Multigrid based aerodynamical simulations for the NACA 0012 airfoil

The major considerations in the design of effective methods for computational aerodynamics are the capability to treat flows over complex geometrical shapes with proper representation of shock waves, discontinuities and viscous effects. The present work extends the numerical method used to solve compressible flows for the solution of almost incompressible fluid flow. The technique is based on the finite volume explicit Runge–Kutta multistage scheme with central spatial discretization in combination with multigrid and preconditioning. The discretization used follows the cell-centered arrangement of the control volume for the flow variables. Numerical tests are carried out for Mach numbers ranging from 0.8 to 0.002 and the results are found to compare well with analytical/experimental data available in the literature. A spectral radii comparison is also presented and helps to understand what the preconditioning really does with the characteristic variables. Besides, some solutions presented here were obtained for parameter values excluded from the range found in the literature (such as Mach 0.002 over the NACA 0012 airfoil) employing the same preconditioning technique