Front Propagation in Random Media

This PhD thesis deals with the problem of the propagation of fronts under random circumstances. A statistical model to represent the motion of fronts when are evolving in a media characterized by microscopical randomness is discussed and expanded, in order to cope with three distinct applications: wild-land fire simulation, turbulent premixed combustion, biofilm modeling. In the studied formalism, the position of the average front is computed by making use of a sharp-front evolution method, such as the level set method. The microscopical spread of particles which takes place around the average front is given by the probability density function linked to the underlying diffusive process, that is supposedly known in advance. The adopted statistical front propagation framework allowed a deeper understanding of any studied field of application. The application of this model introduced eventually parameters whose impact on the physical observables of the front spread have been studied with Uncertainty Quantification and Sensitivity Analysis tools. In particular, metamodels for the front propagation system have been constructed in a non intrusive way, by making use of generalized Polynomial Chaos expansions and Gaussian Processes.The Thesis received funding from Basque Government through the BERC 2014-2017 program. It was also funded by the Spanish Ministry of Economy and Competitiveness MINECO via the BCAM Severo Ochoa SEV-2013-0323 accreditation. The PhD is fundend by La Caixa Foundation through the PhD grant “La Caixa 2014”. Funding from “Programma Operativo Nazionale Ricerca e Innovazione” (PONRI 2014-2020) , “Innotavive PhDs with Industrial Characterization” is kindly acknowledged for a research visit at the department of Mathematics and Applications “Renato Caccioppoli” of University “Federico II” of Naples