In this paper, a consistent and rigorous formulation is developed for the coupling of the G-equation model to an LES flow solver that describes the interactions of the scales of the flame, the turbulence, and the filtering procedure from the resolved turbulence regime to the broadened preheat regions regime. A progress variable equation is introduced to describe the filtered flame Structure. The models provided for the sub-filter diffusivity and the filtered reaction term appearing in this equation are consistent with the Solution of the G-equation model. The solution of the progress variable equation ensures that the resolved part of the turbulent mixing in the preheat region can be described. However, the C-field is underresolved if the sub-filter Damkohler number is not much smaller than unity, and hence the Solution of the C-equation cannot be expected to produce the Correct flame propagation speed. The Coupling With the G-equation ensures that the flame front described by the filtered reaction progress variable moves with the correct propagation velocity, independent of numerical diffusion caused by all underresolution of the flame. Formulations both for low-Mach number flow solvers and for fully compressible solvers are presented. To validate the formulation, the model is applied in compressible LES Of two turbulent flames anchored by a triangular flame-holder. For the statistically stationary case, the mean and RMS progress variable are in very good agreement with experimental data, demonstrating that the model correctly reproduces the flame anchoring and the flame-turbulence interactions in the recirculation zone. For the acoustically pulsed case, the LES fields show the same large scale fluctuations that are present in the experimental data. (c) 2009 The Combustion Institute