This comprehensive review aims to provide a critical overview of the additional lift and reduced drag produced by induced vortices, which grant the compound delta wing structure exceptionally high stall characteristics at higher Reynolds numbers when flying at high AOA. Using a computational model, this study conducts numerical simulations of the flow field over a compound delta wing at Mach numbers 0.8 and 1.3 and at an AOA of 0° using OpenFOAM software. The investigation offers a robust platform to explore the flow physics and vortex behavior in both subsonic and supersonic regimes. Additionally, this study highlights the impact of varying Mach numbers on the aerodynamic performance of the compound delta wing, providing insights into optimizing wing design for improved efficiency and stability in different flight conditions. This research contributes to a deeper understanding of vortex dynamics and their implications for aerodynamic performance, potentially informing future aircraft design and development.