  In this paper we investigate the acceleration of the expansion of premixed
spherical flames and evolution of the cellular patterns on their surfaces. An
asymptotic model is used for the simulations and a spectral numerical algorithm
is employed to study flames over large time intervals. Numerous numerical
experiments indicate that for large enough time intervals the acceleration of
two-dimensional expanding flame ceases and the expansion rate stabilizes to a
value significantly exceeding the burning rate. The importance of the effect of
forcing was also confirmed and the validity of sectorial simulations of closed
flames was studied in order to justify prospective use of the Fourier spectral
model for the three-dimensional spherical flames.
