Despite the significant improvement of computational resources, large eddy simulations (LES) are too expensive to be applied to wide ranges of operating conditions and multiple engine architectures. Efficient models employed in quasi/zero-dimensional approaches may offer an attractive alternative for engine calibration or optimisation. Despite their fair predictive capability, validity is typically limited to around their calibration region and is subject to uncertainties that stem from heuristic simplifications. The validity of the individual sub-models is rarely assessed using detailed three-dimensional (3-D) simulations over a wide range of combustion regimes. The objectives of this work are the following: (i) to present a formal reduction of widely applied 3-D LES combustion sub-models found in the literature with particular emphasis on the early flame development and flame-wall interaction, (ii) to assess the assumptions/approximations introduced in quasi-dimensional (Q-D) modelling using Direct Numerical Simulation (DNS), and (iii) to refine the Q-D models used currently, using formally-derived sub-models. It is found that many of the refinements introduced noticeably improve the accuracy of the Q-D model. The functional form of the models obtained through formal reduction of various LES combustion submodels presents similarities and agrees well with the heuristic functions that can be found in existing QD models. Ultimately, this study enhances the transferability of insights from fundamental investigations to real engine applications, which can be useful for future Q-D model development and validation. (C) 2020 The Combustion Institute. Published by Elsevier Inc. All rights reserved.