Abstract
Front propagation can be studied by two alternative approaches: the level set method and the reaction-diffusion equation. When a front propagates in a random environment it gets a random character and these two approaches can indeed be considered complementary and reconciled. In fact, if the level set contour is randomized accordingly to the probability density function of the front particle displacement, the resulting averaged process emerges to be governed by an evolution equation of the reaction-diffusion type. This approach turns out to be useful to simulate random effects in wildland fire propagation as those due to turbulent heat convection and fire spotting phenomena.
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Acknowledgements
This research is supported by GNFM/INdAM Young Researchers Project 2013, by Bizkaia Talent and European Commission through COFUND programme under Grant AYD-000-226, and also by the Basque Government through the BERC 2014–2017 program and by the Spanish Ministry of Economy and Competitiveness MINECO: BCAM Severo Ochoa accreditation SEV-2013-0323.
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Pagnini, G., Mentrelli, A. (2016). The Randomized Level Set Method and an Associated Reaction-Diffusion Equation to Model Wildland Fire Propagation. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds) Progress in Industrial Mathematics at ECMI 2014. ECMI 2014. Mathematics in Industry(), vol 22. Springer, Cham. https://doi.org/10.1007/978-3-319-23413-7_74
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DOI: https://doi.org/10.1007/978-3-319-23413-7_74
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