University of Birmingham > Talks@bham > Applied Mathematics Seminar Series > Front propagation in cellular flows for fast reaction and small diffusivity

Front propagation in cellular flows for fast reaction and small diffusivity

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  • UserAlexandra Tzella (Birmingham)
  • ClockMonday 17 March 2014, 14:00-15:00
  • HouseWatson LRA.

If you have a question about this talk, please contact Alexandra Tzella.

We investigate the influence of fluid flows on the propagation of chemical fronts arising in Fisher– Kolmogorov type models. For the cellular flows we consider, the front propagation speed can be determined numerically by solving an eigenvalue problem; this is however difficult for small molecular diffusivity and fast reaction, i.e., when the Peclet (Pe) and Damkohler (Da) numbers are large. Here, we employ a WKB approach to obtain the front speed for a broad range of Pe,Da ≫ 1 in terms of a periodic path – an instanton – that minimizes a certain functional, and to derive closed-form results for Da ≪ Pe and for Da ≫ Pe. Our theoretical predictions are compared with (i) numerical solutions of the eigenvalue problem and (ii) simulations of the advection–diffusion–reaction equation. Their relation with previous results obtained using the G-equation is discussed.

Joint work with Jacques Vanneste (Edinburgh)

This talk is part of the Applied Mathematics Seminar Series series.

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