Computational fluid dynamics in aerodynamics: a comparative analysis of supersonic and subsonic flow models

The Navier-Stokes equation holds critical importance in the field of fluid dynamics, particularly in the study of supersonic and subsonic flows within the context of space flight. To effectively analyze transonic flow—a regime where both subsonic and supersonic components coexist—it is essential to solve the fluid dynamic equations numerically for these distinct flow regimes. This study focus on the one-dimensional small perturbation equation for both subsonic and supersonic flows, analyzing them separately under the condition of a constant Mach number. In subsonic flows, perturbations remained localized around the point of disturbance, while in supersonic flows, perturbations propagated in a straight line, with the angle of propagation relative to the flow direction determined by the Mach number. This study provides a foundational approach for future numerical solutions where the Mach number varies as a function of other parameters. The goal is to combine the solutions for subsonic and supersonic flows into more complex transonic numerical simulations, advancing the understanding of fluid behavior in these critical flow regimes and supporting the design and analysis of aerospace systems.