The design of particle simulation methods for collisional plasma physics has always represented a challenge due to the unbounded total collisional cross section, which prevents a natural extension of the classical Direct Simulation Monte Carlo (DSMC) method devised for the Boltzmann equation. One way to overcome this problem is to consider the design of Monte Carlo algorithms that are robust in the so-called grazing collision limit. In the first part of this manuscript, we will focus on the construction of collision algorithms for the Landau-Fokker-Planck equation based on the grazing collision asymptotics and which avoids the use of iterative solvers. Subsequently, we discuss problems involving uncertainties and show how to develop a stochastic Galerkin projection of the particle dynamics which permits to recover spectral accuracy for smooth solutions in the random space. Several classical numerical tests are reported to validate the present approach.

翻译：碰撞等离子体物理中粒子模拟方法的设计始终是一项挑战，原因在于总碰撞截面无界，这阻碍了为Boltzmann方程设计的经典直接模拟蒙特卡罗（DSMC）方法的自然推广。克服这一问题的一种途径是设计在所谓的掠射碰撞极限下具有鲁棒性的蒙特卡罗算法。本文第一部分将重点介绍基于掠射碰撞渐近方法、避免使用迭代求解器的Landau-Fokker-Planck方程碰撞算法构建。随后，我们讨论涉及不确定性的问题，并展示如何发展粒子动力学的随机Galerkin投影方法，该方法可在随机空间中对光滑解恢复谱精度。最后报告若干经典数值测试以验证所提出的方法。