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We have conducted 2D hydrodynamic simulations of the mass tranfer in the short period binary, Algol ($\beta$-Persei). Optical line observations suggest that the Algol system posseses a transient accretion disk, in contrast to long period systems in which a steady accretion disk is inferred. We have used our model to explore the parameter space in search of a regime in which a transient disk is observed. The simulations explored the dependence of the flow on three parameters; the velocity, angle, and density of the stream of gas flowing from the evolved companion star toward the more massive main sequence star. To study the effects of various stream angles and velocities, we ran the simulations with an adiabatic index of 1.01 to simulate strong radiative cooling. We found that for most values of angle and velocity, the stream formed a very steady accretion disk. We then proceeded to investigate the role of radiative cooling by using an adiabatic index of 5/3 and varying the density (and hence cooling rate) in the stream. We found that for a very narrow range in stream density ($10^{-9} {\rm cm}^{-3} < \rho_s < 6\times 10^{-9} {\rm cm}^{-3}$) radiative cooling was partially effective and the flow tended to be much more sporadic, reminiscent of the transient accretion disk suggested by the optical observations. In all of our simulations the dynamics of the accretion flow were modulated by the interaction of the gas stream from the secondary and the gas which had circled the primary star.
