Premixed flame shapes and polynomials

Bruno Denet; Guy Joulin

doi:10.1016/j.physd.2014.10.007

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arXiv · 1410.6037

Premixed flame shapes and polynomials

Bruno Denet·Guy Joulin

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Abstract

The nonlinear nonlocal Michelson-Sivashinsky equation for isolated crests of unstable flames is studied, using pole-decompositions as starting point. Polynomials encoding the numerically computed 2N flame-slope poles, and auxiliary ones, are found to closely follow a Meixner Pollaczek recurrence; accurate steady crest shapes ensue for N>=3. Squeezed crests ruled by a discretized Burgers equation involve the same polynomials. Such explicit approximate shape still lack for finite-N pole-decomposed periodic flames, despite another empirical recurrence.

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Bruno Denet, Guy Joulin. 2014-10-22. Premixed flame shapes and polynomials. https://doi.org/10.1016/j.physd.2014.10.007

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