In this paper, the numerical study of compressible flow around an airfoil is presented. The flow is analyzed in steady state for subsonic, transonic and even in the supersonic regimes at different angles of attack. In finite-volume method convective fluxes are calculated and compared by two schemes. Modified Jameson flux scheme based on flux averaging with pressure correction is used. Modified Roe scheme which is one of the characteristics-based schemes, with modification in calculation of Jacobian matrix based on Mach number is implemented. Second-order accuracy is used with artificial dissipation to overcome numerical oscillations. The fifth-order Runge–Kutta scheme is used for time discretization. A proper boundary condition based on characteristics is applied. Numerical experiments are performed on the NACA 0012 and also NACA 4412 airfoils. The results confirm the superiority of modified upwind Roe scheme regarding the accuracy, stability and convergence. Results are compared to available results in literature and a good agreement is noticed.
