## 1 Introduction
While such models present a remarkable advantage against single or two zone models, a mean temperature and gas composition within each zone has still to be imposed by definition. This implies that the calculation of the chemical source terms is done assuming negligible variations in enthalpy and composition spaces within each zone and hence no TCI effects are considered. These simplifications, together with the lack of detailed chemistry sub-models, impact the quality of engine-out emission predictions. An alternative method to consider turbulent mixing as well as detailed chemistry in 0-D is the Stochastic Reactor Model (SRM). The SRM discretizes the mixture in the combustion chamber in a given number of notional particles under the assumption of statistical homogeneity, as opposed to special homogeneity in multi-zone models. Each notional particle features a realization of possible temperature and mixture compositions. TCI is mimicked by stochastic mixing of particles, stochastic heat exchange with the walls and detailed chemistry evaluations. However, as it is the case for detailed chemistry-based 3-D CFD methods, depending on the size of the chemical mechanism considered, the chemistry step may take up to 99% of the simulation time. In addition to mechanism reduction techniques [12], chemistry storage and run-time retrieval methods are viable solutions to reduce computational costs. Different tabulated chemistry-based methods have been proposed primarily for 3-D CFD applications. These methodologies are based on the decoupling of flow and chemistry. While the flow is computed during run-time, the chemistry solution, usually intended as auto-ignition and/or emission formation processes, is computed in a pre-processing step typically performed on a one-time basis for a given fuel. The two major combustion modeling concepts used to decouple flow and chemistry are various flamelet methods, including Conditional Moment Closure (CMC) and the Well-Stirred Reactor (WSR) methods. Remarkable efforts have been made towards formulation of predictive flamelet-based tabulated chemistry solvers for auto-ignition [13; 14; 15; 16; 17] as well as advanced soot and NOx emission formation modeling [18; 19; 20; 21]. The present article is based on the WSR approach. This is the best choice for Probability Density Function (PDF) methods, such as the herein employed SRM. These methods use operator splitting loops to separate vaporization, mixing, compression, heat transfer and chemistry. In these processes, each particle is considered as a well stirred reactor. The chemistry storage is constructed by means of 0-D adiabatic constant pressure/volume reactors across wide ranges of initial pressure, temperature and equivalence ratio. [PERSON] et al. [22] proposed a method where both the high and low temperature ignition delay times are stored in the look-up table. The validation was done under 0-D adiabatic reactor conditions (assuming constant pressure/volume) as well as under diesel engine conditions in 3-D CFD. An improved version of such model was later proposed by [PERSON] et al. [23] where a progress-variable-based approach was used rather than a tabulation of the ignition delays. In this configuration, an additional tabulation dimension is introduced as the tabulation is done across a predefined set of grid points, varying between unburned and fully burned mixture. During run-time, the progress variable source term was retrieved for each cell, and it was used to reconstruct the chemical state. Later improvements of such method proposed by [PERSON] and co-authors [24] also incorporated a turbulence-chemistry interaction term during the tabulation process. Thanks to an additional tabulation dimension, TCI effects could be accounted for in 3-D CFD reactive flow simulations within the Extended Coherent Flame Model (ECFM) framework.