Innovative Numerical Method to Partially Solve the Airfoil Flow

Abstract

With the meteoric rise of modern computer science, computational fluid dynamics (CFD) has evolved into a formidable tool adept at addressing multifaceted challenges across diverse domains. Historically, CFD's maiden application was in the aviation sector, aimed at refining the aerodynamic contours of airfoils. Fast forward several decades and its deployment in this arena has reached unparalleled sophistication. This paper harnesses numerical methodologies within CFD to decipher flow dynamics around an airfoil. Central to this exploration is the small disturbance equation, a derivative of the full potential equation. The study meticulously discretizes this equation using advanced mathematical techniques. Furthermore, boundary conditions, namely the wall side and Neumann, are judiciously employed to ascertain boundary point values. Leveraging Python-based iterations, we derive numerical solutions for streamlining patterns and Mach number contours. A rigorous error analysis affirms the validity and efficacy of our results. While the study acknowledges certain inherent limitations, the findings compellingly delineate the flow characteristics around the airfoil in both subsonic and supersonic scenarios, offering valuable insights for future aerodynamic endeavors.