High-order methods for kinetic Boltzmann models of rarefied gases

Molecules in a gas undergo both transport and collisions; the Knudsen number of a gas is a non-dimensional measure of how far, on average, a molecule will travel before encountering a collision. The kinetic Boltzmann equation can be used to model and simulate the dynamics of gases over a wide range of Knudsen numbers. Efficient numerical methods for the Boltzmann equation should be asymptotic-preserving, which allows the numerical method to be stable at fixed mesh parameters for any value of the Knudsen number. This work aims to develop accurate and efficient numerical methods that solve variants with simplified collision operators (e.g., BGK and ES-BGK). Current work is focused on both wave-propagation methods and high-order DG-FEM. We are also developing strategies to allow us to do adaptive mesh refinement in these simulations.