Wave Propagation Methods for Astrophysical Flows

天体物理流的波传播方法

基本信息

批准号：
0409972
负责人：
James Rossmanith
金额：
$ 9.36万
依托单位：
Regents of the University of Michigan - Ann Arbor
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2004
资助国家：
美国
起止时间：
2004-08-01 至 2006-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=0409972&HistoricalAwards=false
关键词：
Wave Propagation Methods Astrophysical Flows

项目摘要

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.

这项研究的重点是开发准确有效的数值方法来模拟天体物理流。该项目将建立在过去几年在天体物理学中流行的一类高分辨率冲击捕获方法的基础上。将研究几个数值挑战，包括计算高洛伦兹因子流；维持麦克斯韦方程组规定的无发散磁场；将时空曲率纳入广义相对论流；包括辐射冷却物理学；并准确模拟多组分流。自适应网格细化技术将被纳入模拟中，以便解决解快速变化的流动区域，反之，解决解几乎恒定的区域中的无用分辨率。将特别关注两个应用问题：狭义相对论脉冲星风星云与超新星遗迹相互作用的问题以及旋转黑洞吸积的广义相对论问题。天体物理学，很像天气预报和气候学是一个可以进行观察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，需要复杂的计算数学工具来近似求解模拟天体物理流的非线性方程组。此类流的例子包括脉冲星风星云的形成和物质吸积到黑洞中。这些流的一个特征以及因此对它们进行建模的方程是，它们可以导致具有尖锐不连续性的复杂解。在过去的几十年里，已经开发出一类重要的计算机方法来准确有效地近似此类解决方案。最近这些方法已应用于天体物理流体动力学。这项研究将侧重于开发和实施这些方法的推广，以及将这些方法应用于特定的天体物理问题。 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。