Abstract
In the present article, we study the existing condition of stable helically propagating combustion wave and transition process of wave patterns. Through our three-dimensional numerical simulation, we get the following results: (1) When physical parameters are fixed so that a combustion wave of steady-state mode is stable in the one-dimensional problem, the planar wave of steady-state mode is stable also in the cylindrical domain. (2) Set physical parameters so that a pulsating wave exists stably for the one-dimensional problem. Then, the planar pulsating wave is still stable in the cylindrical domain if the radius is small while a helical wave takes the place of the pulsating wave if the radius becomes larger. Moreover, we obtain new insights about propagation patterns in the interior of cylindrical domain, differences in propagation patterns between the two-and three-dimensional problems and dependence of propagation patterns on the effective activation energy. The article describes also a finite difference approximation for the Laplacian operator in the cylindrical coordinate.
