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Travelling waves and oscillations in Sal'nikov's combustion reaction in a compressible gas

Citation

Paul, RA and Forbes, LK, Travelling waves and oscillations in Sal'nikov's combustion reaction in a compressible gas, The ANZIAM Journal, 56, (3) pp. 233-247. ISSN 1446-1811 (2015) [Refereed Article]

Copyright Statement

Copyright 2015 Australian Mathematical Society

DOI: doi:10.1017/S1446181114000479

Abstract

We consider a two-step Salínikov reaction scheme occurring within a compressible viscous gas. The first step of the reaction may be either endothermic or exothermic, while the second step is strictly exothermic. Energy may also be lost from the system due to Newtonian cooling. An asymptotic solution for temperature perturbations of small amplitude is presented using the methods of strained coordinates and multiple scales, and a travelling wave solution with a sech-squared profile is derived. The method of lines is then used to approximate the full system with a set of ordinary di fferential equations, which are integrated numerically to track accurately the evolution of the reaction front. This numerical method is used to verify the asymptotic solution and investigate behaviours under di fferent conditions. Using this method, temperature waves progressing as pulsatile fronts are detected at appropriate parameter values.

Item Details

Item Type:Refereed Article
Keywords:combustion, solitons, pulsatile waves, strained coordinates
Research Division:Mathematical Sciences
Research Group:Applied Mathematics
Research Field:Dynamical Systems in Applications
Objective Division:Expanding Knowledge
Objective Group:Expanding Knowledge
Objective Field:Expanding Knowledge in the Mathematical Sciences
Author:Paul, RA (Mr Rhys Paul)
Author:Forbes, LK (Professor Larry Forbes)
ID Code:100216
Year Published:2015
Web of Science® Times Cited:2
Deposited By:Mathematics and Physics
Deposited On:2015-05-07
Last Modified:2016-06-01
Downloads:0

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