Runge-Kutta Finite-Volume Simulation of Laminar Transonic Flow over a NACA 0012 Airfoil Using the Navier-Stokes Equations

摘要

For the solution of the compressible Navier-Stokes equations, a finite-volume space discretization of the viscous fluxes is presented. The gradients of the stress tensor are approximated in the cells by means of surface integrals along the cell boundaries. Similar to the inviscid fluxes, the viscous fluxes over the cell interfaces are evaluated by the arithmetic averages of their values in adjacent cells. A linear stability condition is derived for the local time steps of the three stage explicit Runge-Kutta method used for time discretization. Employing a 257x65 O-mesh generated by transfinite interpolation, the method is verified for laminar transonic flow at Reynolds numbers of 0(100) over a NACA0012 airfoil and compared with 193x65 C-mesh results of an implicit finite-difference scheme. The C-mesh is recommended for viscous flow near the trailing edge.