Numerical Methods for Simulating and Understanding the Universe

Abstract

Only within the past century have we discovered the existence of external galaxies outside our own Milky Way. The study of the formation and evolution of galaxies is now an entire field unto itself, with a key part of this field being the direct numerical simulation of galaxy formation. These simulations naturally depend heavily on an assortment of numerical methods, from fluid solvers to detailed prescriptions for metal evolution in stars. This thesis explores existing numerical methods and develops novel methods for simulating astrophysical fluids and analysing the baryon cycle in galaxies. We first show how the commonly used Pressure-SPH (Smoothed Particle Hydrodynamics) method leads to large integration errors when coupled to galaxy formation physics, before developing a new SPH method called Sphenix that does not suffer from the same errors. Sphenix is based on Density-SPH, and employs a novel artificial conduction scheme to reduce errors at contact discontinuities. Sphenix is then shown to solve a number of challenging problems for SPH, including vorticity conservation and fluid mixing, thanks to its conduction and viscosity schemes. Finally, we develop two new numerical schemes to study the baryon cycle in the Simba simulations. The spread metric is used to show that matter can be transported huge distances (≫ 10 Mpc) by redshift z = 0, primarily due to AGN feedback. By comparing the Lagrangian region that gas resides in at the initial state of the simulation to its resident halo at z = 0 we show how matter can be transported between bound haloes at the end of the simulation. Notably, we show that 5-10% of the baryonic mass in a typical Milky Way mass halo originated in the region defined by the dark matter of another halo, leading to potential difficulties for so-called ‘zoom-in’ simulations.