Gauss's Law satisfying Energy-Conserving Semi-Implicit Particle-in-Cell method
Gauss's Law satisfying Energy-Conserving Semi-Implicit Particle-in-Cell method
复制标题
DOI：
10.1016/j.jcp.2019.02.032
复制
发表时间：
2018-08
期刊：
影响因子：
--
通讯作者：
Yuxi Chen;G. Tóth
中科院分区：
文献类型：
--
作者：
Yuxi Chen;G. Tóth
Lapenta（2017）介绍的能量守恒半隐式方法（ECSIM）与经典的半隐式和显式PIC方法相比具有许多优点。最重要的是，能量守恒消除了有限网格不稳定性的增长。我们以一种与原始方法不同且更有效的方式实现了ECSIM。更重要的是，我们已经解决了两个主要的缺点，原来的ECSIM算法：没有机制来执行高斯定律，也没有机制来减少电场的数值振荡。满足高斯定律的经典方法是使用基于广义拉格朗日乘子方法的椭圆或抛物线/双曲线校正来修改电场及其发散。然而，这种修正违反了能量守恒性质，与有限网格不稳定性相关的振荡在修正的ECSIM格式中再次出现。我们发明了一种新的替代方法：在校正步骤中修改粒子位置而不是电场。稍微移动粒子并不改变能量守恒性质，而通过改变电荷密度可以满足高斯定律。我们发现，新的高斯定律满足能量守恒半隐式方法（GL-ECSIM）产生上级的结果相比，原来的ECSIM算法。然而，在一些模拟中，电场中仍然存在一些数值振荡。我们将此归因于能量守恒隐式电场求解器的简单有限差分离散化。我们修改了场求解器的空间离散化，以减少这些振荡，同时只稍微违反能量守恒性质。我们证明了改进质量的GL-ECSIM方法与几个测试。
The Energy Conserving Semi-Implicit Method (ECSIM) introduced by Lapenta (2017) has many advantageous properties compared to the classical semi-implicit and explicit PIC methods. Most importantly, energy conservation eliminates the growth of the finite grid instability. We have implemented ECSIM in a different and more efficient manner than the original approach. More importantly, we have addressed two major shortcomings of the original ECSIM algorithm: there is no mechanism to enforce Gauss's law and there is no mechanism to reduce the numerical oscillations of the electric field. A classical approach to satisfy Gauss's law is to modify the electric field and its divergence using either an elliptic or a parabolic/hyperbolic correction based on the Generalized Lagrange Multiplier method. This correction, however, violates the energy conservation property, and the oscillations related to the finite grid instability reappear in the modified ECSIM scheme. We invented a new alternative approach: the particle positions are modified instead of the electric field in the correction step. Displacing the particles slightly does not change the energy conservation property, while it can satisfy Gauss's law by changing the charge density. We found that the new Gauss's Law satisfying Energy Conserving Semi-Implicit Method (GL-ECSIM) produces superior results compared to the original ECSIM algorithm. In some simulations, however, there are still some numerical oscillations present in the electric field. We attribute this to the simple finite difference discretization of the energy conserving implicit electric field solver. We modified the spatial discretization of the field solver to reduce these oscillations while only slightly violating the energy conservation properties. We demonstrate the improved quality of the GL-ECSIM method with several tests.