This thesis sets out to further develop our understanding of accretion processes in symbiotic stars, in particular the accretion disc formation radius and mass capture fraction from a stellar wind. I then explore how these potentially large discs can deliver mass onto the white dwarf at the nuclear burning rate, allowing the white dwarf to grow in mass rather than going through nova explosions. Finally, if this is not possible, I investigate how nova explosions interact with the disc the white dwarf star may harbour.\ud Using smoothed particle hydrodynamics, I present circularisation radii and mass capture rates for 8 different symbiotic binary star systems undergoing mass transfer from a stellar wind. I explore the wind velocity and secondary star rotation parameter space. I compare these radii against one another and the expected circularisation radii for Roche lobe overflow. Using RS Oph as an example, I determine that it is unlikely for the disc to be maintained in the hot and steady state. Furthermore, unless the mass loss from the red giant is unusually large, the wind velocity must be very slow to enable the required mass transfer from the red giant to the disc to explain RS Oph’s ~ 20 year outburst cycle.\ud I present an analytical method to describe the outburst and recurrence time of 18 cataclysmic variable stars (including 4 Z Cam, 9 U Gem and 5 SW Uma). Using the Markov chain Monte Carlo method, the parameter space is constrained. Extrapolating the analytical method to long period cataclysmic variables, the periods during which average mass transfer through the disc lies within the nuclear burning regime, and the irradiation from this promoting more of the disc into the hot, more viscous state to drive prolonged outbursts, was found. This could enable a 1Mסּ white dwarf to grow to the Chandrasekhar mass in a minimum time of approximately 1 million years.\ud Finally, a new test (the Richtmyer-Meshkov instability) on Godunov smoothed particle hydrodynamics was performed and compared against standard smoothed particle hydrodynamics. Using the same code, nova blast waves into discs of constant and varying density are simulated and compared against the Sedov solution and the Kompaneet approximation respectively. Using simple energy arguments, I calculate how much of the nova and disc material remains bound to the WD. In the less energetic novae, approximately 40% of the disc and more than 80% of the nova material remains bound to the white dwarf, whilst in high energy novae approximately none of the disc and less than 50% of the nova material remains bound to the white dwarf
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