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We describe computational tools that have been developed to simulatedynamical mass transfer in semi-detached, polytropic binaries that areinitially executing synchronous rotation upon circular orbits. Initialequilibrium models are generated with a self-consistent field algorithm; modelsare then evolved in time with a parallel, explicit, Eulerian hydrodynamics codewith no assumptions made about the symmetry of the system. Poisson's equationis solved along with the equations of ideal fluid mechanics to allow us totreat the nonlinear tidal distortion of the components in a fullyself-consistent manner. We present results from several standard numericalexperiments that have been conducted to assess the general viability andvalidity of our tools, and from benchmark simulations that follow the evolutionof two detached systems through five full orbits (up to approximately 90stellar dynamical times). These benchmark runs allow us to gauge the level ofquantitative accuracy with which simulations of semi-detached systems can beperformed using presently available computing resources. We find that we shouldbe able to resolve mass transfer at levels $\dot{M} / M > few x 10^-5$ perorbit through approximately 20 orbits with each orbit taking about 30 hours ofcomputing time on parallel computing platforms.Comment: 34 pages, 20 eps figures, submitted to ApJ

Numerical Methods for the Simulation of Dynamical Mass Transfer in Binaries