Nonlinearly Stable Flux Reconstruction for Aerodynamic Transitional Flow Simulations

The current research aims to demonstrate the implicit large eddy simulation (ILES) of wall-bounded turbulent flows using the Nonlinearly Stable Flux Reconstruction (NSFR) scheme. The NSFR schemes utilize the Flux Reconstruction (FR) formulation, using correction functions to allow larger explicit time steps than Discontinuous Galerkin (DG). For industrial-size cases, such as flows over aerodynamic profiles, the larger time step from the NSFR scheme constitutes a significant reduction in computational cost. The scheme is also provably non-linearly stable, yielding a robust scheme that is stable on arbitrarily coarse meshes. Contrary to conventional DG schemes, the NSFR scheme is also stable without over-integration or upwind-type dissipation. In the case of turbulence simulations, such as LES, this means the scheme does not require the dissipation from an SGS model for stability, and is thus well adapted for ILES. The transitional flow over a Selig–Donovan (SD) 7003 airfoil at Re = 60,000 and angle of attack of 8° is simulated. The complex flow case exhibits a laminar region, followed by a laminar separation bubble (LSB) and by a transition in the separated flow and subsequent turbulent reattachment. The complexity of the flow renders conventional techniques, such as RANS, incapable of accurately resolving the underlying physics. Pressure distribution, skin friction, and boundary profiles are in good agreement with previous numerical studies. Reynolds stresses are also in good agreement with previous studies. This study is the first to investigate the NSFR scheme for the simulation of separated turbulent flows over complex geometries.