Asymptotic Preserving IMEX-LDG Schemes for Kinetic Transport Equations in a Diffusive Scaling
摘要： 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.