The decomposed HOLO scheme: Enabling large time steps for the gray radiative transfer equation across three distinct limits

In this paper, we introduce an asymptotic preserving Decomposed HOLO scheme for solving the gray radiative transfer equation under various scalings. We consider three distinct multiscale parameter regimes: the diffusive regime, the steady state regime, and the free-streaming regime. We decompose the light intensity into three components: the zeroth and first order moments, and a residual part. A Low-Order (LO) nonlinear macroscopic system is solved for the first two moments and the material temperature. The High-Order (HO) system targets the residual component instead of the light intensity in the HOLO algorithm found in the literature. This novel decomposed HOLO system facilitates the analytical proof of the asymptotic preserving properties in three different parameter regimes and eases the achievement of consistency between the HO and LO systems at the discrete level. To bolster stability, in the LO system, we use the characteristic method to provide a predication of the contributions from HO system. Numerical examples demonstrate that our scheme allows for large time steps, comparable to those in fully implicit schemes and independent of the speed of light. Various tests for accuracy and stability across different parameter regimes are presented, including benchmark tests such as the Marshak wave and Hohlraum problems.