Reaction-Diffusion Equation and G-Equation Approaches Reconciled in Turbulent Premixed Combustion Modelling

Stochastic fluctuations described by an adequate probability density function are imposed to the average flame position in order to give a proper formulation of the flame surface propagation in turbulent premixed combustion. An evolution equation of reaction-difffusion type is derived for an observable that can be understood as the effective burned fraction. When stochastic fluctuations are removed, the G-equation along the motion of the mean flame position is recovered suggesting that approaches based on reaction-diffusion equations and G-equation are indeed complementary and they can be reconciled. Moreover, when a plane front is assumed, the Zimont & Lipatnikov model is recovered. This last result suggests that the proposed equation can be considered as the natural extension of the Zimont & Lipatnikov model to the case with non null mean curvature.