HIGH LEWIS NUMBER COMBUSTION WAVEFRONTS: A PERTURBATIVE MELNIKOV ANALYSIS

被引：19

作者：

Balasuriya, Sanjeeva ^{[1
]}

Gottwald, Georg ^{[2
]}

Hornibrook, John ^{[2
]}

Lafortune, Stephane ^{[3
]}

机构：

[1] Connecticut Coll, Dept Math, New London, CT 06320 USA

[2] Univ Sydney, Sch Math & Stat, Sydney, NSW 2006, Australia

[3] Coll Charleston, Dept Math, Charleston, SC 29424 USA

来源：

SIAM JOURNAL ON APPLIED MATHEMATICS | 2007年 / 67卷 / 02期

基金：

澳大利亚研究理事会; 美国国家科学基金会;

关键词：

combustion waves; high Lewis number; Melnikov's method; slow manifold reduction; Evans function;

D O I：

10.1137/050640849

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The wavefronts associated with a one-dimensional combustion model with Arrhenius kinetics and no heat loss are analyzed within the high Lewis number perturbative limit. This situation, in which fuel diffusivity is small in comparison to that of heat, is appropriate for highly dense fluids. A formula for the wavespeed is established by a nonstandard application of Melnikov's method and slow manifold theory from dynamical systems, and compared to numerical results. A simple characterization of the wavespeed correction is obtained: it is proportional to the ratio between the exothermicity parameter and the Lewis number. The perturbation method developed herein is also applicable to more general coupled reaction-diffusion equations with strongly differing diffusivities. The stability of the wavefronts is also tested using a numerical Evans function method.

引用

页码：464 / 486

页数：23

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