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The Burst And Transient Source Experiment on the Compton Gamma Ray Observatory is currently producing beautiful observations of the brightest dozen or so accretion-powered pulsars. These sources, in which a magnetic neutron star accretes matter from a close binary companion, display a rich variety of phenomena. Much of the observed behavior is not currently understood, particularly in the case of accretion from the stellar wind of a massive OB companion star. In these systems, the neutron star shows alternating periods of spin-up and spin-down which last anywhere from several hours to more than one hundred days. Previous hydrodynamical calculations in two dimensions have shown that accretion from a stellar wind can be very unsteady, sometimes leading to the formation of accretion disks which rotate alternately in either direction. While these simulations are suggestive, particularly for bright X-ray transients in which a Be star undergoes episodes of equatorial mass ejection, they are inadequate for modelling accretion from a true three-dimensional stellar wind. \bigskip We present results from two-dimensional hydrodynamical calculations of the wind accretion process which confirm previous studies and display the unsteady behavior discussed above. These calculations have been performed on the Intel Touchstone Delta parallel processing supercomputer using an Eulerian hydrodynamics code which implements the piecewise parabolic method (PPM) to integrate the fluid variables on a fixed cylindrical grid. These results demonstrate the ability of this method to accurately model such a process; the method will soon be extended to perform fully three dimensional calculations using the Intel Paragon parallel processing supercomputer. The results of those three-dimensional simulations will allow detailed modelling of BATSE data. This research has been supported in part by NASA grants NGT-51059, NAGW-830, and NAGW-1284.
