二维Vlasov-Poisson方程的自适应高阶相空间重映射
An adaptive, high-order phase-space remapping for the two-dimensional Vlasov-Poisson equations
AI总结：
针对二维Vlasov-Poisson方程，提出一种自适应高阶相空间重映射方法，通过周期性在层次化相空间网格上高精度重构分布函数来降低PIC方法的数值噪声，并采用局部再分布技术保持分布函数的正性。
摘要：
高维Vlasov方程的数值求解通常采用粒子网格（PIC）方法。然而，由于众所周知的数值噪声，使用PIC方法精确描述相空间中的分布函数具有挑战性。为了控制数值误差，我们引入了一种自适应相空间重映射方法，通过周期性在层次化相空间网格上使用高阶插值重构分布函数来正则化粒子分布。通过使用局部再分布技术，可以保持分布函数的正性。该方法已成功应用于一维经典等离子体问题。在本文中，我们提出了二维Vlasov-Poisson方程的算法。使用了具有无限域边界条件的高效泊松求解器。还将讨论该算法在大型并行计算机上的并行可扩展性。
英文摘要：
The numerical solution of high dimensional Vlasov equation is usually performed by particle-in-cell (PIC) methods. However, due to the well-known numerical noise, it is challenging to use PIC methods to get a precise description of the distribution function in phase space. To control the numerical error, we introduce an adaptive phase-space remapping which regularizes the particle distribution by periodically reconstructing the distribution function on a hierarchy of phase-space grids with high-order interpolations. The positivity of the distribution function can be preserved by using a local redistribution technique. The method has been successfully applied to a set of classical plasma problems in one dimension. In this paper, we present the algorithm for the two dimensional Vlasov-Poisson equations. An efficient Poisson solver with infinite domain boundary conditions is used. The parallel scalability of the algorithm on massively parallel computers will be discussed.
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