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.

磁水动力学描述了在存在磁场的情况下电动传导流体流动的行为。电力传导流体在包括天体物理学，地球物理学，血浆限制，受控的热核融合，核反应器的液态冷却，金属的电磁铸造，用于低轨道卫星的低旋转卫星的离子趋势，用于磁铁的磁力驱动器，用于磁铁和底层的磁液动力，微发射措施，微型富度驱动器和分子，并分析的分子，和分子，和分子，和分子，和分子，和分析生物学。地球核心的流体运动保持陆地磁场，太阳磁场会产生黑子和太阳耀斑，而银河磁场会影响星际云的恒星形成。这些应用需要比目前存在的更高的建模和仿真功能。没有明确分离的问题，例如湍流，仍处于多尺度建模和仿真的边界。当流体进行电导时，湍流运动会伴随着磁波动。对于磁水动力学（MHD）的湍流，数值模拟比它们在流体动力湍流中起着更大的作用，因为实验室实验实际上是不可能的，并且是天体物理系统（太阳能湍流）（太阳能湍流，这是最重要的高reynolds-number mhd MHD的系统，测量值太复杂，无法与理论结果相媲美。 该研究项目将针对这些重要问题开发改进的计算方法。本研究项目研究在数学上进行了严格和计算有效的方法，以分析受MHD模型约束的直接问题和反向问题。这包括对计算算法的数值分析，使用Elsasser变量的隐性明确时间稳定方案，通过时间过滤器进行后处理，空间线性和非线性过滤器，光谱过滤，开发特定于MHD湍流的空间过滤器，最佳控制以及最佳控制以及参数，以及参数估计。该项目的另一个目的是研究几种模型的数学特性，以模拟大型涡流中的大型涡流，不可压缩的，电气传导的流量和新的数值模型，这些模型允许长时间模拟，并通过时间间隔时间进行长时间模拟。该项目对磁性流动力学，湍流和反问题的分析和数值方面的培训本科生和研究生产生了广泛的影响。