Characteristic-Based Flux Splitting to Solve Compressible Flow over an Airfoil

Abstract

Current paper presents the Characteristics-based Flux Splitting to improve the numerical behaviour for the inviscid compressible flows. NACA 0012 airfoil is chosen as the test case at angles of attack in the steady state for subsonic, transonic, and supersonic regimes. To calculate the convective fluxes of the Euler equations by the finite volume approach, the Characteristics-based Flux Splitting (CFS) based on the local Mach number is introduced and compared with the conventional Jameson Averaging Method (JAM). To overcome the numerical oscillations especially at the shocked region, artificial dissipation is implemented for the JAM scheme while there is no need to such dissipations for the CFS scheme. For the time integration the Runge–Kutta method is applied. Consistent boundary condition based on characteristics is employed. The results prove the excellence of the CFS scheme regarding the accuracy, stability and convergence. The results are validated and compared with those of others available in the literature.