New residual distribution hydrodynamics solver for galaxy formation simulations

Numerical simulations are key to our understanding the complex physical processes present in the formation and evolution of galaxies. The vast majority of the baryonic component is in a gaseous state, modelled by solving the fluid equations, using a variety of methods. I present a new implementation of the 2D residual distribution (RD) family of hydrodynamics solvers. Built around an unstructured mesh, RD solvers produce truly multi-dimensional solutions to the underlying fluid equations, with second order accuracy in both time and space. The implementation accurately reproduces the solutions to many standard hydrodynamics tests. I compare the RD results to solutions from state-of-the-art meshless finite mass (MFM) and meshless finite volume (MFV) solvers. I present extensions to the RD method, deriving an adaptive time stepping regime, and the 3D version of the solver. I also show a numerical study of idealised gaseous dynamical friction (DF) using the MFM solver, for both supersonic and subsonic flows, highlighting the need for accurate solvers. This solver produces a wake that systematically under-produces the expected retarding force in supersonic cases. The over-dense wake it forms does not replicate the expected sharp density profile and produces a bow shock where none is predicted. I compare this regime to that found in cosmological simulations, demonstrating that much of the dark matter substructure in the early universe will experience these conditions, suggesting DF driven mergers may be underestimated in current simulations. I propose a new standard gravo-hydrodynamical test based on the idealised DF setup. I add simulations that include molecular chemistry, showing how DF at early times can stimulate the formation of molecular hydrogen, critical to the formation of the first stars and structures.