Viscous computations using a direct solver

Laminar viscous flows over airfoils are investigated analytically, applying the flux-difference splitting scheme of Roe (1986) to solve the thin-layer Navier-Stokes equations. Central-difference discretization is used for the viscous terms, and a fully implicit implementation is employed to minimize the Reynolds-number effect on convergence. Results for flows at freestream Mach number 0.5 and Reynolds number 5000 over NACA0012 airfoils at angles of attack 0 and 3 deg are presented graphically and discussed in detail. Good agreement with previous calculations is obtained, with accurate reproduction of essential features despite the use of coarser meshes.