Implicit Large-Eddy Simulation for the High-Order Flux Reconstruction Method

High-order methods have demonstrated their potential in large-eddy simulations of turbulent flows with relatively low Reynolds numbers. The cost becomes a serious limiting factor for high-Reynolds-number problems. A promising approach to reduce the cost of these simulations is the hybrid Reynolds-averaged Navier-Stokes/large-eddy simulation approach. In this paper, a new hybrid Reynolds-averaged Navier-Stokes implicit large-eddy simulation approach for the high-order flux reconstruction/correction procedure via reconstruction method is developed based on a simple algebraic version of the Spalart-Allmaras model in the vicinity of solid walls and an implicit large-eddy simulation approach elsewhere. Despite its simplicity, this approach has demonstrated good performance in simulating turbulent flow at relatively high Reynolds numbers.