This thesis presents the development of an entropy-corrected full potential flow solver (EC-Flow) within a finite element framework to enhance the representation of shock waves in transonic flow regimes. By addressing limitations in traditional isentropic full potential flow solvers, EC-Flow improves aerodynamic predictions whilst maintaining low computational cost, making it suitable for early design phases in aeroelastic analysis.

The methodology integrates an entropy correction based on the Rankine-Hugoniot relations, with shock detection achieved through gradient-based and normal Mach number methods. An iterative downstream approach ensures consistent application of the correction across the shock-affected domain.

Results for the NACA0012 and RAE2822 airfoils demonstrate improved shock representation, and faster convergence compared to the uncorrected solver. Validation against Euler solutions confirms the effectiveness of the entropy correction in enhancing accuracy without significant computational overhead.