Numerical simulations of a scramjet combustor were conducted to determine the effects of design changes on mixing and combustion characteristics and to investigate the physics of the supersonic combustion flowfield. The mixing and combustion performances might be greatly affected by numerical diffusion due to a low grid density in the computational domains. Two test cases were examined to check the effects of numerical diffusion on the flowfields relating to the scramjet combustor. One was a complex shape closely approximating a scramjet and the other was simple transverse injection through a circular hole in a flat plate. In the two cases, the contamination levels of the flowfields by the numerical diffusion were very different. In the scramjet simulations, comparisons between the physical diffusion and the numerical diffusion indicated that the effects of the numerical diffusion are acceptable for finer solutions. In fact, the combustion efficiency converged within ±5 % at the grid with 2-mm spacing. On the other hand, the numerical diffusion of the flat plate injection using a 0.5-mm grid was comparable to the physical diffusion. The grid convergence was not proved in the current grid systems. These differences were caused by the high eddy viscosity due to the shock train of the scramjet combustor.