Despite the onset of peta-scale computing, simulations of reacting flows with detailed chemistry is still considered computationally expensive. Better understanding of the chemistry of various fuels has led to increase in the complexity of the simulations in an effort to compute flows with real complex fuels. The increase in complexity makes CFD simulations prohibitively expensive even for the next generation of exa-scale computing. To have accurate reacting flow simulations with detailed chemistry at realisable costs some sort of cost mitigation strategy is to be applied. Solution of the chemistry in reacting flows is one of the most expensive steps of such simulations as it involves solving a system of highly non-linear stiff equations. There have been various methods proposed to reduced this computational costs at the expense of some assumptions. These methods can be broadly classified into two categories: (1) methods based on tabulation which include ISAT and Flamelet methods, and (2) methods based on adaptive chemistry. Former methods are developed to work on specific regimes of combustion and are known to predict reacting flows accurately, but when used outside this regime they may fail.

The present project falls under the adaptive chemistry category and aims to develop a numerical framework for the study of turbulent flames at various regimes using high-fidelity numerical simulations with on-the-fly adaptive kinetics. The chemistry reduction process is based on the Path Flux Analysis (PFA) enforcing Adaptive Chemistry (AC) based on local conditions.

PFA is a chemistry reduction method based on truncating reaction pathways. Key species are defined, usually reactants, major products, and species of specific interests like pollutants. PFA classifies reaction pathways between theses key species and eliminates pathways which fall below a specified threshold. PFA algorithm is formulated in a way that multiple generations of intermediate species can be tracked. In literature a universal threshold is specified, however, as the reaction pathways and their weights depend on the local chemical state, a universal definition of the threshold would lead to different levels of reduction and can lead to over-reduced/under-reduced regions. In this work the definition of the threshold is modified to be dependent on the local thermodynamic state, this ensures a uniform level of reduction.

Current state-of-the-art model of dynamic adaptive chemistry rely on an error estimator which decides when and where in the computational domain the reduction algorithm to be applied. This error estimator, usually a correlation function between specific chemical species is user specified and has a great impact on the reduction. This makes it necessary for the user to have an \textit{a priori} understanding of problem and its chemistry. The methodology developed in this project eliminates the need for this error estimator as the reduced chemistry is tabulated based on a set of controlling variables. These controlling variables have global definitions and are identified for different regimes of combustion. The expensive operation of chemistry reduction is tabulated, hence reducing the computational time needed for chemistry reduction significantly.

State of the art reduction models and the proposed model are tested in: (1) laminar steady-state cases: premixed free flame, counterflow diffusion, and partially premixed flames; and (2) transient cases: auto-ignition, flame kernel propagation in stratified mixtures, flame vortex interaction, and a reacting Taylor-Green vortex. The proposed model is found to predict solutions with the same accuracy as the state of the art models in steady state cases and performs better in transient cases due to its nature of chemistry reduction which makes it applicable to a variety of combustion problems without any tuning. Computationally the proposed model was found to be between 5 to 20 $\%$ faster for specific cases than the respective reference case with no chemistry reduction.