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TRAVELLING WAVES AND OSCILLATIONS IN SAL’NIKOV’S COMBUSTION REACTION IN A COMPRESSIBLE GAS

Part of: Compressible fluids and gas dynamics, general

Published online by Cambridge University Press:  19 January 2015

RHYS A. PAUL  and
LAWRENCE K. FORBES
RHYS A. PAUL*
Affiliation:
School of Mathematics and Physics, University of Tasmania, Tasmania 7001, Australia email Rhys.Paul@utas.edu.au, Larry.Forbes@utas.edu.au
LAWRENCE K. FORBES
Affiliation:
School of Mathematics and Physics, University of Tasmania, Tasmania 7001, Australia email Rhys.Paul@utas.edu.au, Larry.Forbes@utas.edu.au
*
✉Rhys.Paul@utas.edu.au
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Abstract

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We consider a two-step Sal’nikov 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 differential 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 different conditions. Using this method, temperature waves progressing as pulsatile fronts are detected at appropriate parameter values.

Keywords

Sal’nikov reactioncombustionsolitonspulsatile wavesstrained coordinatesmultiple scalesmethod of lines

MSC classification

Primary: 76N15: Gas dynamics, general
Type
Research Article
Information
The ANZIAM Journal , Volume 56 , Issue 3 , January 2015 , pp. 233 - 247
Copyright
© 2015 Australian Mathematical Society 

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