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.

这项研究的总体目的是开发用于模拟复杂流体系统的数值模型和有效的能量持续的方法，并特别是获得磁性水力学（MHD）系统的物理精确溶液。这项工作着重于最大程度地减少对这些系统近似解决方案的计算成本，以便为这种类型的问题开发实际模拟。最重要的是要进一步开发离散化和解决方案算法，从而获得每个计算成本的准确性最高。这是通过为MHD系统得出离散的能源定律来实现的，并证明它们与连续数学模型一致。研究人员通过使用能量变化方法（EVA）进一步研究MHD模型本身并确定MHD方程的哪种“风味”是捕获相关物理学的最简单模型，从而实现了这一目标。使用有限元方法解决复杂流体和电磁问题的主要问题之一是无差之处的溶液的精确保存。在这里，研究人员分析了准确满足这些数量的离散化方法，同时仍然可以对有效的解决方案。 最后，到目前为止使用的离散方法中的主要瓶颈是线性求解器的缓慢收敛性。通过进一步开发针对部分微分方程系统的多机方法，研究人员为这些复杂系统创建了一种强大而有效的算法。MHD系统有效的模拟框架的开发对融合能源的研究产生了重大影响，因为此模型是该模型用于描述在融合反应堆中发生的各种现象，包括撕裂模式和锯齿不稳定性。随着诸如法国国际热核实验反应堆（ITER）和劳伦斯·利弗莫尔国家实验室（Lawrence Livermore National Lab）的国家点火设施（NIF），试图获得可持续的融合能量，与这些项目相关的领域中的科学计算是至关重要的。此外，开发的数值工具，例如能源保存有限元离散和PDES系统的最佳多机求解器，适用于多物理和多规模系统中的许多其他问题。 最后，该项目支持一名研究生，将其培训并暴露于与等离子体物理和复杂流体的计算建模中问题相关的最新科学发现和工具。