  The dynamical low-rank (DLR) approximation is an efficient technique to
approximate the solution to matrix differential equations. Recently, the DLR
method was applied to radiation transport calculations to reduce memory
requirements and computational costs. This work extends the low-rank scheme for
the time-dependent radiation transport equation in 2-D and 3-D Cartesian
geometries with discrete ordinates discretization in angle (SN method). The
reduced system that evolves on a low-rank manifold is constructed via an
unconventional basis update and Galerkin integrator to avoid a substep that is
backward in time, which could be unstable for dissipative problems. The
resulting system preserves the information on angular direction by applying
separate low-rank decompositions in each octant where angular intensity has the
same sign as the direction cosines. Then, transport sweeps and source iteration
can efficiently solve this low-rank-SN system. The numerical results in 2-D and
3-D Cartesian geometries demonstrate that the low-rank solution requires less
memory and computational time than solving the full rank equations using
transport sweeps without losing accuracy.

Computational Physics