Chemical front propagation in periodic flows: FKPP vs G equation

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• Alexandra Tzella (School of Mathematics, University of Birmingham)
• Thursday 26 October 2017, 12:00-13:00
• Arts Building, LR5.

If you have a question about this talk, please contact Sergey Sergeev.

We investigate the influence of steady periodic flows on the propagation of chemical pulsating fronts evolving inside an infinite channel domain. We focus on the sharp front arising in Fisher—Kolmogorov—Petrovskii—Piskunov (FKPP) type models in the limit of small molecular diffusivity and fast reaction i.e., when the Peclet and Damkohler numbers are large, and its commonly used heuristic approximation by the G equation. We use a variational approach to express the two front speeds in terms of periodic trajectories that minimise the time of travel across the period of the flow. We show that the only difference lies in the nature of the constraint from where we deduce that the front speed associated with the FKPP equation is greater than or equal to the front speed associated with the G equation. We use numerical optimisation to evaluate the two front speeds for a class of cellular vortex flows widely used in experiments. These computations are verified against closed-form expressions for the archetypal cellular flow.

This talk is part of the Optimisation and Numerical Analysis Seminars series.

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• Arts Building, LR5
• Optimisation and Numerical Analysis Seminars
• School of Mathematics events

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