Advanced numerical methods for multiphysics Magnetohydrodynamics

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The objective of this project is to develop innovative numerical methods capable of solving energy-related problems in the context of renewable and alternative energies. The numerical techniques developed in this project will help design grid-scale liquid metal batteries capable of storing large quantities of renewable energies. This research will also help improve the performance of large power electric transformers cooled by environment-friendly vegetable-based oils containing ferromagnetic particles. Finally, by facilitating the understanding of magneto-hydrodynamic instabilities in liquid metals, this project will help to ascertain the integrity and the efficiency of the electromagnetic pumps that will be used to extract energy from the next generation of Liquid-Metal Fast-Breeder Reactors and Tokamaks. This project will be done in collaboration with an European team; the project will foster diversity, international exchanges, and multidisciplinarity. The educational component of the project will contribute to increase the competitiveness of the STEM workforce in the US in computational magnetohydrodynamics.The research program will be organized into four areas: (1) Development of new efficient semi-implicit algorithms to solve partial differential equations with variable material properties (density, electric conductivity, magnetic permeability) using spectral or very high-order methods; (2) Modeling of ferromagnetic fluids and development of new numerical techniques to solve the magneto-static equations in the context of liquid metals and ferromagnetic fluids; (3) Development of level set techniques to account for more than two phases, and development of new high-order level set techniques to guarantee mass conservation and maximum principle; (4) Integration of the mathematical models and numerical techniques developed in (1)-(2)-(3) into a massively parallel open source code to test the proposed methods on realistic applications (liquid metal batteries, thermo-convection of ferromagnetic oil in high-voltage transformers, liquid metal dynamos). This project will involve the Principal Investigator, one post-doctoral collaborator, one graduate student, and European collaborators.