论文标题
弗拉索夫 - 安培系统具有渐近保护预处理的能源旋转颗粒方法，具有精确的无卷曲约束
An Energy-Conserving Fourier Particle-in-Cell Method with Asymptotic-Preserving Preconditioner for Vlasov-Ampère System with Exact Curl-Free Constraint
论文作者
论文摘要
我们为静电vlasov系统提供了有效，准确的能量持含量粒子〜（PIC）算法，特别强调了其高鲁棒性，用于模拟具有多个物理尺度的复杂等离子体系统。该方法由几个必不可少的元素组成：（\ romannumeral1）将原始的弗拉索夫 - 波森系统重新制作成具有差异/curl-fr-f-figoncons的等效vlasov-ampère系统； （\ romannumeral2）一种新型的具有结构的傅立叶空间离散化，它在离散级别中恰好保留了这些约束； （\ romannumeral3）一种针对高度非线性系统解决方案的预处理的安德森加速算法； （\ romannumeral4）基于广义欧姆的定律，对debye长度的隐式曲柄 - 尼科尔森方案进行了线性性和均匀的近似，该定律可作为拟议方法的渐近保护预处理。进行了数值实验，并进行了比较，在提出的持势方案，经典的跨越方案和一个陌生的操作员分解方案中进行了比较，以证明所提出的方法的优越性，尤其是对于跨越物理规模的等离子体系统。
We present an efficient and accurate energy-conserving implicit particle-in-cell~(PIC) algorithm for the electrostatic Vlasov system, with particular emphasis on its high robustness for simulating complex plasma systems with multiple physical scales. This method consists of several indispensable elements: (\romannumeral1) the reformulation of the original Vlasov-Poisson system into an equivalent Vlasov-Ampère system with divergence-/curl-free constraints; (\romannumeral2) a novel structure-preserving Fourier spatial discretization, which exactly preserves these constraints at the discrete level; (\romannumeral3) a preconditioned Anderson-acceleration algorithm for the solution of the highly nonlinear system; and (\romannumeral4) a linearized and uniform approximation of the implicit Crank-Nicolson scheme for various Debye lengths, based on the generalized Ohm's law, which serves as an asymptotic-preserving preconditioner for the proposed method. Numerical experiments are conducted, and comparisons are made among the proposed energy-conserving scheme, the classical leapfrog scheme, and a Strang operator-splitting scheme to demonstrate the superiority of the proposed method, especially for plasma systems crossing physical scales.
