This is my webpage for the AMSC 663/664 Advanced Scientific Computing Course. Here is the abstract for my project:
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The model of the Earth's magnetic field has been investigated in recent years through experiments and numerical models. At the University of Maryland, experimental studies are implemented in a three-meter spherical Couette device filled with liquid sodium driven by two independently rotating concentric shells, an applied approximately dipole magnetic field, and dynamo action. These experiments incorporate high velocity flows with Reynolds numbers ~10^9 similar to those achievable by convection-driven flows in celestial bodies like the Earth. Collaborators at ISTerre have created the numerical code XSHELLS which features finite difference methods in the radial direction and pseudospectral spherical harmonic transforms for the angular directions. Highly turbulent flows are unfeasible to resolve limiting the abilities of purely numerical models. Experiments can produce highly turbulent flows but measurement can be intrusive. Our goal is to synchronize the numerical code with the experimental magnetic boundary data to get an idea of the unknown velocity field. In this project, we propose a validation study using Local Ensemble Transform Kalman Filtering (LETKF) on the numerical model and synthetic observation data to study the behavior. This would allow us to pre- pare for scaling to the experimental data which introduces additional constraints such as asynchronous observations and model error.