Article Dans Une Revue Physica D: Nonlinear Phenomena Année : 2015

Premixed-flame shapes and polynomials

Résumé

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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hal-01084853 , version 1 (20-11-2014)

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Bruno Denet, Guy Joulin. Premixed-flame shapes and polynomials. Physica D: Nonlinear Phenomena, 2015, 292, pp.46 - 50. ⟨10.1016/j.physd.2014.10.007⟩. ⟨hal-01084853⟩
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