Enhancing shock buffet predictions on a supercritical airfoil via high-order low-dissipation schemes

High-fidelity simulations of shock wave/boundary-layer interactions (SWBLI) require numerical methods with superior accuracy, resolution, and stability. This study incorporates optimized weighted essentially non-oscillatory (WENO-K) schemes into a finite difference solver on structured grids. The WENO-K schemes, with robust shock-capturing capabilities and adaptively optimized spectral properties, significantly improve unsteady Reynolds-averaged Navier-Stokes (URANS) simulations for SWBLI. Numerical simulations investigate unsteady shock buffet on the upper surface of a supercritical airfoil at Mach 0.73 and an angle of attack of 3.5°. The third-, fifth-, and seventh-order WENO-K schemes are employed to evaluate the influence of accuracy in convection flux discretization and numerical dissipation on shock buffet predictions. Results show excellent agreement with the experiment in predicting shock buffet frequency, as well as statistical pressure and velocity profiles. Notably, URANS simulations using WENO-K schemes outperform several published results obtained by URANS and hybrid URANS/LES (large eddy simulation) methods under comparable grid and time scales. The seventh-order WENO-K scheme effectively resolves intricate transient SWBLI flow features, including (1) periodic shock oscillations, (2) strong shear layers emanating from the shock, (3) separation bubble formation downstream of the shock, (4) wake vortex oscillations induced by the dynamic evolution of separation bubbles and shear layer instability, and (5) pressure wave propagation and feedback. These results highlight the importance of high-order, low-dissipation schemes in resolving the complex feedback mechanisms between shock waves, boundary layers, and wake dynamics. This study demonstrates that URANS method with high-order WENO-K schemes significantly enhances accuracy in predicting shock buffet in engineering.