Abstract
Self gravity is central to the evolution of type Ia supernova progenitors, especially in dynamical double degenerate systems where orbital motion, tidal disruption, and masstransfer are all controlled by the gravitational field. Capturing this physics in multidimensional hydrodynamic simulations requires a gravity solver that is both accurate and computationally scalable. In FLASH, that requirement motivates the use of approximate methods such as the Barnes-Hut tree solver, which reduces the cost of long range gravity from pairwise evaluation to a hierarchical approximation. This thesis evaluates the Barnes-Hut tree solver for self gravitating astrophysical flows relevant to type Ia supernova research. I focus on how the solver behaves in a set of controlled verification problems, with particular attention to convergence, boundary condition sensitivity, and the tradeoff between accuracy and computational cost. The results show that the tree approximation is effective in isolated settings, while periodic domains introduce long range effects that can dominate the error budget at higher refinement. Taken together, these tests provide a practical basis for choosing gravity methods in large FLASH simulations of compact binary evolution and thermonuclear explosion problems.