To elucidate complex flow phenomena in the solid rocket motor (SRM), it is beneficial to reduce development costs by employing computational fluid dynamics simulation, as conducting full-scale model experiments for SRM is expensive. This study focuses on numerically simulating the internal flow in the cylinder simulating the SRM geometry using the Building-Cube Method (BCM). First, the objective of this study is to develop a radial injection flow model (RIF model) for the BCM solver that can be utilized in the numerical simulation of internal flow in the cylinder simulating the SRM geometry. The numerical model geometry is based on the Ariane 5 SRM, which is a 1/30th scale axisymmetric model. The calculation results are validated through comparisons with experimental measurements, demonstrating the effectiveness of the RIF model using the immersed boundary method for accurate internal flow simulations of cylinder simulating the SRM geometry. Next, the effect of differences in wall injection conditions on the internal flow field of the cylinder simulating a solid rocket motor geometry was investigated using the BCM solver. The results indicate that the internal flow field and the vortex structure inside the cylinder simulating a SRM geometry change due to the effect of the injection velocity.