Fast-forward the Sedimentation of Solid Particles in Protoplanetary Disks
Abstract: Numerical simulations have become an essential tool for studying particle-gas systems. One such system is the protoplanetary disk consisting of vast number of solid particles interacting with the surrounding gas. However, the particles tend to have a non-uniform distribution due to sedimentation, among other processes, creating an imbalanced workload for computers in different regions of the disk. In this thesis we present an adaptive-particle algorithm which relieves this imbalance, reducing the computational task in dense areas by merging particles while allowing sparse areas to be efficiently probed by splitting particles. Using the assignment schemes from the Particle-Mesh methods, including Nearest-Grid-Point and Cloud-In-Cell, we split and merge particles while conserving all important physical properties of the particles on the grid. Coupled to a Runge-Kutta integrator of order three, the algorithm was tested on a simulation model for the sedimentation process of particles in a turbulent gas disk. The theoretical density profile was compared to the numerical ones with and without adapting particles, and they were in good agreement in most cases. Moreover, while the simulations without adaptive particles failed to sample the particle properties at high altitudes of the disk, those with adaptive particles successfully reproduced the density profile in the same region. Finally, the adaptive-particle algorithm maintains a roughly equal number of particles per cell at all time, and thus demonstrates its ability to balance the workload over the entire computational domain.
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