Projects

Numerical Methods for BGK Equations

In this project, our goal is to derive and analyze fast numerical methods for the BGK and multi-species BGK equations. We are, in particular, interested in designing a new class of fully implicit methods for avoiding restrictive time step conditions. A summary of the project can be found here.

This work is joint with Cory Hauck and is funded by the US Department of Energy.

Positivity-Preserving Numerical Methods

Our goal in this project is to develop high-order energy stable and postivity-preserving numerical methods for non-isothermal gradient flows where the energy/entropy of the flow has singular potential terms. The resulting schemes are usually highly nonlinear and singular, and they require sophisticated numerical solvers.

This work is joint with Cheng Wang and is funded by the US National Science Foundation through grants NSF-DMS 2012634 and NSF-DMS 2309547.

All Projects, Current and Completed

• DOE, ORNL, UT-Battelle, ongoing.
• NSF-DMS 0818030, 9/08 – 9/11.
• NSF-DMS 1115390, 7/11 – 9/14.
• NSF-DMS 1418692, 9/14 – 8/17.
• NSF-DMS 1719854, 8/17 – 7/20.
• NSF-DMS 2012634, 8/20 – 7/24.
• NSF-DMS 2309547, 8/23 – 7/26.