是所谓的流体动力效应。 发电机现象出现在天体物理学中。它负责在具有液体核心的恒星和行星周围观察到的磁场。这种现象也出现在旨在再现发电机效应的实验装置中。这种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，或者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排热过程产生不利影响。这一研究也将为托卡马克等离子体流动的进一步发展奠定基础。这项研究项目将涉及大规模并行计算，并将导致新的数值策略来模拟高速流动与磁场的相互作用。

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.