Numerical methods for incompressible multiphase flows applied to magnetohydrodynamics

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The development of Earth-friendly technologies such as electric cars leads to greater consumption of electric power. To address this, the development of renewable energies, such as wind, solar and tidal waves, is a key societal challenge. These sources of energies are highly intermittent by nature and bring more stress to an electric grid that needs to balance demand and supply with a limited or saturated energy storage capacity. Thus, the development of green energy is tied to the development of efficient large scale energy storage devices. In this context, this project aims to develop efficient numerical tools that will help to design effective and robust liquid metal batteries, a promising type of battery that is considered for grid-scale energy storage devices. These numerical methods will model the action of various phenomena that arise in such batteries (e.g. multiphase flows, thermal-solutal convection, magnetohydrodynamics). Thus, this project also has applications in geophysics and metallurgy industry by improving our understanding of various instabilities that arises in liquid metals. This project will provide research training opportunities for graduate students to introduce them to the development, analysis and application of state of the art numerical methods in an interdisciplinary environment. In this project, the PI will use theoretical and computational mathematics to develop and analyze numerical methods for solving multiphysics problems applied to magnetohydrodynamics setups in energy storage industry and geophysics. High-order numerical methods will be developed to approximate the solutions of nonlinear Partial Differential Equations in fluid dynamics that involve space-time dependent coefficients. These methods will use sequential semi-implicit algorithms and will be made suitable for spectral and high-order finite element methods. The objectives of this project are organized around four research directions: (1) Analysis and development of new numerical methods to approximate incompressible multiphase flows where the density and viscosity of fluids vary in space and time; (2) Modeling of multiphysics mechanisms that arise in a liquid metal battery, a promising grid-scale energy storage device. This includes the development of multiphase algorithms for thermodynamics and compositional (solutal) convection problems; (3) Integration of the above techniques in the massively parallel code SFEMaNS and their applications to liquid metal batteries and geophysics setups that involve magnetohydrodynamics effects; (4) Transition of the code SFEMaNS to current high performance computing standards (multithreading, cache handling, SIMD vectorisation, etc), and distribution to the magneto-hydrodynamic scientific community.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.