Adaptive numerical simulation of pulsating planar flames for large Lewis and Zeldovich ranges

We study numerically the behaviour of pulsating planar flames in the thermo-diffusive approximation. The numerical scheme is based on a finite volume discretization with an adaptive multi-resolution technique for automatic grid adaption. This allows an accurate and efficient computation of pulsating flames even for very large activation energies. Depending on the Lewis number and the Zeldovich number, we observe different behaviours, like stable or pulsating flames, the latter being either damped, periodic, or a-periodic. A bifurcation diagram in the Lewis–Zeldovich plane is computed and our results are compared with previous computations [Rogg B. The effect of Lewis number greater than unity on an unsteady propagating flame with one-step chemistry. In: Peters N, Warnatz J, editors, Numerical methods in laminar flame propagation, Notes on numerical fluid mechanics, vol. 6. Vieweg; 1982. p. 38–48.] and theoretical predictions [Joulin G, Clavin P. Linear stability analysis of nonadiabatic flames: diffusional-thermal model. Combust Flame 1979;35:139–53]. For Lewis numbers larger than 6 we find that the stability limit is again increasing towards larger Zeldovich numbers and not monotonically decreasing as predicted by the asymptotic theory. A study of the flame velocities for different Zeldovich numbers shows that the amplitude of the pulsations strongly varies with the Lewis number. A Fourier analysis yields information on their frequency.