Dynamics of curved reaction fronts under a single-equation model

Article

Bhanot, R. P. and Strunin, D.V.. 2018. "Dynamics of curved reaction fronts under a single-equation model." Australia and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal. 57, pp. C398-C412. https://doi.org/10.21914/anziamj.v57i0.10446
Article Title

Dynamics of curved reaction fronts under a single-equation model

ERA Journal ID43
Article CategoryArticle
AuthorsBhanot, R. P. (Author) and Strunin, D.V. (Author)
Journal TitleAustralia and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal
Journal Citation57, pp. C398-C412
Number of Pages15
Year2018
PublisherCambridge University Press
Place of PublicationAustralia
ISSN1446-1811
1446-8735
Digital Object Identifier (DOI)https://doi.org/10.21914/anziamj.v57i0.10446
Web Address (URL)https://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/10446
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.

ANZSRC Field of Research 2020490105. Dynamical systems in applications
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Byline AffiliationsFaculty of Health, Engineering and Sciences
School of Agricultural, Computational and Environmental Sciences
Institution of OriginUniversity of Southern Queensland
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