The statistical behaviour and closure of sub-grid scalar fluxes in the context of turbulent premixed combustion has been assessed based on an a priori analysis of a detailed chemistry Direct Numerical Simulation (DNS) database consisting of three hydrogen air flames spanning the corrugated flamelets (CF), thin reaction zones (TRZ) and broken reaction zones (BRZ) regimes of premixed turbulent combustion. The sub-grid scalar fluxes have been extracted by explicit filtering of DNS data. It has been found that the conventional gradient hypothesis model is not appropriate for the closure of sub-grid scalar flux for any scalar in the context of a multi-species system. However, the predictions of the conventional gradient hypothesis exhibit a greater level of qualitative agreement with DNS data for the flame representing the BRZ regime. The aforementioned behaviour has been analysed in terms of the properties of the invariants of the anisotropy tensor in the Lumley triangle. The flames in the CF and TRZ regimes are characterised by a pronounced two dimensional anisotropy due to strong heat release whereas a three dimensional and more isotropic behaviour is observed for the flame located in the BRZ regime. Two sub-grid scalar flux models which are capable of predicting counter-gradient transport have been considered for a priori DNS assessment of multi-species systems and have been analysed in terms of both qualitative and quantitative agreements. By combining the latter two sgs flux closures a new modelling strategy is suggested where one model is responsible for properly predicting the conditional mean accurately and the other model is responsible for the correlations between model and unclosed term. Detailed physical explanations for the observed behaviour and an assessment of existing modelling assumptions have been provided. Finally, the classical Bray-Moss-Libby theory for the scalar flux closure has been extended to address multispecies transport in the context of Large Eddy Simulations (LES).

A new direct numerical simulation (DNS) code for multi-component gaseous reacting flows has been developed at KAUST, with the state-of-the-art programming model for next generation high performance computing platforms. The code, named KAUST Adaptive Reacting Flows Solver (KARFS), employs the MPI+X programming, and relies on Kokkos for "X" for performance portability to multi-core, many-core and GPUs, providing innovative software development while maintaining backward compatibility with established parallel models and legacy code. The capability and potential of KARFS to perform DNS of reacting flows with large, detailed reaction mechanisms is demonstrated with various model problems involving ignition and turbulent flame propagations with varying degrees of chemical complexities.

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