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EFFICIENT COMPUTATION OF COORDINATE-FREE MODELS OF FLAME FRONTS

Part of: Thermodynamics and heat transfer Partial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  29 April 2021

B. F. AKERS  and
D. M. AMBROSE Open the ORCID record for D. M. AMBROSE [Opens in a new window]
B. F. AKERS*
Affiliation:
Department of Mathematics and Statistics, Air Force Institute of Technology, WPAFB, OH45433, USA
D. M. AMBROSE
Affiliation:
Department of Mathematics, Drexel University, Philadelphia, PA19104, USA; dma68@drexel.edu.
*
Email: benjamin.akers@afit.edu
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Abstract

We present an efficient, accurate computational method for a coordinate-free model of flame front propagation of Frankel and Sivashinsky. This model allows for overturned flames fronts, in contrast to weakly nonlinear models such as the Kuramoto–Sivashinsky equation. The numerical procedure adapts the method of Hou, Lowengrub and Shelley, derived for vortex sheets, to this model. The result is a nonstiff, highly accurate solver which can handle fully nonlinear, overturned interfaces, with similar computational expense to methods for weakly nonlinear models. We apply this solver both to simulate overturned flame fronts and to compare the accuracy of Kuramoto–Sivashinsky and coordinate-free models in the appropriate limit.

Keywords

flame frontscoordinate-free modelsoverturned interfaces

MSC classification

Primary: 65M70: Spectral, collocation and related methods
Secondary: 80A22: Stefan problems, phase changes, etc.
Type
Research Article
Information
The ANZIAM Journal , Volume 63 , Issue 1 , January 2021 , pp. 58 - 69
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Copyright
© Australian Mathematical Society 2021

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