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." Australian 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 TitleAustralian and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal
Australia and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal
Journal Citation57, pp. C398-C412
Number of Pages15
Year2018
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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