标题： 用于带有麦克斯韦-玻尔兹曼电子的Vlasov--Poisson方程的几何粒子-网格方法 显示英文标题

标题： Geometric particle-in-cell methods for Vlasov--Poisson equations with Maxwell--Boltzmann electrons

摘要： 本文介绍了带有麦克斯韦-玻尔兹曼电子的Vlasov--Poisson方程的变分和哈密顿形式。通过离散作用积分和泊松括号构造了保持结构的粒子-网格方法。我们使用哈密顿分裂方法和离散梯度方法进行时间离散，分别保持几何结构和能量。离散化也保持了全局电中性条件。在取准中性极限时，这些格式是渐近保持的，极限格式对于极限模型是保持结构的。有限网格不稳定性、兰道阻尼和双流不稳定的数值实验展示了所提出数值方法的行为。 显示英文摘要

摘要： In this paper, variational and Hamiltonian formulations of the Vlasov--Poisson equations with Maxwell--Boltzmann electrons are introduced. Structure-preserving particle-in-cell methods are constructed by discretizing the action integral and the Poisson bracket. We use the Hamiltonian splitting methods and the discrete gradient methods for time discretizations to preserve the geometric structure and energy, respectively. The global neutrality condition is also conserved by the discretizations. The schemes are asymptotic preserving when taking the quasi-neutral limit, and the limiting schemes are structure-preserving for the limiting model. Numerical experiments of finite grid instability, Landau damping, and two-stream instability illustrate the behavior of the proposed numerical methods.