Young Researchers Workshop:
Kinetic and macroscopic models for complex systems

Exponential asymptotic preserving scheme for the Boltzmann equation and related

Qin Li

California Institute of Technology

When the Knudsen number goes to zero, the macroscopic quantities of the Boltzmann equation satisfy the limiting compressible Euler equation. Numerically, to capture this limit, however, time needs to be discretized so that the small Knudsen number is resolved, which generates prohibitive computational cost. In the talk, I will present a class of cheap numerical solvers that captures solutions with high order accuracy in both kinetic and fluid regime (and thus preserves the asymptotic limits). I will also give a brief summary on the comparison between current AP schemes, and the extension of this high order AP scheme we developed to multi-species and quantum systems will be showed. The work is done with L. Pareschi and J. Hu.