Open AccessModeling and simulation of fingering pattern formation in a combustion model
Author(s) -
Lina Hu,
Claude-Michel Brauner,
Jie Shen,
Gregory Sivashinsky
Publication year - 2014
Publication title -
mathematical models and methods in applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.582
H-Index - 85
eISSN - 1793-4060
pISSN - 0218-2025
DOI - 10.1142/s0218202515500165
Subject(s) - chaotic , viscous fingering , mechanics , pattern formation , planar , combustion , nonlinear system , partial differential equation , front (military) , computer simulation , computer science , statistical physics , mathematics , mathematical analysis , physics , geology , meteorology , chemistry , computer graphics (images) , geotechnical engineering , organic chemistry , porous medium , quantum mechanics , artificial intelligence , porosity , biology , genetics
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 are presented to demonstrate the evolution of sparse fingers (I) and chaotic fingering (II)
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