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Computations of internal viscous flowfields of scramjet models were conducted at inflow Mach numbers of 3.4 and 5.45. A hybrid unstructured grid method was used to compute the scramjet models with and without a short strut. The numerical method to solve the Navier-Stokes equations on the hybrid unstructured grid was developed using a finite volume cell vertex scheme and the lower-upper symmetric Gauss-Seidel (LU-SGS) implicit time integration algorithm. The computational results revealed that a thick subsonic region did not exist in the combustor near the top wall at Mach number 5.45. It was a desirable feature to avoid unstarting the engine. With the use of a strut, the relatively low velocity regions increased and the downward flow toward the cowl behind the step became strong. An overconcentration of fuel toward the top wall during weak combustion was observed in the experiment. The reason for this was that the airflow near the injector was turned to the top wall due to the small influence of combustion in the experiment.