Front propagation in random media

Résumé

This PhD thesis deals with the problem of the propagation of fronts under random circumstances. Astatistical model to represent the motion of fronts when are evolving in a media characterized bymicroscopical randomness is discussed and expanded, in order to cope with three distinctapplications: wild-land fire simulation, turbulent premixed combustion, biofilm modeling. In thestudied formalism, the position of the average front is computed by making use of a sharp-frontevolution method, such as the level set method. The microscopical spread of particles which takesplace around the average front is given by the probability density function linked to the underlyingdiffusive process, that is supposedly known in advance. The adopted statistical front propagationframework allowed a deeper understanding of any studied field of application. The application ofthis model introduced eventually parameters whose impact on the physical observables of the frontspread have been studied with Uncertainty Quantification and Sensitivity Analysis tools. Inparticular, metamodels for the front propagation system have been constructed in a non intrusiveway, by making use of generalized Polynomial Chaos expansions and Gaussian Processes.