Self-Adaptive Turbulence Eddy Simulation with a high-order finite differencing method for high Reynolds number complex flows

Accurate prediction of high Reynolds number wall-bounded flows is a challenge for turbulence modeling and numerical discretization. Moreover, complex engineering applications increase the difficulties in implementing robust and low-dissipation numerical schemes. A newly developed unified turbulence approach, Self-Adaptive Turbulence Eddy Simulation (SATES), is assessed in the simulation of a multi-element 30P30N airfoil at a high Reynolds number of 1.71 × 106. To reduce the numerical error, high-order finite differencing-based weighted compact nonlinear schemes (WCNSs) are successfully applied. The effects of grid resolution, numerical schemes and turbulence model are investigated by grouping studies. The SATES shows low sensitivity to grid resolution and predicts satisfactory results even on a coarse grid containing approximately 7.2 million cells. Compared with second-order accurate central differencing, the high-order accurate WCNS has less numerical dissipation and significantly improves the resolution of turbulence structures and the accuracy of numerical results. Z-type nonlinear weighted averaging interpolation, designed for shock capturing property in the WCNS scheme, leads to extra numerical dissipation and affects the accuracy of the results. The numerical results of the SATES are more accurate than those of the Smagorinsky Large Eddy Simulation (LES) and the Improved Delayed Detached Eddy Simulation (IDDES). The SATES provides sufficient modeling of the boundary layer on the coarse grid and a fast 'transition' from the RANS to the LES mode for accurate prediction of the separated shear layer and flap boundary layer separation. These results confirm that the SATES turbulence modeling approach is efficient for high Reynolds number flows and that the high-order accurate WCNS schemes show sufficient robustness and accuracy for engineering applications.