This thesis presents the results of calculating model atmospheres for the accretion column of a magnetic white dwarf. A basic stellar atmosphere calculation is refined to model the specific conditions at the base of an accretion column. Calculated spectra for a variety of different input conditions are shown. The calculated spectra are fitted with black body spectra in order to ascertain the errors associated with black body fitting of observed spectra. Simulated lightcurves are calculated using these model atmosphere spectra. The resultant lightcurves are folded through the EXOSAT (European X-ray Observatory Satellite) detectors and used to fit lightcurves from the magnetic polar system AM Herculis. Following the assumption that a thin accretion disc around a supermassive black hole is the central power source for active galactic nuclei (AGN's) a large grid of model atmospheres is calculated. This grid is then used to calculate the spectrum from such a disc.

The non-hydrostatic dynamical core ENDGame (Even Newer Dynamics for the General Atmospheric Modelling of the Environment) is extended into the thermosphere to test its feasability as a whole-atmosphere dynamical core that can simulate the large scale fluid dynamics of the whole atmosphere from the surface to the top of the thermosphere at 600km. This research may have applications in the development of a Sun-to-Earth modelling system involving the Met Office Unified Model, which will be useful for space weather forecasting and chemical climate modelling. Initial attempts to raise the top boundary of ENDGame above ∼100km give rise to instabilities. To explore the potential causes of these instabilities, a one dimensional column version of ENDGame: ENDGame1D, is developed to study the effects of vertically propagating acoustic waves in the dynamical core. A 2D ray-tracing scheme is also developed, which accounts for the numerical effects on wave propagation. It is found that ENDGame’s numerics have a tendency towards the excessive focussing of wave energy towards vertical propagation, and have poor handling of large amplitude waves, also being unable to handle shocks. A key finding is that the physical processes of vertical molecular viscosity and diffusion prevent the excessive growth of wave amplitudes in the thermosphere in ENDGame, which may be crucial to improving ENDGame’s stability as it is extended upwards. Therefore, a fully implicit-in-time implementation of vertical molecular viscosity and diffusion is developed in both ENDGame1D and the full three-dimensional version of ENDGame: ENDGame3D. A new scheme is developed to deal with the viscous and diffusive terms with the dynamics terms in a fully coupled way to avoid time-splitting errors that may arise. The combination of a small amount of off-centring of ENDGame’s semi-implicit formulation and the inclusion of vertical molecular viscosity and diffusion act to make ENDGame significantly more stable, as long as the simulation is able to remain stable up to the molecularly diffused region above an altitude of ∼130km.