The objective of this study is to enhance the methodology for the design of a supersonic wind tunnel, improving the process with advanced computational techniques. The supersonic wind tunnel is intended to operate within a flight envelope of Mach 2.5 to 4 and altitudes between 18 and 20 km; this study focuses on the operative condition of Mach 3.5. The research is based on computational fluid dynamics, enabling a deeper understanding of fluid flow phenomena that can deteriorate the operability of the wind tunnel. Additionally, a detailed mesh independence study has been conducted to ensure the reliability and robustness of the computational results. These new analyses allowed for a more comprehensive optimization in the state of the art of tunnel geometry and operational conditions, further enhancing the ability to sustain supersonic flow for extended durations. Particular attention was given to the second throat, which plays a crucial role in the overall performance of the facility, especially during the start-up process. Its design has been refined to improve efficiency by reducing the minimum starting pressure.