关键词：自适应控制系统；燃烧；保护；电离
摘 要：The number of particles simulated within a kinetic simulation has a direct impact on the accuracy of the results. In the case of chain-branching reactions such as those found in ionization and combustion events, the exponential growth of computational particle populations may also result in computationally intractable problems. Adaptive control of the number of computational particles is therefore an important topic for improving these types of simulations. Particle merging and its inverse splitting procedures can potentially enable this type of control, but only if they do not result in additional accumulated error. Merging multiple particles down to a single particle can be shown to either violate conservation of momentum or kinetic energy because a single particle consists of too few degrees of freedom to fully represent the original two. This has resulted in a proliferation of merging strategies relying on nearby particle pairs in velocity space or merging moments to computational grids as shown for example in Refs. 1-3. If instead multiple particles are merged down to two rather than one, it can be shown that mass, momentum, and kinetic energy as well as center of mass and mean square deviation of position can be conserved simultaneously. However, when previously attempted in this reference for electromagnetic particle-in- cell (PIC), the approach was found to result in excessive thermalization, incorrect collisionless shock wave-speeds, and was not obviously amenable to near-neighbor particle selection. To mitigate the thermalization effects, the ternary merge has been coupled with octree velocity space binning. This method has been shown to match direct unmerged solutions well for several 3D3V simulations with predominately one-dimensional variations aligned to the original coordinate system. Though these results were encouraging, the preferential selection of original spatial coordinate system for the moment decomposition suggested an orientation.