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Computational gas dynamical simulations using the WENO-LF method are applied to modeling the high Mach number astrophysical jet XZ Tauri, including the effects of radiative cooling.Mach 55 simulations of the pulsed proto-jet are presented and analyzed in terms of interacting nonlinear waves: terminal Mach disks, bow shocks, and Meshkov-Richtmyer instabilities of the leading jet contact boundary.