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现代科学和工程中起着越来越重要的作用，例如热核融合，卫星放大器和计算机芯片制造。血浆物理学中的基本模型是Vlasov-Maxwell系统，该系统是一个非线性动力学传输模型，描述了由于自一致的电磁力而导致带电颗粒的动力学。作为研究复杂动力学系统时的预测模拟工具，有效，可靠和准确的运输方案具有基本意义。此类研究中的主要数值挑战在于高维，非线性耦合以及时空和时间上固有的多尺度性质。该项目中有关的另一个应用程序是大气科学。一个例子是在平流层臭氧和许多其他化学成分的进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物种，以充分代表复杂的物理和化学过程，从而在计算机模拟中产生了巨大的计算成本。 PI将开发和分析一类高效，可靠和高度准确的数值方法，用于血浆物理和大气科学中的运输问题。通过采用高阶不连续的Galerkin空间离散化来利用其许多有吸引力的属性，例如灵活性，紧凑性以及解决涉及多个尺度的特征的卓越能力，可以通过使用高阶盖尔金空间离散化来设计半拉格朗日框架。通过计划公式的仔细设计，所提出的方案没有分裂误差并能够保存系统的总质量。由PI开发能够恢复磁静态限制的麦克斯韦求解器的快速保护求解器的工作的动机，将解决与Vlasov-Maxwell模拟相关的时间尺度分离问题。对于全球化学气候建模中的应用，可以方便地根据基于立方体球形几何形状来方便地适应球形传输模拟。理论问题将进行包括稳定性分析和错误估计值在内的理论问题。该奖项反映了NSF的法定任务，并认为使用基金会的知识分子优点和更广泛的影响评估标准，被认为值得通过评估。