An asymptotic-preserving dynamical low-rank method for the multi-scale multi-dimensional linear transport equation

We introduce a dynamical low-rank method to reduce the computational complexity for solving multi-scale multi-dimensional linear transport equation. The is based on macro-micro decomposition of proposed numerical uses low rank approximation only micro part solution. time and spatial discretizations are done properly so that overall scheme second order accurate asymptotic-preserving (AP); is, in diffusive regime, becomes macroscopic solver limiting diffusion equation automatically rank. demonstrate accuracy efficiency by number two-dimensional examples.