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

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学、空间物理学和工程中的问题，如托卡马克、等离子体推进和工程设备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很明显。特别是当处理稀等离子体时，电荷分离在MHD中无法适应。为了匹配全范围的观测数据和实验，必须为等离子体物理界提供超越MHD近似值的能力。该工作旨在开发高阶精确、高效和易于使用的数值方法，用于复杂几何上的多尺度电磁流体动力学问题的模拟驱动发现。事实上，所开发的方法实际上将为电磁学或弹性应用之外的任何守恒定律提供高阶精度和极其强大的性能。因此，在科学和工程中非常重要的其他几个领域，实际上对国家科学基金会的使命非常重要，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。与研究相关的课程，如数值偏微分方程、先进科学计算、不确定性量化和机器学习等，已经由研究人员引入，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，用于模拟复杂几何结构中包含连续和稀薄状态的多尺度高能量密度等离子体流。本文提出了一种新的高阶发散约束保持中心不连续Galerkin （DG）格式，用于模拟耦合麦克斯韦方程组的连续等离子体，以及用于模拟稀等离子体流动的Vlasov-Maxwell-Boltzmann （VMB）方程的渐近保持中心DG格式。结合这些方案的创新数据支持随机并发耦合算法也将用于多尺度模拟。在这种耦合算法中，提出了一种新的数据支持的随机异构域分解方法，在连续和稀薄状态的界面上交换统计分布。这将是首次尝试随机耦合连续体和动力学等离子体流模型。目前还没有整合这些独特进步的能力，研究人员将是第一个向等离子体物理社区提供这种前瞻性能力的团队。所有数值模拟将通过本项目开发的先进的数据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。它不仅使等离子体物理界能够首次对与多尺度电磁流体动力物理相关的新发现进行转换模拟，而且还降低了新的计算科学家将新的尖端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，如电子传输增强，这在恶劣的等离子体环境中很难进行实验研究。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.