Large-eddy simulations of compressible Rayleigh–Taylor turbulence with miscible fluids using spatial gradient model

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Large-eddy simulations (LES) and implicit LES (ILES) of three-dimensional compressible Rayleigh–Taylor turbulence with miscible fluids are performed and compared with direct numerical simulation (DNS) at the Atwood number At=0.5 and stratification parameters Sr = 1.0 and 4.0. Three sub-grid-scale (SGS) models including constant-coefficient spatial gradient model (CSGM), dynamic Smagorinsky model (DSM), and dynamic mixed model (DMM) are considered. The CSGM model achieves a high accuracy by using the velocity gradients at the neighboring LES grids. The a priori tests show that the CSGM model has significantly higher correlation coefficients and lower relative errors than traditional SGS models. In the a posteriori tests, the probability density functions of SGS terms predicted by the CSGM model are consistent with the filtered DNS results. The CSGM model can accurately predict the small bubble and spike structures, resulting in good predictions of mixing heights and concentration fields. The instantaneous structures, spectra, and statistics of velocity and vorticity fields are also examined, showing the excellent performance of the CSGM model compared to the ILES, DSM, and DMM models. Moreover, the predictions of the temperature and pressure fields by the CSGM model are significantly better than the traditional SGS models and ILES.