The one-dimensional hydrodynamic model of a stationary plasma thruster (SPT) previously described by Morozov and Savelyev [in Reviews of Plasma Physics, Vol. 21, Consultants Bureau, New York, 2000, pp. 360-369] is solved using the space-time conservation element/solution element (CE/SE) method. The hydrodynamic model consists of three equations describing the mass conservation of ions and neutral particles and the momentum of the ions. These equations are coupled nonlinearly through source terms describing the ionization of neutrals, and a non-local term describing current through the plasma. This model is one of the simplest to produce the low-frequency oscillatory behavior (on the order of 10 kHz) known as the "breathing mode" that is observed in ground testing of SPTs. Numerical solutions to the model are challenging due to the highly coupled, nonlinear nature of the equations. The simulation outlined here was successful, but displays some of the Courant number sensitivity noted in other CE/SE simulations.
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