Spectral Element Method for the Study of Current Sheets in Astronomical Magnetic Fields

本研究将开发一个谱元磁流体动力学(MHD)模拟程序，结合自适应网格加密(AMR)技术，研究天文磁场中电流片的形成和几何形状。这一进展建立在参与者在流体模拟、电流片上的分析和数值结果以及磁重联算法方面的最新成就的基础上。该项目将在谱元方法的应用数学方面取得重大进展，并为当前薄片是否在帕克模型中形成这一重要问题提供严格和决定性的答案。这些帮助更好地解决流体系统奇点的算法也将在其他领域有用。这项工作整合了各级研究和教育，包括为当地高中生设立暑期学院，对研究生进行跨学科培训，以及指导一名初级研究科学家，并将促进应用数学家、计算机科学家和等离子体天体物理学家之间广泛的跨学科互动。

AST-0434322NgThis research will develop a spectral element magnetohydrodynamics (MHD) simulation code, incorporating Adaptive Mesh Refinement (AMR) techniques, to investigate the formation and geometry of current sheets in astronomical magnetic fields. This development builds on recent accomplishments of the participants in fluid simulations, analytical and numerical results on current sheets, and algorithms for magnetic reconnection. The project will make significant advances in applied mathematics for the spectral element method, and provide a rigorous and conclusive answer to the important question of whether current sheets form in the Parker model. These algorithms to help better resolve singularities in fluid systems will also be useful in other areas.The work integrates research and education at all levels, including a summer institute for local high school students, interdisciplinary training of graduate students, and mentorship of a junior research scientist, and will promote wide-ranging inter-disciplinary interactions between applied mathematicians, computer scientists, and plasma astrophysicists.