一种用于维拉索-泊松方程的四阶粒子-细胞方法及其相空间重映射
A 4th-Order Particle-in-Cell Method with Phase-Space Remapping for the Vlasov-Poisson Equation
AI总结：
本文提出一种四阶精度的粒子-细胞方法，用于求解维拉索-泊松方程，通过高阶扩展和六阶相空间重映射步骤，提升计算精度与稳定性。
摘要：
维拉索-泊松方程的数值解在等离子体物理和宇宙学中有重要应用。本文提出了一种新的粒子-细胞方法，该方法在空间和时间上均为四阶精度。该方法是之前方法的高阶扩展，对标准粒子-细胞更新的所有阶段，包括电荷沉积、力插值、场求解和粒子推动，均采用四阶精度，并包含六阶精度的相空间重映射步骤以控制粒子噪声。我们在一系列一维和二维静电等离子体测试问题上展示了该方法的收敛性，并将其精度与二阶方法进行了比较。正如预期的那样，四阶方法可以使用更少的分辨率元素实现与二阶方法相当的精度。
英文摘要：
Numerical solutions to the Vlasov-Poisson system of equations have important applications to both plasma physics and cosmology. In this paper, we present a new Particle-in-Cell (PIC) method for solving this system that is 4th-order accurate in both space and time. Our method is a high-order extension of one presented previously [B. Wang, G. Miller, and P. Colella, SIAM J. Sci. Comput., 33 (2011), pp. 3509--3537]. It treats all of the stages of the standard PIC update - charge deposition, force interpolation, the field solve, and the particle push - with 4th-order accuracy, and includes a 6th-order accurate phase-space remapping step for controlling particle noise. We demonstrate the convergence of our method on a series of one- and two- dimensional electrostatic plasma test problems, comparing its accuracy to that of a 2nd-order method. As expected, the 4th-order method can achieve comparable accuracy to the 2nd-order method with many fewer resolution elements.
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