Tesi di LAUREA SPECIALISTICA Titolo Metodi di collocazione stocastica per la simulazione di flussi in mezzi porosi eterogenei Data 2011-10-04 Autore/i Tesei, Francesco Relatore Nobile, F. Relatore Tamellini, L. Full text non disponibile Abstract This thesis focuses on the study of different kinds of fluxes in a porous me- dia, through a stochastic collocation method on a Smolyak-type sparse grid. The main aim is the quantification, via statistical moments, of the uncertainties due to random input data. In particular, we provide a solution for the Darcy formulation for the problem depending on the pressure. We consider the case with a log-normal distributed permeability stationary field with exponential or normal covariance function, together with the case where a set of direct permeability measures is available in the domain that can be used to condition the original field. In the first part of the work, we provide a formulation of the problem depending on a finite number of ran- dom uncorrelated variables using a truncated Karhunrn-Loève expansion of the random permeability field, followed by the description of the collocation method on sparse grids. In the second part, we study numerically the convergence properties and we present some results on two test cases. The results show that the collocation method is more effective than Monte Carlo in terms of error versus computational cost.