Large Eddy Simulations in Magnetohydrodynamics Flows

磁流体动力学流动中的大涡模拟

• 批准号: 1522574
• 负责人: Catalin Trenchea
• 金额: $ 18.3万
• 依托单位: University of Pittsburgh
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-08-01 至 2018-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1522574&HistoricalAwards=false
• 关键词: Large; Eddy; Simulations; Magnetohydrodynamics; Flows

Magnetohydrodynamics describes the behavior of an electrically conducting fluid flow in the presence of magnetic fields. Electrically conducting fluids arise in applications including astrophysics, geophysics, plasma confinement, controlled thermonuclear fusion, liquid-metal cooling of nuclear reactors, electromagnetic casting of metals, ion thrusters for low orbiting satellites, magnetohydrodynamic drive for ships and submarines, microfluidic devices, and molecular biology. The fluid motion of the Earth's core maintains the terrestrial magnetic field, the solar magnetic field generates sunspots and solar flares, and the galactic magnetic field influences the formation of stars from interstellar clouds. These applications require substantially better modeling and simulation capabilities than presently exist. Problems without a clear scale separation, such as turbulence, are still at the frontier of multiscale modeling and simulation. When the fluid is electrically conducting, the turbulent fluid motions are accompanied by magnetic fluctuations. For Magnetohydrodynamic (MHD) turbulence, numerical simulations play a greater role than they play for hydrodynamic turbulence, since laboratory experiments are practically impossible and astrophysical systems (solar-wind turbulence, the most important system of high-Reynolds-number MHD accessible to in situ measurements) are too complex to be comparable with theoretical results. This research project will develop improved computational methods for these important problems.This research project studies mathematically rigorous and computationally efficient methods to analyze direct and inverse problems constrained by MHD models. This includes the numerical analysis of computational algorithms, implicit explicit time-stepping schemes using the Elsasser variables, post processing via time-filters, spatial linear and nonlinear filters, spectral filtering, development of spatial filters specific to MHD turbulence, optimal control, and parameter estimation. Another objective of this project is to investigate the mathematical properties of several models for the simulation of the large eddies in turbulent viscous, incompressible, electrically conducting flows and new numerical models that permit long-time simulations, by time-splitting. The project has a broad impact for training undergraduate and graduate students in analytical and numerical aspects of magnetohydrodynamics, turbulence, and inverse problems.

磁流体动力学描述了在磁场存在下导电流体流动的行为。导电流体出现在包括天体物理学、微物理学、等离子体约束、受控热核聚变、核反应堆的液态金属冷却、金属的电磁铸造、用于低轨道卫星的离子推进器、用于船舶和潜艇的磁流体动力学驱动、微流体装置和分子生物学的应用中。地球核心的流体运动维持地球磁场，太阳磁场产生太阳黑子和太阳耀斑，银河磁场影响星际云中恒星的形成。这些应用程序需要比目前更好的建模和仿真能力。没有明确的尺度分离的问题，如湍流，仍然处于多尺度建模和模拟的前沿。当流体导电时，湍流流体运动伴随着磁波动。对于磁流体动力学（MHD）湍流，数值模拟发挥了更大的作用，比他们发挥流体动力学湍流，因为实验室实验几乎是不可能的，天体物理系统（太阳风湍流，最重要的系统，高雷诺数MHD访问现场测量）太复杂，无法与理论结果进行比较。 本研究课题将针对这些重要问题开发更完善的计算方法，研究在MHD模型约束下的正问题和逆问题的数学分析方法。这包括计算算法的数值分析、使用Elsasser变量的隐式显式时间步进方案、通过时间滤波器的后处理、空间线性和非线性滤波器、光谱滤波、特定于MHD湍流的空间滤波器的开发、最优控制和参数估计。该项目的另一个目标是研究几种模型的数学特性，用于模拟湍流粘性、不可压缩、导电流中的大涡流，以及通过时间分裂进行长时间模拟的新数值模型。该项目对培养本科生和研究生在磁流体力学、湍流和逆问题的分析和数值方面具有广泛的影响。