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

Current paper presents the Characteristics-based Flux Splitting to improve thenumerical behaviour for the inviscid compressible flows. NACA ۰۰۱۲ airfoilis 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 theEuler equations by the finite volume approach, the Characteristics-based FluxSplitting (CFS) based on the local Mach number is introduced and comparedwith the conventional Jameson Averaging Method (JAM). To overcome thenumerical oscillations especially at the shocked region, artificial dissipation isimplemented for the JAM scheme while there is no need to such dissipationsfor the CFS scheme. For the time integration the Runge–Kutta method isapplied. 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 thoseof others available in the literature.

Keywords:

Finite-volume method , Euler equations , Compressible flow , Method of Characteristics , NACA ۰۰۱۲