A separable and asymptotic-preserving dynamical low-rank method for the Vlasov–Poisson–Fokker–Planck system

We present a dynamical low-rank (DLR) method for the Vlasov–Poisson–Fokker–Planck (VPFP) system. Our main contributions are twofold: (i) a conservative spatial discretization of the Fokker–Planck operator that factors into velocity-only and space-only components, enabling efficient low-rank projection, and (ii) a time discretization within the DLR framework that properly handles stiff collisions. We propose both first-order and second-order low-rank IMEX schemes. For the first-order scheme, we prove an asymptotic-preserving (AP) property when the field fluctuation is small. Numerical experiments demonstrate accuracy, robustness, and AP property at modest ranks.