Wave Propagation Methods for Astrophysical Flows

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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.