AI 中文总结
本文提出含Fokker-Planck碰撞项的统一气体动理学波粒方法UGKWP-FP，用于Vlasov-Poisson-Fokker-Planck系统多尺度模拟，通过算子分解实现自适应波粒表示，经数值实验验证可准确模拟相关等离子体现象。
AI 中文摘要
本文开发了一种含Fokker-Planck碰撞项的统一气体动理学波粒方法（UGKWP-FP），用于求解Vlasov-Poisson-Fokker-Planck系统。碰撞算子采用Lenard-Bernstein算子建模，其随机表示对应速度空间中的Ornstein-Uhlenbeck过程。为将UGKWP框架扩展至传统Bhatnagar-Gross-Krook（BGK）碰撞模型之外，研究将Fokker-Planck算子分解为非刚性漂移-扩散贡献与刚性热化贡献；前者通过改进的Ornstein-Uhlenbeck过程保留在粒子动力学中，后者则通过向局域麦克斯韦分布的BGK型松弛表示。该分解实现了自适应波粒表示：在稀薄区域，方法遵循随机粒子动力学；当趋近连续介质区域时，方法通过解析波分量表示快速平衡的分布。改进的摩擦系数被构造为在稀薄极限下恢复原始Fokker-Planck动力学，同时在强碰撞下保持流体动力学极限。数值实验表明，所提方法可捕捉速度空间的漂移与扩散，在一系列克努森数范围内恢复预期的动力学与连续介质行为，并重现碰撞等离子体现象的特征演化。
英文摘要
A unified gas-kinetic wave--particle method with Fokker--Planck collisions (UGKWP-FP) is developed for the Vlasov--Poisson--Fokker--Planck system. The collision operator is modeled by the Lenard--Bernstein operator, whose stochastic representation corresponds to the Ornstein--Uhlenbeck process in velocity space. To extend the UGKWP framework beyond the conventional Bhatnagar--Gross--Krook (BGK) collision model, the Fokker--Planck operator is decomposed into a nonstiff drift--diffusion contribution and a stiff thermalization contribution. The former is retained in the particle dynamics through a modified Ornstein--Uhlenbeck process, whereas the latter is represented by a BGK-type relaxation toward the local Maxwellian. This decomposition enables an adaptive wave--particle representation: the method follows stochastic particle dynamics in rarefied regimes and increasingly represents the rapidly equilibrating distribution by the analytical wave component as the continuum regime is approached. The modified friction coefficient is constructed to recover the original Fokker--Planck dynamics in the rarefied limit while preserving the hydrodynamic limit under strong collisions. Numerical experiments demonstrate that the proposed method captures velocity-space drift and diffusion, recovers the expected kinetic and continuum behavior across a range of Knudsen numbers, and reproduces the characteristic evolution of collisional plasma phenomena.
