The G-equation combustion model is based on the turbulent premixed combustion flamelet theory of Peters (2000) [69] . This theory addresses two regimes of practical interest:
The corrugated flamelet regime where the entire reactive-diffusive flame structure is assumed to be embedded within eddies of the size of the Kolmogorov length scale η; and
The thin reaction zone regime where the Kolmogorov eddies can penetrate into the chemically inert preheat zone of the reactive-diffusive flame structure, but cannot enter the inner layer where the chemical reactions occur.
For application of the G-equation model to IC engine applications, this theory was further developed by Tan et al. [94] and by Liang et al. [[51], [52]].
The G-equation model consists of a set of Favre-averaged level-set equations. This includes
the equations for the Favre mean, 
, and its variance, 
, as well as a model equation for the turbulent/laminar flame surface area
ratio 
. Application of the equation for the turbulent/laminar flame surface
area ratio results in an explicit expression for the turbulent flame speed 
. Together with the Reynolds-averaged Navier-Stokes equations and the
turbulence modeling equations, these provide a complete set of equations to describe premixed
turbulent flame-front propagation. The equation set used in Ansys Forte is:
 | (7–15) |
 | (7–16) |
where 
denotes the tangential gradient operator;
is the fluid velocity; 
is the velocity of the moving vertex; 
and 
are the average densities of the unburned and burned mixtures, respectively;
is the turbulent diffusivity; 
is the Favre mean flame front curvature; 
, 
, 
, and 
are modeling constants (cf. ref. [69]);
and 
are the Favre mean turbulent kinetic energy and its dissipation rate from the
RNG k-ε model; 
is the turbulence intensity.