Collaborative Research: Design and Analysis of Data-Enabled High-Order Accurate Multiscale Schemes and Parallel Simulation Toolkit for Studying Electromagnetohydrodynamic Flow

合作研究：用于研究电磁流体动力流的数据支持的高阶精确多尺度方案和并行仿真工具包的设计和分析

• 批准号: 1821242
• 负责人: Zhiliang Xu
• 金额: $ 10万
• 依托单位: University of Notre Dame
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2018
• 资助国家: 美国
• 起止时间: 2018-09-01 至 2020-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1821242&HistoricalAwards=false
• 关键词: Collaborative; Research; Design; Analysis; Data

Various magnetohydrodynamics (MHD) approximations have served scientists and engineers well for studying problems in astrophysics, space physics and engineering such as tokamaks, plasma propulsion, and plasma instability in engineering devices. Even so, the limitations in this approximation have now become evident. Especially when dealing with dilute plasmas, charge separation cannot be accommodated in MHD. To match the full range of observational data and experiments, it is imperative to provide the plasma physics community with a capability that goes beyond the MHD approximation. The work aims at developing high-order accurate, efficient and easy-to-use numerical methods for simulation-driven discoveries related to multiscale electromagnetohydrodynamic problems on complex geometry. Indeed, the methods developed will actually offer high-order accuracy and extremely robust performance for any conservation law beyond electromagnetics or elasticity applications. Therefore, several other fields of great importance in science and engineering, and indeed of great importance to the NSF mission, will be directly benefited by the methods developed here. Training a new generation of computational scientists capable of conducting interdisciplinary research is one of the central activities of the work. Courses relevant to the research such as numerical partial differential equations, advanced scientific computing, uncertainty quantification and machine learning have been introduced by the investigators and will be renovated by incorporating outcomes from the project into course materials. The specific objectives of this project are to develop, analyze and evaluate data-enabled high-order accurate and robust computational modeling tools for simulating multiscale high energy density plasma flows containing both continuum and rarefied regimes in complex geometry. Both new high-order divergence-constraint-preserving central discontinuous Galerkin (DG) scheme on overlapping unstructured grid cells for simulating continuum plasma coupled with Maxwell's equations, and asymptotic preserving central DG scheme for solving Vlasov-Maxwell-Boltzmann (VMB) equations to model the dilute plasma flow will be developed. An innovative data-enabled stochastic concurrent coupling algorithm combining these schemes will be also devised for multiscale simulations. In this coupling algorithm, a novel data-enabled stochastic heterogeneous domain decomposition method to exchange statistical distribution at the interface of continuum and rarefied regimes will be developed. This will be the first attempt to stochastically couple continuum and kinetic plasma flow models. There is no current capability that integrates these unique advances, and the investigators will be the first group to deliver such a forward-looking capability to the plasma physics community. All numerical simulations will be validated by advanced data-enabled uncertainty quantification method developed in this project. A large-scale parallel code with these capabilities will be developed and released to the plasma physics community. It will not only enable the plasma physics community to carry out transformational simulations for new discoveries related to the multiscale electromagnetohydrodynamic physics for the first time but also lower the threshold for new computational scientists to use the new cutting-edge numerical methods for other applications such as nonlinear optics. Simulations will be used to explain new observations such as enhanced electron transport, which are difficult to study experimentally in a harsh plasma environment.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.

各种磁流体动力学（MHD）近似已经很好地服务于科学家和工程师研究天体物理、空间物理和工程中的问题，例如托卡马克、等离子体推进和工程装置中的等离子体不稳定性。即便如此，这种近似的局限性现在已经变得显而易见。特别是当处理稀等离子体时，电荷分离不能被容纳在MHD中。为了匹配全方位的观测数据和实验，必须为等离子体物理界提供超越MHD近似的能力。这项工作的目的是开发高阶精确，高效和易于使用的数值方法，模拟驱动的发现相关的多尺度电磁流体动力学问题的复杂几何形状。事实上，开发的方法实际上将提供高阶精度和非常强大的性能，任何守恒定律超越电磁学或弹性应用。因此，其他几个在科学和工程中非常重要的领域，实际上对NSF使命非常重要，将直接受益于这里开发的方法。培养能够进行跨学科研究的新一代计算科学家是这项工作的核心活动之一。调查人员已经开设了与研究有关的课程，如数值偏微分方程、高级科学计算、不确定性量化和机器学习，并将通过将项目成果纳入课程材料来进行更新。 该项目的具体目标是开发，分析和评估数据支持的高阶精确和强大的计算建模工具，用于模拟复杂几何形状中包含连续和稀薄区域的多尺度高能量密度等离子体流。本文将发展一种新的用于模拟连续等离子体与麦克斯韦方程耦合的高阶保发散约束中心间断Galerkin（DG）格式和用于模拟稀等离子体流动的Vlasov-麦克斯韦-玻尔兹曼（VMB）方程的渐近保中心DG格式。一个创新的数据使能的随机并发耦合算法结合这些计划也将被设计用于多尺度模拟。在这种耦合算法中，一种新的数据使能的随机非均匀区域分解方法交换统计分布在连续和稀薄制度的接口将被开发。这将是第一次尝试随机耦合连续介质和动力学等离子体流模型。目前还没有能力整合这些独特的进步，研究人员将是第一个向等离子体物理界提供这种前瞻性能力的小组。所有数值模拟将通过本项目开发的先进数据支持的不确定性量化方法进行验证。具有这些功能的大规模并行代码将被开发并发布给等离子体物理社区。它不仅将使等离子体物理学界能够首次对多尺度电磁流体力学物理学的新发现进行变革性模拟，而且还将降低新的计算科学家将新的前沿数值方法用于其他应用（如非线性光学）的门槛。模拟将用于解释新的观察结果，例如增强的电子传输，这些观察结果很难在恶劣的等离子体环境中进行实验研究。该奖项反映了NSF的法定使命，并且通过使用基金会的知识价值和更广泛的评估被认为值得支持影响审查标准。

项目成果

An efficient class of WENO schemes with adaptive order for unstructured meshes

• DOI: 10.1016/j.jcp.2019.109062
• 发表时间: 2020-03
• 期刊: J. Comput. Phys.
• 作者: D. Balsara;S. Garain;V. Florinski;W. Boscheri