Numerical methods for incompressible multiphase flows applied to magnetohydrodynamics

电动汽车等对地球友好的技术的发展导致了更大的电力消耗。为了解决这一问题，风能、太阳能和潮汐等可再生能源的开发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，因为电网需要用有限或饱和的储能能力来平衡供需。因此，绿色能源的发展与高效大规模储能设备的开发息息相关。在这种背景下，该项目旨在开发高效的数值工具，以帮助设计有效和坚固的液态金属电池，这是一种被认为是电网规模储能设备的有前途的电池类型。这些数值方法将模拟这类电池中出现的各种现象(如多相流、热-溶液对流、磁流体动力学)的行为。因此，该项目通过提高我们对液态金属中各种不稳定性的理解，在地球物理和冶金工业中也有应用。这个项目将为研究生提供研究培训机会，向他们介绍最先进的数值方法在跨学科环境中的发展、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应用于储能工业和地球物理中的磁流体装置的多物理问题的数值方法。发展高阶数值方法来逼近包含时空相关系数的流体力学中的非线性偏微分方程解。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。该项目的目标围绕四个研究方向进行：(1)分析和开发新的数值方法来近似不可压缩多相流，其中流体的密度和粘度在空间和时间上变化；(2)液态金属电池中出现的多物理机制的模拟，这是一种很有前途的网格尺度储能设备。这包括开发热力学和成分(溶解)对流问题的多相算法；(3)将上述技术集成到大规模并行程序SFEMaNS中，并将其应用于液态金属电池和涉及磁流体效应的地球物理装置；(4)将SFEMaNS代码过渡到当前的高性能计算标准(多线程、高速缓存处理、SIMD矢量化等)，并分发给磁流体科学界。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.