Stochastic and Deterministic Methods for Simulating the Evolution of Solid Bodies in Protoplanetary Disks

Planets emerge from the rotating disk of gas and dust surrounding young stars. Although the process of planet formation has been subject to theoretical and numerical studies for several decades, it has only very recently become possible to not only detect protoplanetary disks but also resolve their substructures. The annular accumulations of dust observed in many protoplanetary disks are suspected to provide favourable conditions for the formation of planetary cores through runaway growth.

To simulate the growth of rocky planets from agglomeration of dust grains, many orders of magnitude in particle number and mass have to be spanned, necessitating the use of statistical methods for abundant types of particles. Unlike grid-based statistical methods, representative particle methods allow for a natural combination with an N-body simulation, but they are often hampered by their high computational cost.

In this work, an extension of the „Representative Particle Monte Carlo“ method is developed, overcoming some conceptual restrictions that heretofore impeded its use in simulating runaway growth processes. To address the problem of computational cost, a novel computational scheme for stochastic processes is developed that enjoys linear scaling characteristics with regard to the number of representative particles, as opposed to the quadratic scaling characteristics of the traditional scheme. Moreover, a paradigm of interval-aware programming is proposed which allows for a simpler implementation of interval-valued numerical routines as required for the new computational scheme.