The 2-D thennal-diffusive model of premixed flames is solved numerically. The growth rates of the thermal-diffusive instability are compared to the linear theory. It is shown that the discrepancy, although large (a relative error than can be larger than 100%), behaves like O(I/β) as expected by asymptotics (β being the reduced activation energy or Zeldovich number). We additionally present results far in the non-linear domain. They exhibit turbulent behaviour which are qualitatively similar to the dynamical properties of the Kuramoto-Sivashinsky model-equation.
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Denet et al. (1992) studied this question.
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