Abstract：The kinetic transport equation in a diffusive scaling converges to a limiting diffusion equation,

as the Knudsen number goes to 0. To deal with multi-scale problems for this model, we develop a family

of asymptotic preserving schemes. These schemes have high order accuracy and are able to capture the

correct diffusion limit without resolving the small physical regime. They are based on micro-macro

decomposition and a reformulation of the decomposed system. We apply high order implicit-explicit

Runge-Kutta  (IMEX-RK) method in time and a local discontinuous Galerkin spatial discretization.

Our schemes are unconditionally stable in the diffusive regime and have the standard hyperbolic time

step restriction in the hyperbolic regime.

Brief Introduction: Zhichao Peng is currently a 4th year P.h.D student in Rensselaer Polytechnic Institute.

His research interest includes asymptotic preserving schemes for multi-scale problems, positivity preserving

schemes, numerical methods for kinetic equations and Maxwell equations in nonlinear media and discontinuous Galerkin method.