Multi-dimensional dust evolution in protoplanetary discs

The past few decades have seen an explosion in our ability to probe both extrasolar planetary systems and their progenitors, protoplanetary discs. From surveys in the latter half of the last century that identified thermal emission generated by circumstellar dust in the spectral energy distributions of young stellar objects, to recent high resolution observations of dust and gas substructures that are ubiquitous in these circumstellar discs, we now have a vast pool of data to analyse and interpret in our quest to answer the extant questions in the field of planet formation. In this thesis, I present the work that I have undertaken to tackle some of these questions by creating self-consistent models of dust evolution in protoplanetary discs. The motivation behind generating such models is that the physical processes that govern features of disc evolution are fundamentally inextricably linked. My work has therefore attempted to include the major physical processes that affect dust in discs, coupling these processes to create self-consistent simulations whilst also maintaining a level of computational efficiency that allows calculations to be run for the desired astrophysical timescales in reasonable computational timescales. After introducing the field and the relevant physical processes, I outline the numerical methods that I employ, detailing deviations from the standard disc model that I find by including additional dimensionality and the coupling of physical processes. I go on to study the effect of radiation pressure on dust outflows in dispersing, photoevaporating discs, a problem that fundamentally requires resolving the vertical dimension. Finally I detail my work studying the dynamics and thermodynamics of molecular condensation fronts, or snowlines, in discs. Through this work, I have demonstrated that studying protoplanetary discs through a multi-dimensional approach is vital if we are to develop a complete and robust picture of their structure and evolution.