Complex dynamics generated by a sharp interface model of self-propagating high-temperature synthesis

Weakly Nonlinear and Numerical Analyses of Dynamics in a Solid Combustion Model

“…The authors attributed a lack of sequential secondary bifurcations to the difference between the point-source and distributed-kinetics models (as in [1]). Later, however, in [9], the entire spectrum of behavior was observed for the free-interface model, as previously had been seen for distributed kinetics.…”

“…Simulations on all these models show the same dynamical behaviors as one pushes the bifurcation parameters deeper into the instability regions. In particular, numerical simulations and analysis in [9] show that dynamics of the two-sided and one-sided problems agree extremely closely.…”

“…In [9], the authors performed numerical computations on a second model of solid combustion as well. They motivate it by noting that both the reaction-diffusion model as in [18] and the free-interface model in [14] assume a constant value of thermal diffusivity.…”

“…All the models discussed in this literature review exhibit the same spectrum of dynamics as experiments. Specifically, we refer to computed solutions of (i) the reaction-diffusion system governed by the full Arrhenius kinetics (e.g., [5]), (ii) the reaction-diffusion system with Arrhenius kinetics with a cutoff (e.g., [1]), and models that use point-source kinetics like (iii) the free-interface ("two-sided") model with constant heat diffusivity (e.g., [9]), as well as (iv) the freeboundary ("one-sided") model, in which heat transfer behind the flame front (in the burned matter) is qualitatively unimportant (e.g., [9]). Simulations on all these models show the same dynamical behaviors as one pushes the bifurcation parameters deeper into the instability regions.…”

On Oscillatory Instability in Convective Burning of Gas-Permeable Explosives

“…In this context the model has been explored extensively in recent years, and there is a sizable volume of analytical and numerical results on its intrinsic dynamics (see, for example, Refs. [13][15] and literature therein). At κ = 1 the model is also formally identical to that for the pressure-driven subsonic combustion in an inert porous bed filled with an explosive gas [6].…”