With the aid of virtual prototyping and casting numerical simulation, this work presents the optimization of an injection system used in a non-traditional investment casting process that applies perpendicular centrifugal force to inject the molten metal into refractory plaster molds. In this study, advanced techniques of simulation and production of complex geometries in Computer-Aided Design CAD (Computer-Aided Design) are used in the design of the casting system of a miniaturized simple-cubic cell structure. The cast part has a complex shape profile and needs a high surface finish with strict dimensional tolerance. The alloy used to fill the mold is an aluminum bronze shape memory alloy (SMA). CAD was used to model the part and the proposed models for casting optimization. ProCAST software was used for the numerical simulation of the casting process. Experimental parameters were used as input data for the numerical simulation. The simulation results were analyzed focusing on the identification of defects in the Cu–Al–Mn SMA simple-cubic structures. Different feeding systems have been designed to eliminate the identified defects. Concerning the molten recirculation, the optimal nozzle model has a truncated cone profile, with a larger radius of 6.5 mm, a smaller radius of 2.0 mm and a height of 8.0 mm (called here model 3). Experimental observations from cast SMA parts agree with the simulated results of the optimized nozzle model 3. In addition to the elimination of alloy recirculation with the nozzle optimization in this work, the shrinkage porosity at the upper base of the part was eliminated with the addition of a compensation volume close to the region where porosity is more intense. By exploring the possibilities offered by commercial software, the work contributes to advance the knowledge and application of the non-traditional investment casting process, highlighting its advantages and potential applications.