MICROSCOPIC SIMULATION OF A WAVE-FRONT - FLUCTUATION EFFECTS ON PROPAGATION VELOCITY AND WIDTH

Following the direct simulation Monte Carlo method introduced by Bird, we realize a stochastic simulation of the Boltzmann equation associated with a dilute reacting gas mixture. The corresponding macroscopic equation, first studied by Fisher, and by Kolmogorov, Petrovsky and Piskunov, admits wave front solutions propagating into an unstable state with a velocity which is not imposed by the dynamics but depends on the initial conditions. Starting with a step function initial condition for which the theoretical deterministic results are well known, we simulate a uniformly translating profile whose average properties agree with the macroscopic predictions. Moreover, a strong correlation between front width and propagation velocity fluctuations is observed. This property can be viewed as a first step toward the elucidation of a stochastic selection mechanism for the propagation velocity.