Afterlive: A performant code for Vlasov-Hybrid simulations

A parallelized implementation of the Vlasov-Hybrid method Nunn (1993) is presented. This method is a hybrid between a gridded Eulerian description and Lagrangian meta-particles. Unlike the Particle-in-Cell method Dawson (1983) which simply adds up the contribution of meta-particles, this method does a reconstruction of the distribution function f in every time step for each species. This interpolation method combines meta-particles with different weights in such a way that particles with large weight do not drown out particles that represent small contributions to the phase space density. These core properties allow the use of a much larger range of macro factors and can thus represent a much larger dynamic range in phase space density. The reconstructed phase space density f is used to calculate momenta of the distribution function such as the charge density p. The charge density p is also used as input into a spectral solver that calculates the self-consistent electrostatic field which is used to update the particles for the next time-step. Afterlive (AF ourier-based T ool in the E lectrostatic limit for the R apid L ow-noise I ntegration of the V lasov E quation) is fully parallelized using MPI and writes output using parallel HDF5. The input to the simulation is read from a JSON description that sets the initial particle distributions as well as domain size and discretization constraints. The implementation presented here is intentionally limited to one spatial dimension and resolves one or three dimensions in velocity space. Additional spatial dimensions can be added in a straight forward way, but make runs computationally even more costly.

本文提出了Nunn（1993）提出的Vlasov混合方法（Vlasov-Hybrid method）的并行化实现方案。该方法属于网格欧拉描述与拉格朗日宏粒子（Lagrangian meta-particles）的混合框架。与仅对宏粒子贡献进行简单求和的Dawson（1983）提出的粒子网格法（Particle-in-Cell method）不同，该方法会在每个时间步长内，针对每种粒子种类重构分布函数f。该插值方法将不同权重的宏粒子进行合理组合，避免高权重粒子掩盖对相空间密度贡献较小的粒子。这些核心特性使其可支持更大范围的宏因子取值，进而能够在相空间密度中覆盖更宽的动态范围。重构得到的相空间密度f可用于计算分布函数的各类矩量，例如电荷密度p。电荷密度p同时作为谱求解器的输入，该求解器可计算自洽静电场，用于更新下一时刻的粒子状态。Afterlive（全称：基于傅里叶的静电极限下Vlasov方程快速低噪声积分工具，A Fourier-based Tool in the Electrostatic limit for the Rapid Low-noise Integration of the Vlasov Equation）采用消息传递接口（MPI，Message Passing Interface）实现全并行化，并通过并行HDF5（Hierarchical Data Format 5）格式写入输出结果。该模拟的输入由JSON格式的配置文件读取，该配置文件可设定初始粒子分布、计算域尺寸以及离散化约束条件。本文提出的实现方案仅支持单空间维度，但可对速度空间的一维或三维进行解析求解。若需扩展至更多空间维度，可通过直观的方式实现，但会进一步提升计算开销。