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