In this project you will develop numerical techniques for the simulation of the supersonic escape of hydrogen gas from the atmospheres of extrasolar planets (see the final part of the following presentation: [pdf]).

More than hundred extrasolar planets have been discovered in recent years. Most of these planets are gas giants with very small orbital distances to their stars. Because of the strong irradiation by their stars, it is believed that the atmospheres of these planets are in a state of continuous supersonic escape, very much like the supersonic solar wind, and this belief has actually been corroborated by recent observations.

In this project, you will numerically solve the Euler equations of Gas Dynamics to model supersonic escape from extrasolar planet atmospheres. Important questions to be answered include the long-time stability of these atmospheres, and the determination of flow patterns within the atmospheres.

Solving the transonic Euler equations poses severe numerical problems: convergence to the steady state tends to be extremely slow. This project may involve the development of new techniques for efficiently solving transonic steady state flows. Alternatively, large-scale 2D and 3D simulations of the atmospheric flow patterns may be considered as well. A strong interest in numerical algorithms for the solution of hyperbolic PDEs is required.

This work will be done in collaboration with Feng Tian of the Astrophysics Department of the University of Colorado at Boulder, USA.

This topic is suitable for a PhD or Master's thesis project. Some aspects may also qualify for an undergraduate summer research project. Please contact Hans De Sterck if you are interested.

Created by Hans De Sterck.
Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.
Phone: 1-519-888-4567 ext 7550, Fax: 1-519-746-4319, E-mail: hdesterck@math.uwaterloo.ca.
Office: MC 5016. campus map