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# The G-equation model

The flame front propagation can be modelled in term of a G-equation (Kerstein et al. 1988, Karpov et al. 1996):

$\frac{\partial G}{\partial t} +\tilde{u}_{i} \frac{\partial G}{\partial x_{i} } =S_{T} \left|\nabla G\right|,$

where the turbulent flame brush is identified by a given level G^* of the G field. One of the advantages of this approach is that the internal flame structure does not need to be resolved on the computational mesh. Only the G-field, generally much thicker, needs to be resolved. On the other hand, the above G-equation leads to both numerical difficulties and modelling problems such as the not obvious coupling between the G-equation and the mass fraction or energy balance equation and such as the quantification of the turbulent flame speed. This formulation seems to be more suitable for the LES than for RANS (Poinsot and Veynante 2001) .

A more refined formalism based on G-field has been developed by Peters (1999, 2000).

Kerstein A.R., Ashurst W., Williams F., (1988) Field equation for interface propagation in an unsteady homogeneous flow field. Phys. Rev. A., 37, 2728-2731.

Karpov V., Lipatnilov A., Zimont, V. (1996), A test of an engineering model of premixed turbulent combustion. 26th Symposium (Int.) on Combustion, The Combustion Institute, Pittsburgh, 249-257.

Poinsot T. and Veynante D. (2001), Theoretical and Numerical Combustion, Edwards Inc.

Peters N, (1999) The turbulent burning velocity for large-scale and small scale turbulence. J. Fluid Mech. 384, 107-132.

Peters N, (2000) Turbulent combustion, Cambridge University Press.