Application of Block-structured Adaptive Mesh Refinement to Particle Simulation

Abstract

We implemented the particle treatment in the block-structured adaptive mesh refinement (AMR) framework which we have developed. In the AMR framework, the simulation domain is divided into multiple sub-domains and they are assigned to a number of processes for parallel calculation using MPI. A sub-domain is composed of multiple block-structured regions each of which has the fixed number of grids. When high resolution is required at a certain region in the sub-domain, a block-structured region with refined grids, which is called child block, is locally created. To apply this AMR framework to the particle simulations such as particle-in-cell simulation, we set up several arrays for the particle treatment for each sub-domain assigned to one process. These arrays are shared among all the blocks consisting of the corresponding sub-domain. For the particle calculation in each block, we also set up several other arrays which are privately defined and used in each block. The functions for these arrays for the particle treatment are described in this paper. To test the implementation of the particle treatment in the AMR framework, we performed test simulations by adopting the sugarscape model which was proposed for the simulation of an artificial society by using many agents representing inhabitants in a certain area. We treated the inhabitants as a bunch of particles and assign the sugar amount at each grid as the environment in a two-dimensional simulation domain. In the simulation, we initially place two peaks of sugar and randomly distribute the inhabitants. For simplicity, we examined the motions of the inhabitants agents by assuming no temporal variation of the sugar. The simulation results show that the inhabitant agents were accelerated and gathered to the two sugar peaks as we expected. When the inhabitant density exceeded a certain criteria, child blocks with refined grids were adaptively created at the corresponding region. We confirmed that the motions of the inhabitants were not influenced by the block boundaries, which ensures that the particle treatment to the AMR framework has been properly implemented.