Direct numerical simulation of 2D transonic flows around airfoils

High-accuracy, time-accurate compressible Navier-Stokes solvers have been developed for transonic flows. These solvers use optimized upwind compact schemes (OUCS) and four-stage, fourth order explicit Runge-Kutta (RK4) time integration scheme, details of which can be obtained in Sengupta [Sengupta TK. High Accuracy Computing Methods, fluid flows and wave phenomena. UK: Cambridge Univ. Press; 2013]. Although these compact schemes have been developed originally for direct simulation of incompressible flows, it is shown here that the same can be used for compressible flows, with shock-boundary layer interactions clearly captured for flow past NACA 0012 and NLF airfoils. Numerical higher order diffusion terms which are used for incompressible flows, have been replaced here by the pressure-based artificial diffusions proposed by Jameson et al. [Jameson A, Schmidt W, Turkel E. Numerical solution of the Euler equations by finite volume methods using Ruge-Kutta time stepping schemes. AIAA Paper 1981-1259. AIAA 14th fluid and plasma dynamics conference. Palo Alto, CA; 1981]. Such second and fourth order diffusion terms are used adaptively at selective points, located by the pressure switch. Developed computational methods used here are validated for cases with and without shocks, for which experimental results are available. Apart from surface pressure coefficient, contours of physical quantities are presented to explain the time-accurate results. Presented methods are robust and the results can be gainfully used to study shock formation, drag divergence and buffet onset of flow over airfoils.