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arXiv · 2601.11900

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

Shiheng Zhang·Jingwei Hu
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Abstract

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.

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Shiheng Zhang, Jingwei Hu. 2026-01-17. A separable and asymptotic-preserving dynamical low-rank method for the Vlasov-Poisson-Fokker-Planck system. https://doi.org/10.1051/m2an%2F2026047

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