  We describe computational tools that have been developed to simulate
dynamical mass transfer in semi-detached, polytropic binaries that are
initially executing synchronous rotation upon circular orbits. Initial
equilibrium models are generated with a self-consistent field algorithm; models
are then evolved in time with a parallel, explicit, Eulerian hydrodynamics code
with no assumptions made about the symmetry of the system. Poisson's equation
is solved along with the equations of ideal fluid mechanics to allow us to
treat the nonlinear tidal distortion of the components in a fully
self-consistent manner. We present results from several standard numerical
experiments that have been conducted to assess the general viability and
validity of our tools, and from benchmark simulations that follow the evolution
of two detached systems through five full orbits (up to approximately 90
stellar dynamical times). These benchmark runs allow us to gauge the level of
quantitative accuracy with which simulations of semi-detached systems can be
performed using presently available computing resources. We find that we should
be able to resolve mass transfer at levels $\dot{M} / M > few x 10^-5$ per
orbit through approximately 20 orbits with each orbit taking about 30 hours of
computing time on parallel computing platforms.
