The behavior of the flow about gas atomizers with a supersonic nozzle containing an under-expanded or over-expanded jet is very important with respect to performance and stability characteristics. Since detailed experiments are expensive, computational fluid mechanics have been applied recently to various relating flow field. In this study, a higher order upwind method with the 3rd order MUSCL type TVD scheme is used to solve the full Reynolds Wavier-Stokes equations. To delineate the purely exhaust jet effects, the melt flow is not considered. Comparison is made with some experimental data in terms of density fields. The influence of the exhaust-jet-to freestream pressure ratio and the effect of the protrusion length of the melt orifice are studied. The present study leads us to believe that the computational fluid mechanics should be considered as powerful tool in predicting the gas atomizer flows.