Zhichao Peng: An asymptotic preserving numerical scheme and a reduced order model for the radiative transfer equation

Abstract: As the Knudsen number goes to zero, the radiative transfer equation (RTE) asymptotically converges to its diffusion limit. On one hand, it is a challenge to design efficient numerical schemes preserving the underlying physical limit. On the other hand, this limit also suggests the existence of a low-rank structure in the angular space which can be utilized to design reduced order models (ROMs). In the first part of this talk, we present an asymptotic preserving method solving time-dependent RTE based on the micro-macro decomposition and Schur complement. The proposed method is unconditionally stable in the diffusive regime and has standard CFL conditions in the transport regime. In the second part of the talk, we present a reduced basis method to build an angular-space ROM for the steady state RTE.