This thesis presents a global stability analysis of two-dimensional open cavity flows, focusing on the influence of Reynolds and Mach numbers on flow instabilities. The study is conducted using the high-order compressible flow solver IC3, developed by ISAE-Supaero, which enables direct numerical simulations and global stability computations through a matrix-free approach. To ensure the reliability of the numerical framework, different domain geometries and boundary conditions are examined and validated. The linearized Navier-Stokes equations are used to identify dominant instability modes and their dependence on flow parameters. Comparisons with existing results from literature validate the solver’s implementation, and the analysis reveals critical thresholds and behaviors associated with the primary shedding modes.