Wildland fire propagation modelling: A novel approach reconciling models based on moving interface methods and on reaction-diffusion equations. (English) Zbl 1363.93030

Brandts, J. (ed.) et al., Proceedings of the international conference ‘Applications of mathematics’, Prague, Czech Republic, November 18–21, 2015. In honor of the birthday anniversaries of Ivo Babuška (90), Milan Práger (85), and Emil Vitásek (85). Prague: Czech Academy of Sciences, Institute of Mathematics (ISBN 978-80-85823-65-3). 85-99 (2015).
The paper deals with formulation of a model of wildland fire propagation problem and inclusion of two stochastic processes into two existing models of the fire front motion. The fire propagation problem is split into two parts: the drifting part and the fluctuating part. The drifting part is simulated using either the Eulerian Level Set Method (LSM), or the Lagrangian Discrete EVent system Specification (DEVS), both described and analyzed by other authors. The contribution of this work is in inclusion of a model of the fluctuating part to both LSM and DEVS models and presentation of several computational results. The fluctuating part includes problems of air turbulence and fire spotting e.g. due to burn trees. Modeling of the random processes is handled by their Probability Density Function (PDF). The paper includes also a comparison of simulation results using LSM and DEVS methods. The topic is interesting not in theory itself but in numerical comparisons. The results are well interpreted and differences between the two approaches are discussed.
For the entire collection see [Zbl 1329.00187].


93A30 Mathematical modelling of systems (MSC2010)
93C95 Application models in control theory
93E03 Stochastic systems in control theory (general)
60J60 Diffusion processes
62P12 Applications of statistics to environmental and related topics
60K37 Processes in random environments
62P30 Applications of statistics in engineering and industry; control charts
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