Development of an Adaptive Grid Code for Particle in Cell Simulation in Plasmaphysics

开发了一个在自适应网格上模拟空间等离子体的粒子网格程序。与静态网格相比，自适应网格是自适应的。其网格参数在空间和时间上是可变的。网格尺寸应自动适应局部等离子体结构。时间步长也应该相应地适应数值稳定性准则。新的代码将基于已知的流体动力学和磁流体动力学自适应网格代码。主要的新发展将是等离子体粒子的处理。由于动态网格尺寸，代表一种等离子体物质的相同数值粒子必须由具有浮动数值权重的数值粒子代替。为了确保可接受的颗粒统计，代码必须在小网格单元中保持与大网格单元中相同数量级的数值颗粒数。然而，在较小的单元格中，数值权重必须较小，反之亦然。在小单元中必要的粒子分裂和在大单元中的聚结必须以这样的方式进行，即保持所有网格单元内的等离子体的动力学特性。采用自适应网格可以显著提高计算效率。代码的实现必须在并行计算机上显示出有效的可用性。

Development of a particle-in-cell code for simulation of space plasma operating on an adaptive grid is to accomplish. In contrast to a static grid the adaptive grid is self adapting. Its grid parameters are variable in space and time. The mesh sizes should adapt automatically to the local plasma structures. The time steps also should adapt accordingly to the numerical stability criteria. The new code will be based on known hydrodynamic and magnetohydrodynamic adaptive grid codes. The major new development will be the handling of the plasma particles. In consequence of the dynamic mesh sizes identical numerical particles representing one plasma species have to be replaced by numerical particles with floating numerical weight. In order to ensure an acceptable particle statistics the code has to preserve the same order of magnitude of the numerical particle number in small grid cells as in big cells. However, in smaller cells the numerical weight has to be smaller, and vice versa. The necessary particle splitting in small cells and the coalescence in big cells has to be performed in such a way that the kinetic character of the plasma within all grid cells is maintained. With an adaptive grid a significant increase of the numerical efficiency will be reached. The implementation of the code has to show an effective usability on a parallel computer.