Approximation Techniques for MHD Flows In Highly Heterogeneous Domains
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The objective of this research program is to develop solution methods for solving magneto-hydrodynamics flows in three-dimensional domains comprising conducting and nonconducting regions and variable/discontinuous magnetic permeability. The method to be developed will be robust enough to handle High Reynolds flows and high Prandtl numbers. Lagrange finite elements will be used and novel mathematical formulations will be developed to make Lagrange finite elements to converge in non-smooth domains and with non-smooth interfaces. The code to be developed will be fully parallel. The applications targeted are the geodynamo, sea-water/oil separation and liquid metal flows. The solution strategy to be developed will be flexible enough so as to be easily modifiable to simulate plasma flows in Tokamak geometries and thus to contribute to the ongoing global international effort on magnetic confinement of plasmas. The focus of the research program is to propose and analyze new numerical strategies for simulating three-dimensional fluid flows interacting with electromagnetic fields in heterogeneous media at high speed. One phenomenon of interest is the so-called fluid dynamo effect. The dynamo phenomenon arises in astrophysics. It is responsible for the magnetic fields that are observed around stars and planets with liquid cores. This phenomenon arises also in experimental setups aiming at reproducing the dynamo effect. The fluid may be plasma in stars and in tokamaks, molten iron in planets, or liquid gallium or sodium in experimental setups. The dynamo effect may have undesired consequence on heat extraction processes from fast breeder reactors. This research will also prepare the ground for further developments on plasma flows in Tokamak geometries. This research project will involve large scale parallel computing and will lead to new numerical strategies to simulate high speed flows interacting with magnetic fields.