“…Concerning the reaction modeling, the situation is even more pressing, and some models employ a simplified set of equations (typically a mixture fraction and a progress variable) to describe the progress of reaction, [5], together with very intricate modeling, [10,11], that result in models that are difficult to use when analyzing practical combustion devices, whereas other models rely on crude assumptions for the modeling of the filtered reaction rates, [12,13]. The present approach, departs noticeably from the conventional lowpass filtered LES, but has similarities with LEM-LES, [8,14], and other recently suggested multi-scale methods, [15,16]. In this approach, we use a multi-scales expansion technique to decompose the reactive Navier-Stokes Equations (NSE) into a cascade of equations for different scales, thereby representing the large-and small scales, respectively.…”