Current objectives at NASA Johnson Space Center ate directed at future upgrade and replacement of the U.S. Space Shuttle's, currently toxic, Reaction Control System thrusters with dual mode thrusters that use nontoxic propellants. Experimentation to determine any performance advantages obtained using a dual mode thruster has not been performed by NASA. A computational fluid dynamics analysis is performed to evaluate the internal flow characteristics of this thruster under low thrust mode, torch igniter only, conditions. Several computational models, both two- and three-dimensional, are constructed to simulate the internal, steady-state flow characteristics. Comparison is made with current data on a similar type of flow (highly underexpanded free-jet flow) to show the appearance of barrel shocks and Mach disks. Regions of stagnate flow where heat transfer to chamber surfaces will be high and engine thrust performance are predicted based on computational data. Two different flow solvers, one using a finite volume method and the other using a finite difference method, are used to predict the engine's performance. A comparison of the two flow solvers is given based on their relative performance to compute solutions to this problem.