A Parallel, Energy-Stable Low-Rank Integrator for Nonlinear Multi-Scale Thermal Radiative Transfer

Thermal radiative transfer (TRT) governs phenomena ranging from supernovas in astrophysics to laser-driven fusion experiments in plasma physics. The interaction of radiation and matter involves prohibitively small time scales, nonlinear coupling, and high-dimensional particle dynamics, making conventional numerical methods prohibitively expensive. Dynamical low-rank approximation (DLRA), combined with asymptotic-preserving discretizations, offers a promising direction, but until now its use for nonlinear TRT has been fundamentally limited: stability regions of existing DLRA integrators are unknown in realistic nonlinear regimes, and coefficient updates remain computationally costly. We present an asymptotic-preserving, locally conservative, rank-adaptive, and parallel integrator for a macro–micro decomposition-based DLRA of the nonlinear TRT equations. Unlike previous approaches, our method is provably energy stable in the nonlinear setting, with step-size restrictions that capture both hyperbolic and parabolic CFL conditions. The integrator is constructed from the parallel BUG integrator, thus eliminating the need for augmented coefficient updates. ... mehrIn the setting of the parallel integrator and micro-macro decompositions, we propose a strategy to enforce reflection-transmission type boundary conditions in the low-rank factors. These advances resolve long-standing stability and efficiency obstacles, enabling DLRA to be applied robustly to nonlinear TRT with stability guarantees. Numerical experiments confirm the accuracy and efficiency of the proposed approach.