A separable and asymptotic-preserving dynamical low-rank method for the Vlasov-Poisson-Fokker-Planck system
This work provides an efficient low-rank solver for a challenging kinetic plasma model, benefiting computational plasma physics.
The authors develop a dynamical low-rank method for the Vlasov-Poisson-Fokker-Planck system with a conservative, separable discretization of the Fokker-Planck operator and asymptotic-preserving time integrators. Numerical tests show accuracy and robustness at modest ranks.
We present a dynamical low-rank (DLR) method for the Vlasov-Poisson-Fokker-Planck (VPFP) system. Our main contributions are two-fold: (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.