Modeling and simulation of fingering pattern formation in a combustion model

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

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

Funding

FundersFunder number
US–Israel Binational Science Foundation2012-057
National Natural Science Foundation of China11371298, 91130002
Israel Science Foundation335/13

    Keywords

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

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