A sweep-based low-rank method for the discrete ordinate transport equation

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