Advanced Numerical Techniques for Supersonic Flow Analysis: From Euler Equations to Practical Applications in Aerospace and Turbomachinery Engineering

Abstract

This paper explores advanced numerical techniques for analyzing supersonic flow, with a particular focus on the application of Euler equations in aerospace and turbomachinery engineering. Theoretical foundations such as boundary conditions, error evaluation, grid partitioning, and the Successive Over-Relaxation (SOR) method are thoroughly examined. Rigorous numerical simulations are conducted to investigate the final velocity field distribution and convergence characteristics under various conditions. The research underscores the precision and efficiency of these numerical methods, highlighting their practical applications in the aerodynamic design of aircraft and potential use in turbomachinery design. The findings contribute significantly to the advancement of computational fluid dynamics in supersonic flow regimes, providing valuable insights for engineers and researchers engaged in this specialized area. The study not only enhances understanding of complex flow dynamics but also supports the development of more effective engineering solutions in high-speed applications.