Modeling and simulation of fingering pattern formation in a combustion model

Lina Hu, Claude Michel Brauner, Jie Shen, Gregory I. Sivashinsky

Research output: Contribution to journalArticlepeer-review

Abstract

We consider a model of gas-solid combustion with free interface proposed by L. Kagan and G. I. Sivashinsky. Our approach is twofold: (I) We eliminate the front and get to a fully nonlinear system with boundary conditions; (II) We use a fourth-order pseudo-differential equation for the front to achieve asymptotic regimes in rescaled variables. In both cases, we implement a numerical algorithm based on spectral method and represent numerically the evolution of the char. Fingering pattern formation occurs when the planar front is unstable. A series of simulations is presented to demonstrate the evolution of sparse fingers (I) and chaotic fingering (II).

Original languageEnglish
Pages (from-to)685-720
Number of pages36
JournalMathematical Models and Methods in Applied Sciences
Volume25
Issue number4
DOIs
StatePublished - 22 Apr 2015

Keywords

  • Asymptotics
  • Fingering
  • Free interface
  • Gas-solid combustion
  • Pattern formation.
  • Smouldering
  • Spectral method

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