论文标题
多尺度等离子体传输的随机动力学方案，具有不确定性定量
A stochastic kinetic scheme for multi-scale plasma transport with uncertainty quantification
论文作者
论文摘要
在本文中，将开发出一个面向物理的随机动力学方案，其中包括通过随机盖尔金和搭配方法的杂交从流量和电磁场中的随机输入。基于多组分Boltzmann方程的BGK型弛豫模型，在物理和粒子速度空间中设计了依赖量表的动力学中心风向函数，并且在离散的时间速度速度速度领域中构建了管理方程。通过使用波传播方法求解麦克斯韦的方程，在整个仿真过程中耦合了离子，电子和电磁场的发展。我们证明，该方案在vlasov，磁流失动力学和中性欧拉制度中正式渐近地保护，其中包括随机变量。因此，它可用于研究不确定性的影响下多尺度和多物理等离子体系统，并在数值细胞大小，粒子平均自由路径和gyroradius（或时间步长，局部粒子碰撞时间和等离子时间和等离子周期）之间提供规模适应性物理溶液。数值实验，包括一维Landau阻尼，二流不稳定性和具有一维速度设置的Brio-Wu冲击管问题，以及每个具有一维不确定性的随机初始条件，以验证该方案。
In this paper, a physics-oriented stochastic kinetic scheme will be developed that includes random inputs from both flow and electromagnetic fields via a hybridization of stochastic Galerkin and collocation methods. Based on the BGK-type relaxation model of the multi-component Boltzmann equation, a scale-dependent kinetic central-upwind flux function is designed in both physical and particle velocity space, and the governing equations in the discrete temporal-spatial-random domain are constructed. By solving Maxwell's equations with the wave-propagation method, the evolutions of ions, electrons and electromagnetic field are coupled throughout the simulation. We prove that the scheme is formally asymptotic-preserving in the Vlasov, magnetohydrodynamical, and neutral Euler regimes with the inclusion of random variables. Therefore, it can be used for the study of multi-scale and multi-physics plasma system under the effects of uncertainties, and provide scale-adaptive physical solutions under different ratios among numerical cell size, particle mean free path and gyroradius (or time step, local particle collision time and plasma period). Numerical experiments including one-dimensional Landau Damping, the two-stream instability and the Brio-Wu shock tube problem with one- to three-dimensional velocity settings, and each under stochastic initial conditions with one-dimensional uncertainty, will be presented to validate the scheme.
