Large-Eddy Simulation of Transonic Buffet Using Matrix-Free Discontinuous Galerkin Method

Abstract

We present an implicit large-eddy simulation of transonic buffet over the OAT15A supercritical airfoil at Mach number 0.73, angle of attack 3.5 deg, and Reynolds number . The simulation is performed using a matrix-free discontinuous Galerkin (DG) method and a diagonally implicit Runge–Kutta scheme on graphics processor units. We propose a Jacobian-free Newton–Krylov method to solve nonlinear systems arising from the discretization of the Navier–Stokes equations. The method successfully predicts the buffet onset, the buffet frequency, and turbulence statistics owing to the high-order DG discretization and an efficient mesh refinement for the laminar and turbulent boundary layers. A number of physical phenomena present in the experiment are captured in our simulation, including periodical low-frequency oscillations of shock wave in the streamwise direction, strong shear layer detached from the shock wave due to shock-wave/boundary-layer interaction and small-scale structures broken down by the shear-layer instability in the transition region, and shock-induced flow separation. The pressure coefficient, the root mean square of the fluctuating pressure, and the streamwise range of the shock wave oscillation agree well with the experimental data. The results suggest that the proposed method can accurately predict the onset of turbulence and buffet phenomena at high Reynolds numbers without a subgrid scale model or a wall model.