Wave Propagation Methods for Astrophysical Flows

这项研究的重点是发展精确和有效的数值方法模拟天体物理流动。这个项目将建立一类高分辨率的激波捕捉方法，这些方法在过去几年中在天体物理学中得到了普及。几个numericalchallenges将调查，包括计算高洛伦兹factorflows;保持发散自由磁场所规定的麦克斯韦方程;纳入时空曲率的广义relativisticflows;包括辐射冷却物理;和准确地模拟多组分流。自适应网格细化技术将被结合到模拟中，以解决解快速变化的流动区域，反之，解决方案几乎保持不变的区域的无用分辨率。将特别注意两个应用问题：脉冲星风星云与超新星遗迹相互作用的特殊相对论问题和旋转黑洞吸积的广义相对论问题天体物理学，就像天气预报和气候学一样，是一个可以进行观测的科学领域，但不能进行直接的实验。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动的非线性方程组。这类流动的例子包括脉冲星风星云的形成和物质向黑洞的吸积。这类流动的一个特点，以及由此产生的模拟它们的方程，就是它们可以导致具有尖锐间断的复杂解。在过去的几十年里，一类重要的计算机方法已经发展到准确和有效地近似这样的解决方案。最近这些方法已被应用到天体物理流体动力学。这项研究将集中在发展和实施这些方法的推广，也对这些方法的应用，以具体的天体物理问题。私家侦探积极参与密歇根大学数学系和天文系研究人员之间的合作。

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.