Young Researchers Workshop: Kinetic models in biology and social sciences

Asymptotic preserving schemes on kinetic models with singular limits

Changhui Tan

University of South Carolina

In this talk, I will discuss kinetic models with mono-kinetic hydrodynamic limits. Due to the singular limit, standard asymptotic-preserving (AP) schemes lose accuracy when the parameter is close to the limit. To overcome such difficulty, we introduce a velocity scaling method that transforms the singular limit to a non-singular one, and build AP schemes on the transformed systems. As an example, I will present kinetic swarming models and the corresponding AP schemes based on velocity scaling. This is a joint work with Alina Chertock and Bokai Yan.