Numerical Study of Possion Equation in Subsonic and Supersonic Airfoil Flow

Abstract

In the context of subsonic and supersonic airfoil flows in fluid mechanics, this study aims to numerically simulate the Poisson equation. The focus is on analyzing the variation of fluid flow under stable conditions of incompressible fluid. The research classifies the flow into four distinct cases based on the Mach number and its constancy and employs Python for intricate numerical computation. The culmination of the study involves generating Mach number contour plots and streamlining diagrams for each case using Python, which visually depicts the nuanced evolution of the flow field. Moreover, the study conducts a rigorous comparative analysis of the simulation results for the different cases, exploring the intricate differences in flow behavior across a spectrum of Mach numbers and flow conditions. The discussion section further broadens the scope of inquiry by addressing potential limitations and charting out prospective research directions. By providing a comprehensive exploration of the widespread application of the Poisson equation in fluid mechanics, this paper stands as a beacon for further investigations in the domain and presents invaluable insights for the progressive advancement of fluid mechanics studies in the future.