Dynamical low-rank approximation for Marshak waves

Marshak waves are temperature waves which can arise from the background radiation in a material. A core limitation in the simulation of these temperature waves is the high-dimensional phase space of the radiation solution, which depends on time, the spatial position as well as the direction of flight. To obtain computationally efficient methods, we propose to use dynamical low-rank approximation (DLRA) which is a model order reduction method that dynamically determines and adapts dominant modes of the numerical solution. This is done by projecting the original dynamics onto the tangent space of the low-rank manifold. In this work, we investigate discontinuous Galerkin discretizations for two robust time integrators. By performing the derivation of the DLRA evolution equations on the continuous level, we are able to apply the needed slope limiter on the low-rank factors instead of the full solution. The efficiency of the method is presented through computational results for a Marshak wave originating from a heated wall.