Delta-wing aircraft create strong swirling air currents called vortices, which become especially complex at high speeds near the speed of sound. In these conditions, vortices interact with shock waves, sometimes becoming unstable or breaking down, which can affect lift, drag, and overall aircraft stability. This study uses advanced computer simulations to examine how these vortices form, change, and interact on double and triple delta-wing shapes. We focus on understanding three key behaviors: when and how vortices break down, how they interact with shock waves, and how multiple vortices influence each other. The results are compared with experimental measurements to ensure accuracy. By improving our understanding of these flow behaviors, this work supports the design of more efficient and stable high-speed aircraft.