A 2-D compressible Navier-Stokes algorithm using an adaptive unstructured grid

The results of a two-dimensional, compressible, Navier-Stokes solver using an unstructured grid with adaptive remeshing are presented in this paper. Roe’s flux-difference splitting method and Gauss’s Theorem were used correspondingly to represent the inviscid and viscous terms of the Navier-Stokes equation. Temporal integration is performed with a modified Runge-Kutta method. Mesh adaptation is accomplished through five simple error indicators. They are the undivided difference of density, velocity and energy, and the Laplacian of velocity and temperature. After the adaptive process, a global remeshing of the domain was performed using an efficient mesh generator. Two problems were analyzed by the adaptive algorithm. The first was a supersonic flat plate boundary layer at a free stream Mach number M, = 2.0 and Reynolds number (based on the plate length) = 6.5 x lo4. The results were compared with the theoretical Blasius solution. The second case was viscous flow past a NACA 0012 airfoil at zero angle of attack. The free stream Mach number M, = 0.2 and the Reynolds number (based on the airfoil chord) Re, = lo4. The numerical solutions was compared to computational results obtained by the Beam-Warming scheme. Good agreement was observed for both the boundary layer and airfoil computations.Technical report hpcd-tr-1