Large-eddy simulation of turbulence and turbulent mixing in compressible turbulent flows without and with shear

Turbulent flows are commonly encountered in the natural world and practical applications. Accurate prediction of turbulent flows represents one of the most challenging problems in computational engineering and science. Direct numerical simulations, which completely resolve all turbulent scales, are not affordable for practical turbulent flows. Thereby, large-eddy simulation has emerged as a promising alternative wherein large, energy carrying flow structures are resolved, whereas smaller structures are left unresolved and sub-grid scale models are incorporated to model their effect. The current research is concerned with the development of an accurate, robust large-eddy simulation code, and the investigation and comparison of different numerical schemes and sub-grid scale models for the prediction of turbulence and turbulent mixing phenomena in compressible turbulent flows without and with shear. In particular, these schemes and models are tested in the following three configurations: the viscous Taylor-Green vortex (without shear), the temporally evolving mixing layer (with shear) and the temporally evolving planar jet (with shear).To improve the spectral resolution of the numerical discretisation of the diffusive terms, narrow-stencils are implemented. The results indicate that these schemes can resolve the dissipation of diffusive terms at higher wavenumbers, thereby it is not essential to apply low-pass filtering to obtain a stable solution in compressible large-eddy simulations. Results for the configurations studied show that when functional sub-grid scale models are implemented in conjunction with narrow-stencils, their performance is enhanced considerably compared to the case when they are used with low-pass filtering. Furthermore, for the first time, temporally evolving planar jets are systematically studied at weakly and moderately compressible regimes at large Reynolds number (10,000) using direct numerical simulations and large-eddy simulations. Results obtained for these cases demonstrate significant improvements in the accuracy of large-eddy simulation concerning the mixing of a passive scalar using the shear-improved Smagorinsky sub-grid scale model (recently proposed for incompressible flows). Nonetheless, in cases wherein the effects of compressibility become significant, the results indicate that further modifications are still needed to achieve better levels of accuracy and predictability