Hydrodynamical simulations of semidetached, polytropic binary stars are presented in an effort to study the onset and stability of dynamical mass transfer events. Initial, synchronously rotating equilibrium models are constructed using a self-consistent field technique and then evolved with an Eulerian hydrodynamics code in a fully self-consistent manner. We describe code improvements introduced over the past few years that permit us to follow dynamical mass transfer events through more than 30 orbits. Mass transfer evolutions are presented for two different initial configurations: a dynamically unstable binary with initial mass ratio (donor/accretor) q_0 = 1.3 that leads to a complete merger in ～ 10 orbits, and a double-degenerate binary with initial mass ratio q_0 = 0.5 that, after some initial unstable growth of mass transfer, tends to separate as the mass transfer rate levels off.
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