Towards faster and more physical MHD and multi-fluid data-driven global coronal models

Space weather modelling has never been as relevant as it is today when the majority of our society relies on technology that is, in some capacity, susceptible to space weather effects. These effects may originate from phenomena such as coronal mass ejections, corotating interaction regions, and solar energetic particles, and they may cause communication blackouts, satellite outages, and even power failures. To allow for the accurate operation of space weather forecasting tool chains that generally aim to model the propagation of the solar plasma, high-energy particles and radiation from the Sun to the Earth or other objects of interest, the conditions in the solar corona must be well resolved. Currently, semi-empirical methods such as the Wang-Sheeley-Arge model are used to determine the state of plasma in the corona up to 0.1 AU. These models are, however, limited in terms of how much accuracy and insight into the coronal phenomena they can provide. This thesis work primarily focuses on the development of the global coronal model COCONUT. This model represents the environment between roughly 1 and 25 solar radii and couples to heliospheric software. The thesis work, specifically, discusses the formulation of the code, the grid design, the boundary condition design, a time-accurate extension, a multi-fluid extension and finally, the modelling of drift-wave physics to approximate their possible contribution to coronal heating. The main recommendations regarding the future development of the solver are i) to further work on improving the computational efficiency, especially in the case of multi-fluid and time-accurate setups, ii) to keep evolving the prescription of the inner boundary condition in line with the latest observations and consensus, iii) to extent the computational domain in order to include the lower atmospheric layers which can be resolved with the multi-fluid setup, and iv), to keep investing efforts in studying the potential contributions of drift-wave instabilities to the solar coronal momentum and energy budgets.