Numerical methods for incompressible multiphase flows applied to magnetohydrodynamics

电动汽车等环保技术的发展导致了更大的电力消耗。为了解决这个问题，开发可再生能源，如风能、太阳能和潮汐能，是一项关键的社会挑战。这些能源本质上是高度间歇性的，给电网带来了更大的压力，电网需要在有限或饱和的储能能力下平衡供需。因此，绿色能源的发展与高效的大规模储能装置的发展息息相关。在这种情况下，该项目旨在开发有效的数值工具，以帮助设计有效且坚固的液态金属电池，这是一种有前途的电池类型，被认为是用于电网规模的储能设备。这些数值方法将模拟这种电池中出现的各种现象的作用（例如多相流、热溶质对流、磁流体动力学）。因此，通过提高我们对液态金属中出现的各种不稳定性的理解，该项目也可以应用于地球物理和冶金工业。本项目将为研究生提供研究训练机会，使他们在跨学科的环境中了解最新数值方法的发展、分析和应用。在这个项目中，PI将使用理论和计算数学来开发和分析用于解决多物理场问题的数值方法，这些问题适用于储能行业和地球物理学中的磁流体动力学设置。将发展高阶数值方法来近似求解流体动力学中涉及时空相关系数的非线性偏微分方程。这些方法将使用顺序半隐式算法，并将适用于谱和高阶有限元方法。本项目主要围绕以下四个研究方向展开：(1)分析和发展新的数值方法来近似流体密度和粘度随时间和空间变化的不可压缩多相流；(2)建立了液态金属电池的多物理场机制，这是一种很有前途的电网规模储能装置。这包括热力学和组成（溶质）对流问题的多相算法的发展；(3)将上述技术集成到大规模并行代码SFEMaNS中，并应用于涉及磁流体力学效应的液态金属电池和地球物理装置；(4)将代码SFEMaNS转换为当前高性能计算标准（多线程、缓存处理、SIMD矢量化等），并分发给磁流体力学科学界。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.