EU Regional School - Hauck Seminar
Prof. Hauck - Numerical Topics in Collisional Kinetic Equations: Moment Models, Asymptotic Preserving Methods, and Hybrid Approaches
University of Tennessee
Kinetic equations describe the evolution of a particle system via the evolution a probability distribution function that is typically defined over a six-dimensional phase-space. The mathematical, computational, and physical aspects of these equations are very interesting, but also very complicated. From the numerical point of view, simulations are challenging due to both the large phase-space and the existence of structure at multiple scales. In particular, the number of unknowns needed to accurately represent the solution can be quite large. In this talk, I will discuss the basic goals and challenges of these type of simulations and present some of my own attempts at tackling these challenges. In particular we will discuss the moment-based formalism, numerical approaches for capturing macroscopic behavior with under-resolved meshes, and finally some ideas on hybrid approaches.