Numerical simulation of burning front propagation

Abstract

In the context of a numerical experiment, it is shown that the switching wave described by the reaction-diffusion equation can be delayed at a medium inhomogeneity with a thickness Δ and amplitude Δβ for a finite time τ = τ(Δβ, Δ) up to a complete stop at it (τ = ∞). Critical values Δβ _c and Δ _c corresponding to the autowave stop are found. The similarity laws $\tau \sim (\Delta _c - \Delta )^{ - \gamma _\Delta }$ and $\tau \sim (\Delta \beta _c - \Delta \beta )^{ - \gamma _\beta }$ are established, and the critical indices and are found. The similarity law is established for critical values of amplitude and width of the inhomogeneity corresponding to the autowave stop Δβ _c ∼ Δ ^-δ _c where δ ≈ 1.