TVD Formulations of the 2D Navier-Stokes Equations for Airfoil Analysis

The application of total variation diminishing (TVD) implicit and explicit schemes to transonic flow around airfoils is presented. Several upwind and symmetric TVD flux limiters from the Non-MUSCL family are examined and compared with Jameson's non-linear artificial dissipation model. Inviscid results indicate that TVD schemes reduce shock smearing while practically eliminating numerical oscillations. Analytical results are presented for a NACA 0012 airfoil for various transonic flow conditions using TVD formulations of the 2D Navier-Stokes equations. Comparisons of computed results with experimental data show good agreement.