This research is focused on developing accurate and efficient numerical methods for the simulation of astrophysical flows. This project will build on a class of high-resolution shock-capturing methods that have in the last few years gained popularity in astrophysics. Several numerical challenges will be investigated including computing high Lorentz factor flows; maintaining divergence-free magnetic fields as dictated by Maxwell's equations; incorporating space-time curvature for general relativistic flows; including radiative cooling physics; and accurately simulating multi-component flows. Adaptive mesh refinement techniques will be incorporated into the simulations in order to resolve regions of the flow where the solution is rapidly varying, and conversely, to use less resolution in regions where the solution remains nearly constant. Special attention will be given to two application problems: the special relativistic problem of the interaction of pulsar wind nebulae with supernovae remnants and the general relativistic problem of accretion onto a rotating black hole.
Astrophysics, much like weather prediction and climatology, is a field of science in which observations are possible, but direct experimentation is not. Therefore, direct experiments are replaced by computer simulations. In order to carry out these simulations, sophisticated tools from computational mathematics are required to approximately solve the nonlinear system of equations that model astrophysical flows. Examples of such flows include the formation 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, is that they can lead to complicated solutions with sharp discontinuities. Over the past few decades, an important class of computer methods has been developed to accurately and efficiently approximate such solutions. More recently these methods have been applied to astrophysical fluid dynamics. This research will focus on developing and implementing generalizations of these methods and also on the application of these methods to specific astrophysical problems. The P.I. is actively involved in collaborations between researchers in both the Mathematics and Astronomy Departments at the University of Michigan.
