N-Body Simulations using the Particle-Mesh Method

This project was part of my third year scientific computing module. I was given 'n-body' as the topic of my report, but the direction of the research was left quite open. As you will read in the report, I chose to go down the route of large scale n-body simulations. The algorithms used in these simulations typically trade accuracy of the individual bodies for computational efficiency, but retain accuracy of large scale behaviour.

Abstract

N-body simulations give us the ability to model the universe on scales that would be otherwise impossible. Here I describe and implement the Particle-Mesh method of simulating motion under the influence of gravity. The accuracy of the model is tested: comparing the results of a top hat collapse to the analytical solution, and the effect of periodic boundaries is negated by adding buffer particles to the corners of the simulation. Model universes are simulated to analyse how the formation of structure changes with particles of different masses. It is found that when particle mass is increased, the size of the clusters decreases, and the sharing of particles between the clusters increases.