Collaborative Research: Advanced Numerical Techniques for the Simulation of Magnetohydrodynamics

合作研究：磁流体动力学模拟的先进数值技术

• 批准号: 1216972
• 负责人: James Adler
• 金额: $ 29.9万
• 依托单位: Tufts University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-09-01 至 2016-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1216972&HistoricalAwards=false
• 关键词: Collaborative; Research; Advanced; Numerical; Techniques

The overall objective of this research is to develop numerical models and efficient energy-consistent methods for simulation of complex fluid systems and to obtain physically-accurate solutions for magnetohydrodynamic (MHD) systems, in particular. This work focuses on minimizing the computational cost of approximating solutions to these systems in order to develop practical simulations for this type of problem. The bottom line is to further develop discretization and solution algorithms that yield the most accuracy per computational cost. This is achieved by deriving discrete energy laws for MHD systems and proving that they are consistent with the continuous mathematical model. The investigators accomplish this by using the Energetic-Variational Approach (EVA) to further investigate the MHD model itself and determining which "flavor" of the MHD equations is the simplest model that captures the relevant physics. One of the main issues with using finite-element methods for solving complex fluid and electromagnetic problems has been the precise preservation of divergence-free solutions. Here, the investigators analyze discretization methods that satisfy these quantities accurately, while remaining amenable to efficient solution. Finally, the main bottleneck in the discretization methods used so far is the slow convergence of the linear solvers. By further developing multigrid methods for systems of partial differential equations, the investigators create a robust and efficient algorithm for these complex systems.The development of an efficient simulation framework for MHD systems has a major impact on the study of fusion energy, as this model is used to describe various phenomena that occur in fusion reactors, including tearing mode and sawtooth instabilities. With projects such as the International Thermonuclear Experimental Reactor (ITER) in France and the National Ignition Facility (NIF) at Lawrence Livermore National Lab attempting to obtain sustainable fusion energy, scientific computing in fields related to these projects is critical. In addition, the numerical tools being developed, such as energy-preserving finite-element discretizations and optimal multigrid solvers for systems of PDEs, are applicable to a wide variety of other problems in multi-physics and multi-scale systems. Finally, the project supports a graduate student, training and exposing them to the latest scientific findings and tools related to modeling, discretization, and solution of problems in the computational modeling of plasma physics and complex fluids.

这项研究的总体目标是开发用于模拟复杂流体系统的数值模型和高效的能量一致性方法，特别是获得磁流体系统的物理精确解。这项工作集中在最小化这些系统的近似解的计算成本，以便为这类问题开发实际的模拟。底线是进一步开发离散化和求解算法，以产生每计算成本最高的精度。这是通过推导MHD系统的离散能量定律并证明它们与连续数学模型一致来实现的。研究人员通过使用能量变分方法(EVA)来进一步研究MHD模型本身，并确定MHD方程的哪种“味道”是捕捉相关物理的最简单模型，从而实现了这一点。使用有限元方法求解复杂的流体和电磁问题的主要问题之一是精确地保持无散度解。在这里，研究人员分析了准确满足这些量的离散化方法，同时仍然服从于有效的解。最后，迄今使用的离散化方法的主要瓶颈是线性求解器收敛缓慢。通过进一步发展偏微分方程组的多重网格方法，研究人员为这些复杂系统创建了一种稳健而高效的算法。MHD系统高效仿真框架的开发对聚变能的研究具有重要影响，因为该模型用于描述聚变堆中发生的各种现象，包括撕裂模式和锯齿不稳定性。随着法国的国际热核实验反应堆(ITER)和劳伦斯利弗莫尔国家实验室的国家点火设施(NIF)等项目试图获得可持续的聚变能源，与这些项目相关领域的科学计算至关重要。此外，正在开发的数值工具，如能量守恒有限元离散和偏微分方程组的最优多重网格求解器，也适用于多物理和多尺度系统中的各种其他问题。最后，该项目支持一名研究生，培训他们并使他们接触到与等离子体物理和复杂流体计算建模中的建模、离散化和问题解决相关的最新科学发现和工具。