Wave Propagation Methods for Astrophysical Flows

天体物理流的波传播方法

• 批准号: 0619037
• 负责人: James Rossmanith
• 金额: $ 5.57万
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-11-01 至 2008-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0619037&HistoricalAwards=false
• 关键词: Wave; Propagation; Methods; Astrophysical; Flows

This research is focused on developing accurate and efficient numericalmethods for the simulation of astrophysical flows. This project will buildon a class of high-resolution shock-capturing methods that have in thelast few years gained popularity in astrophysics. Several numericalchallenges will be investigated including computing high Lorentz factorflows; maintaining divergence-free magnetic fields as dictated by Maxwell'sequations; incorporating space-time curvature for general relativisticflows; including radiative cooling physics; and accurately simulatingmulti-component flows. Adaptive mesh refinement techniques will beincorporated into the simulations in order to resolve regions of theflow where the solution is rapidly varying, and conversely, to useless resolution in regions where the solution remains nearly constant.Special attention will be given to two application problems: the specialrelativistic problem of the interaction of pulsar wind nebulae withsupernovae remnants and the general relativistic problem of accretiononto a rotating black hole.Astrophysics, much like weather prediction and climatology, is a field ofscience in which observations are possible, but direct experimentation isnot. Therefore, direct experiments are replaced by computer simulations. Inorder to carry out these simulations, sophisticated tools from computationalmathematics are required to approximately solve the nonlinear system ofequations that model astrophysical flows. Examples of such flows include theformation of pulsar wind nebulae and the accretion of matter into a black hole.A feature of these flows, and consequently the equations that model them, isthat they can lead to complicated solutions with sharp discontinuities. Overthe past few decades, an important class of computer methods has beendeveloped to accurately and efficiently approximate such solutions. Morerecently these methods have been applied to astrophysical fluid dynamics. Thisresearch will focus on developing and implementing generalizations of thesemethods and also on the application of these methods to specific astrophysicalproblems. The P.I. is actively involved in collaborations between researchersin both the Mathematics and Astronomy Departments at the University of Michigan.

本研究的重点是发展精确、高效的天体物理流数值模拟方法。这个项目将建立一种高分辨率的冲击波捕获方法，这种方法在过去几年里在天体物理学中很受欢迎。将研究几个数字挑战，包括计算高洛伦兹因子流；维持麦克斯韦级数规定的无发散磁场；广义相对论流动中时空曲率的引入包括辐射冷却物理；准确模拟多组分流。自适应网格细化技术将被纳入模拟中，以解决解决方案快速变化的区域，相反，解决方案保持几乎恒定的区域的无用分辨率。特别注意两个应用问题：脉冲星风星云与超新星残余物相互作用的特殊相对论性问题和旋转黑洞吸积的广义相对论性问题。天体物理学，就像天气预报和气候学一样，是一个可以进行观测，但不能进行直接实验的科学领域。因此，直接实验被计算机模拟所取代。为了进行这些模拟，需要使用复杂的计算数学工具来近似地求解模拟天体物理流的非线性方程组。这种流的例子包括脉冲星风星云的形成和物质进入黑洞的吸积。这些流动的一个特点是，它们可以导致具有明显不连续的复杂解。在过去的几十年里，一类重要的计算机方法得到了发展，以准确而有效地近似这类解。最近，这些方法已被应用于天体物理流体动力学。这项研究将集中于发展和实施这些方法的推广，以及这些方法在具体天体物理问题上的应用。P.I.积极参与密歇根大学数学系和天文学系研究人员之间的合作。