Asymptotic Analysis in a Gas-Solid Combustion Model with Pattern Formation

TL;DR

This paper derives a nonlinear equation for flame front dynamics in a gas-solid combustion model, showing asymptotic behavior approaching the Kuramoto-Sivashinsky equation, supported by numerical simulations of pattern formation.

Contribution

It introduces a new third-order nonlinear equation for the flame front in a combustion model and demonstrates its asymptotic relation to the Kuramoto-Sivashinsky equation.

Findings

The interface dynamics asymptotically approach the Kuramoto-Sivashinsky equation.

Numerical simulations illustrate complex pattern formation.

The derived equation captures key features of flame front evolution.

Abstract

We consider a free interface problem which stems from a solid-gas model in combustion with pattern formation. We derive a third-order, fully nonlinear, self-consistent equation for the flame front. Asymptotic methods reveal that the interface approaches a solution of the Kuramoto-Sivashinsky equation. Numerical results are presented which illustrate the dynamics.