In this study we generate optimal Runge-Kutta (RK) schemes for converging the Artificial Compressibility Method (ACM) using dual time-stepping with high-order unstructured spatial discretizations. We present optimal RK schemes with between s = 2 and s = 7 stages for Spectral Difference (SD) and Discontinuous Galerkin (DG) discretizations obtained using the Flux Reconstruction (FR) approach with solution polynomial degrees of k = 1 to k = 8. These schemes are optimal in the context of linear

more »

... ction with predicted speedup factors in excess of 1.80× relative to a classical R K 4,4 scheme. Speedup factors of between 1.89× and 2.11× are then observed for incompressible Implicit Large Eddy Simulation (ILES) of turbulent flow over an SD7003 airfoil. Finally, we demonstrate the utility of the schemes for incompressible ILES of a turbulent jet, achieving good agreement with experimental data. The results demonstrate that the optimized RK schemes are suitable for simulating turbulent flows and can achieve significant speedup factors when converging the ACM using dual time-stepping with high-order unstructured spatial discretizations.