G equation

In Combustion, G equation is a scalar ${\displaystyle G(\mathbf {x} ,t)}$ field equation which describes the instantaneous flame position, first introduced by Forman A. Williams in 1985 as a model for a premixed turbulent combustion.

The G equation reads as

where

The flame location is given by ${\displaystyle G(\mathbf {x} ,t)=G_{o}}$ which can be defined arbitrarily such that ${\displaystyle G(\mathbf {x} ,t)>G_{o}}$ is the region of burnt gas and ${\displaystyle G(\mathbf {x} ,t)<G_{o}}$ is the region of unburnt gas. The normal vector to the flame is ${\displaystyle \mathbf {n} =-\nabla G/|\nabla G|}$. The burning velocity is constant for unstretched flame and for the the stretched flame the expression is given by

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