Space-time DG-FEMs for Fluid and Kinetic Plasma Models

用于流体和动力学等离子体模型的时空 DG-FEM

• 批准号: 1016202
• 负责人: James Rossmanith
• 金额: $ 13.94万
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-08-15 至 2013-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1016202&HistoricalAwards=false
• 关键词: Space; time; DG; FEMs; Fluid

The investigator, along with his students and collaborators, will develop efficient high-order time-stepping methods that will be used in conjunction with discontinuous Galerkin spatial discretizations. In particular, adaptive space-time methods will be developed that will allow for either (1) explicit local time-stepping that allows for different time-steps in different flow regimes, or, (2) implicit time-stepping, which is sometimes required in certain applications. A key feature that will be integrated into these numerical schemes is error control in the form of adaptive mesh refinement. Several error estimators will be investigated, as well as several shock-capturing strategies. The resulting numerical schemes will be applied to a variety of model equations that arise in plasma physics, including ideal magnetohydrodynamics, two-fluid Euler-Maxwell, and kinetic Vlasov equations. Specific application problems that are of interest include the dynamics of solar coronal loops, the formation and propagation of astrophysical jets, and the simulation of collisionless magnetic reconnection.Plasma is the fourth state of matter (after solid, liquid, and gas), which can be characterized as an ionized gas (i.e., a gas that is able to conduct electricity). Plasma appears in a wide range of applications including astrophysics and space physics, as well as in laboratory settings such as in magnetically confined fusion. Modeling and understanding the basic phenomenon in plasma have long been topics in scientific computing, yet many problems remain far too numerically intensive for modern parallel computers. The main difficulty is that plasmas span a wide range of spatial and temporal scales. The scope of this research is to develop accurate and efficient computational methods that can better solve various equations that model plasma behavior. A key aspect of this research is the development of adaptive numerical methods that are able to dynamically estimate and control the errors that are produced during the course of a computation.

调查员以及他的学生和合作者将开发有效的高阶时间稳定方法，这些方法将与不连续的Galerkin空间离散化一起使用。特别是，将开发自适应时空方法，这将允许（1）（1）允许在不同流程度中进行不同时间阶段的明确时间stepping，或（2）有时需要的隐式时间steppping在某些应用中。将集成到这些数值方案中的一个关键功能是以自适应网格细化的形式进行错误控制。将研究一些错误估计器，以及几种震撼策略。所得的数值方案将应用于等离子体物理学中出现的多种模型方程，包括理想的磁流失动力学，两流体的Euler-Maxwell和动力学Vlasov方程。感兴趣的特定应用问题包括太阳能冠状环的动力学，天体物理喷气机的形成和传播以及无碰撞磁重新连接的模拟。铂是物质的第四个状态（固体，液体和气体之后），可以以电离气体为特征（即能够导电的气体）。等离子体出现在包括天体物理学和空间物理学以及实验室环境（如磁性限制的融合中）的广泛应用中。长期以来，在等离子体中的基本现象的建模和理解一直是科学计算的主题，但是对于现代平行计算机而言，许多问题在数值上仍然太密集了。主要困难是等离子体跨越各种空间和时间尺度。这项研究的范围是开发准确有效的计算方法，以更好地求解对等离子体行为进行建模的各种方程式。这项研究的一个关键方面是能够动态估计和控制计算过程中产生的误差的自适应数值方法的发展。