Development and Application of Efficient High-order Semi-Lagrangian Schemes

高效高阶半拉格朗日格式的开发与应用

• 批准号: 1830838
• 负责人: Wei Guo
• 金额: $ 5.56万
• 依托单位: Texas Tech University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2017
• 资助国家: 美国
• 起止时间: 2017-08-16 至 2020-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1830838&HistoricalAwards=false
• 关键词: Development; Application; Efficient; order; Semi

Understanding behaviors of plasmas plays an increasingly important role in modern science and engineering such as thermo-nuclear fusion, satellite amplifier, and computer chip manufacturing. A fundamental model in plasma physics is the Vlasov-Maxwell system, which is a nonlinear kinetic transport model describing the dynamics of charged particles due to the self-consistent electromagnetic forces. As predictive simulation tools in studying the complex kinetic system, efficient, reliable and accurate transport schemes are of fundamental significance. The main numerical challenges in such studies lie in the high dimensionality, nonlinear coupling, and inherent multi-scale nature in both space and time. Another application concerned in this project is in atmospheric science. One example is the chemistry-climate model in the study of evolution of stratospheric ozone and many other chemical constituents. The present generation of global climate models include hundreds of tracer species in order to adequately represent complex physical and chemical processes, resulting in huge computational cost in computer simulations. The PI will develop and analyze a class of efficient, reliable and highly accurate numerical methods for transport problems in plasma physics and atmospheric science. A semi-Lagrangian framework will be devised by employing a high order discontinuous Galerkin spatial discretization to take advantage of its many attractive properties, such as flexibility, compactness, and excellent ability to resolve features involving multiple scales. By a careful design in the scheme formulation, the proposed scheme is free of splitting error and able to conserve total mass of the system. Motivated by the work of PI on developing a fast asymptotic preserving Maxwell solver that is capable of recovering the magneto-static limit, the temporal scale separation issue associated with the Vlasov-Maxwell simulations will be addressed. For the applications in the global chemistry-climate modeling, the new schemes can be conveniently adapted to the spherical transport simulations based on the cubed-sphere geometry. Theoretical issues including the stability analysis and error estimates will be investigated.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.

了解等离子体的行为在热核聚变、卫星放大器和计算机芯片制造等现代科学和工程中发挥着越来越重要的作用。等离子体物理学的基本模型是弗拉索夫-麦克斯韦系统，它是一种非线性动力学输运模型，描述由于自洽电磁力而导致的带电粒子的动力学。作为研究复杂动力学系统的预测模拟工具，高效、可靠、准确的输运方案具有根本意义。此类研究的主要数值挑战在于高维性、非线性耦合以及空间和时间上固有的多尺度性质。该项目涉及的另一个应用是大气科学。一个例子是平流层臭氧和许多其他化学成分演化研究中的化学气候模型。目前的全球气候模型包括数百种示踪剂物种，以便充分表示复杂的物理和化学过程，导致计算机模拟中的计算成本巨大。 PI 将针对等离子体物理和大气科学中的输运问题开发和分析一类高效、可靠和高精度的数值方法。半拉格朗日框架将通过采用高阶不连续伽辽金空间离散化来设计，以利用其许多有吸引力的特性，例如灵活性、紧凑性以及解决涉及多个尺度的特征的出色能力。通过方案制定中的仔细设计，所提出的方案没有分裂误差，并且能够保存系统的总质量。受 PI 开发能够恢复静磁极限的快速渐近保持麦克斯韦求解器工作的推动，与 Vlasov-Maxwell 模拟相关的时间尺度分离问题将得到解决。对于全球化学-气候建模中的应用，新方案可以方便地适应基于立方球几何的球形输运模拟。将调查包括稳定性分析和误差估计在内的理论问题。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。