  Hydrodynamical simulations of semi-detached, 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 $\sim 10$ 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.
