Mathematical Sciences: Analytical and Numerical Studies of Nonlinear Hyperbolic Systems

数学科学：非线性双曲系统的分析和数值研究

• 批准号: 9023196
• 负责人: Robert Glassey
• 金额: $ 12.62万
• 依托单位: Indiana University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-06-01 至 1995-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9023196&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Analytical; Numerical; Studies

This project involves the study of nonlinear hyperbolic systems of partial differential equations from both analytical and numerical points of view, with emphasis on problems from Plasma Physics and the Vlasov-Maxwell system. Particle Methods for higher-dimensional systems will be studied, with the goal of obtaining convergence as well as higher-order accuracy. Collisional effects (e.g. those from the LANDAU system) will also be included. Many of the presently-used numerical schemes have little (if any) theoretical justification. For those few that are well founded, the known accuracy is relatively poor. Thus from a practical point of view, much improvement is possible. Moreover, at this time there are no rigorous studies (neither theoretical nor computational) of collisional effects. These studies will have application in areas such as fusion energy.

本项目涉及非线性双曲 系统的偏微分方程从分析 和数字的观点，重点是问题， 等离子体物理学和Vlasov-Maxwell系统 粒子方法 将研究高维系统，目标是 获得收敛性以及高阶精度。 碰撞效应（例如来自朗道系统的碰撞效应）也将 包括. 许多目前使用的数值方案， 很少（如果有的话）有理论依据。 对于那些 是有根据的，已知的准确性相对较差。 因此 从实际的角度来看，可以作出很大的改进。 此外，目前还没有严格的研究（ 理论上或计算上）的碰撞效应。 这些 研究将在聚变能等领域得到应用。