Dynamics of curved reaction fronts under a single-equation model

Bhanot, R. P. and Strunin, D.V. (2018) Dynamics of curved reaction fronts under a single-equation model. Australian and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal, 57. C398-C412. ISSN 1445-8735

Abstract

Fronts of reaction in certain systems (such as so-called solid flames)can be modelled by a high-order nonlinear partial differential equation, which we analyse numerically in this paper. Previously Strunin obtained stable spinning solutions of the equation using the Galerkin method. Here we use a more sophisticated and arguably more powerful method to study the equation further, namely the one-dimensional radial basis function method. As an initial step, we elaborated the numerical code and tested it by reproducing the spinning regimes for a range of initial conditions. In new series of experiments, we found a regime where the front is shaped as a pair of kinks spinning in a stable joint formation. The settled character of this regime is demonstrated.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Published version embargoed until 1 April 2020 (2 years), in accordance with the copyright policy of the publisher. Published as part of the Proceedings of the 12th Biennial Engineering Mathematics and Application Conference.
Faculty/School / Institute/Centre: Current - Faculty of Health, Engineering and Sciences - School of Agricultural, Computational and Environmental Sciences
Date Deposited: 18 Mar 2019 00:32
Last Modified: 11 Jun 2019 00:07
Fields of Research : 01 Mathematical Sciences > 0102 Applied Mathematics > 010204 Dynamical Systems in Applications
Socio-Economic Objective: E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
Identification Number or DOI: doi:10.21914/anziamj.v57i0.10446
URI: http://eprints.usq.edu.au/id/eprint/36176

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