Octree particle management for DSMC and PIC simulations

The ratio of physical to computationally modeled particles is of critical importance to the fidelity of particle-based simulation methods such as Direct Simulation Monte Carlo (DSMC) and Particle-in-Cell (PIC). Like adaptive mesh refinement for continuum/grid-based simulations, particle remapping enables dynamic control of simulation fidelity in regions of interest so that computational resources can be efficiently distributed within the problem. This is particularly important for simulations involving high dynamic range in the density for one or more species such as problems involving chain-branching reactions like combustion and ionizing breakdown. In this work, a new method of particle remapping is presented which strictly conserves mass, momentum, and energy while simultaneously remaining faithful to the original velocity distribution function through the use of octree binning in velocity space.