摘要
当前,科学计算的验证主要针对基于确定性偏微分方程组的网格离散方法。放电等离子体的粒子云网格PIC方法作为一种粒子-网格耦合的仿真手段,其验证方法具有显著不同的特点:第一,PIC仿真除了在时间和空间上进行离散,还需要对粒子数权重进行离散;第二,离散粒子的相空间分布函数是否适合作为验证研究的观测量;第三,粒子-网格耦合过程中的电场插值和电荷分配会影响PIC仿真的全局收敛精度。另外,当PIC方法与蒙特卡罗(MC)方法耦合时,离散误差和随机误差通常叠加在一起,理查德森外推需要结合系综平均进行。提出了一种分层级验证的方法。首先对单粒子轨道、电磁场求解、二体粒子碰撞进行收敛精度阶测试;然后采用空间电荷限制流、气体的傅里叶流动等具有精确解的经典物理模型分别对集成PIC、MC模块进行离散误差评估;最后采用放电物理过程对程序功能进行基准校验。
The verification of scientific computing currently places a strong emphasis on grid discretization methods for systems of deterministic partial differential equations.However,verifying particle-in-cell(PIC)simulations,which employ a particle-mesh method to model discharging plasmas,presents distinctive challenges.Firstly,PIC simulations require discretization not only in time and space but also in macro-particle weights.Secondly,challenges arise regarding the utilization of the discretized particle phase space distribution function for verification purposes.Thirdly,the interpolation of electric fields and charge distribution can significantly impact the overall accuracy of PIC convergence.When PIC methods are integrated with Monte Carlo(MC)methods,discretization and stochastic errors often combine,necessitating Richardson extrapolation in conjunction with ensemble averaging.To tackle these challenges,this paper introduces a hierarchical verification approach.It commences with order-ofaccuracy tests for individual particle trajectories,electromagnetic field solvers,and binary-particle collisions.Discretization errors for integrated PIC and MC modules are then evaluated using classical physical models that possess exact solutions,such as space-charge-limited current and Fourier flow in gases.Finally,a code-to-code comparison is performed with benchmark examples of simplified discharge simulations.
作者
尚天博
杨薇
宋萌萌
周前红
Shang Tianbo;Yang Wei;Song Mengmeng;Zhou Qianhong(Institute of Applied Physics and Computational Mathematics,Beijing 100094,China;Graduate School of China Academy of Engineering Physics,Beijing 100088,China)
出处
《强激光与粒子束》
CAS
CSCD
北大核心
2024年第3期4-12,共9页
High Power Laser and Particle Beams
基金
国家自然科学基金项目(12375245、12005023)
中国工程物理研究院院长基金项目(YZJJLX2022016)。
关键词
PIC方法
验证技术
精度阶测试
放电模拟
PIC method
verification techniques
order of accuracy test
discharge simulation
作者简介
尚天博,联系方式:shangtianbo1231@163.com;通信作者:杨薇,yangwei861212@126.com。
