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978-3-8439-1981-4, Reihe Mathematik
Sarah Maria Eberle
Forest Fire Determination: Theory and Numerical Aspects
227 Seiten, Dissertation Technische Universität Kaiserslautern (2014), Softcover, A5
Due to the climate change, forests in Rhineland-Palatinate will be endangered by forest fires in the future. On the one hand, there will be different influences (e.g., lower rainfalls during growing periods) and, on the other hand, more susceptible systems (e.g., bright pinewoods on dry locations). Because of this expectation, it is very important to obtain information about how forest fires expand to enhance prevention concerning forest protection and firefighting on a local level. This thesis is based on the cooperation with the Rhineland-Palatinate Centre of Excellence for Climate Change Impacts. Thus, we take a look at the interacting factors which influence forest fires. By reason of the complexity of these activities, mathematical models are needed.
The aim of this thesis is the modeling of forest fire spreading based on physical and chemical laws. The resulting time dependent non-linear convection-diffusion-reaction-problem is solved by different numerical methods (with a collocation method and also a finite difference method approach for the space discretization). For the convection-dominated case, we consider stabilization methods in order to reduce artificial oscillations (Gibbs phenomenon). Therefore, we introduce a new numerical method, where we combine a collocation method with Flux Corrected Transport tools. In addition, we compare the (Essentially) Non-Oscillatory (ENO) scheme and Flux Corrected Transport (FCT) scheme with each other. In doing so, we are able to simulate forest fire spreading for Rhineland-Palatinate and other regions.