Finite Difference Equations for Transport Effects in Kinetic Theory

动力学理论中传递效应的有限差分方程

• 批准号: 9731956
• 负责人: Jack Schaeffer
• 金额: $ 7.36万
• 依托单位: Carnegie-Mellon University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-08-01 至 2002-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9731956&HistoricalAwards=false
• 关键词: Finite; Difference; Equations; Transport; Effects

9731956 Schaeffer This award supports research on systems of nonlinear partial differential equations which model plasma behavior. In particular a kinetic model of plasma in which the density of ions in phase space satisfies the Landau-Fokker-Planck equation is considered. A major focus is to develop finite difference schemes which correctly track the transport effects. In the case where collisions are neglected, particle methods are widely used, but the computation of the collision operator may be carried out more easily on a regular grid. Hence the interest in a finite difference method. The goals here are to study both the results of implementing such methods and analysis of convergence (as feasible). The starting point for this work is the context in which solutions have spherical symmetry. An additional problem of interest is the Vlasov-Einstein system in which the relativistic motion of matter is coupled to the Einstein field equations.

9731956谢弗 该奖项支持对等离子体行为模型的非线性偏微分方程系统的研究。 特别考虑了相空间中离子密度满足朗道-福克-普朗克方程的等离子体动力学模型。 一个主要的重点是开发有限差分格式，正确跟踪运输的影响。 在忽略碰撞的情况下，粒子方法被广泛使用，但碰撞算子的计算可以更容易地在规则网格上进行。 因此，在有限差分方法的兴趣。 这里的目标是研究实施这些方法的结果和收敛性分析（如可行）。 这项工作的出发点是解决方案具有球对称性的背景。 另一个感兴趣的问题是弗拉索夫-爱因斯坦系统，其中物质的相对论运动耦合到爱因斯坦场方程。