Title: Hybrid numerical schemes for the kinetic transport equations
Abstract:
Kinetic transport equations, which govern the evolution of particle distribution functions under the influence of collisions, external fields, and spatial transport, present a significant challenge in both analytical and numerical modeling. These equations naturally operate in a high-dimensional phase space, often encompassing multiple scales in time and space, and require the simultaneous resolution of intricate interactions between particles and their environment. As a result, standard discretization schemes frequently encounter severe computational burdens, numerical instabilities, and difficulties in achieving accurate, physically meaningful solutions. The complex interplay of nonlinearity, stiff source terms, and boundary conditions further complicates the analysis and simulation process. We introduce the advanced numerical methods, such as asymptotic-preserving schemes and efficient collision-based hybrid decomposition that address these challenges.