Different NS method for calculating steady and unsteady transonic viscous flows around airfoils

The flow field around airfoil was analyzed by solving the 2-dimensional time-averaged compressible NS equations with the Baldwin-Lomax turbulence model. An implicit lower-upper-factorized algorithm was constructed in a body-fitted coordinate system. In the algorithm, a simple third-order upwind scheme was adopted. The grid of type C that was generated by an algebraic method was visualized to be rigidly attached to the airfoil so as to save computation time. Some examples for the steady and unsteady transonic viscous flows around NACA 0012 airfoil were calculated. The part of the grid of type C for NACA 0012 airfoil and the characteristics of the variations of coefficients C_N and C_M with angle of attack α for two different unsteady transonic flows are shown. Numerical results are in good agreement with experimental data.