FORMATION OF WRINKLES IN OUTWARDLY PROPAGATING FLAMES

Numerical integrations of the partial differential equation proposed b y Filyand, Sivashinsky, and Frankel [Physica D 72, 110 (1994)] to desc ribe the dynamics of outward accelerating flames are presented. The co mputational results reported by Filyand, Sivashinsky, and Frankel are confirmed: as time increases, a repetitive formation of cusps, as well as a rapid (power-law) expansion of the mean flame radius, are observ ed. However, the identification of invariant subspaces for the equatio n shows that even when the initial condition belongs to such subspaces , numerical round-off errors are responsible for excursions of the sol ution outside these subspaces. In Fourier space, this corresponds to t he generation of spurious Fourier modes that grow as time increases. T his computational error is controlled here by a filter that forces the solution, at each time step, to stay inside the invariant subspaces. The results of our filtered simulations are very similar to those resu lting from unfiltered integrations, showing that both the formation of cusps and the rapid acceleration of the dame front are independent of the growth of spurious Fourier modes. The connection between such dyn amics and exact pole solutions of the equation (in which the number of poles is fixed) is investigated. It is found that the latter are unst able and the more complicated (stable) dynamics consists of successive instabilities through which the dame front closely follows a (2N + 1) -pole solution before approaching a (2N + 3)-pole solution. These migr ations are responsible for both the formation of new cusps and the rap id power-law acceleration of the mean front.