Implicit large-eddy simulations of turbulent flow in a channel via spectral/hp element methods

The spectral/hp element method [which is the hp-version finite element method, where h denotes the h-version finite element method and p denotes the p-version finite element method (or the spectral element method) with elementwise expansion based on (modified) orthogonal polynomials up to pth-order in each element] together with the regularized spectral vanishing viscosity (SVV) is employed to perform implicit large eddy simulation (iLES) of the turbulent separated flows in a channel with streamwise periodic hill-shaped constriction. The simulations are conducted at a Reynolds number of 10 595 based on the hill height and the bulk velocity magnitude above the crest, where the standard benchmark was presented with abundant experimental and numerical data. The flow statistical properties are discussed in detail, including mean velocities, Reynolds stresses, anisotropy measures, and spectra, which are in good agreement with the available numerical and experimental data in the literature. It is demonstrated that the SVV-iLES model performs at least as well as the established explicit models and therefore, the high-order spectral/hp element method via the calibrated model-free iLES is well-prepared for highly resolved wall-bounded turbulent simulations with large-scale separations and certainly for industrial complex flows.