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Density Estimation of Two-phase Flow with Multiscale and Randomly Perturbed Data

Abstract. In this paper, we describe an efficient approach for quantifying uncertainty in multi-phase flow applications due to perturbations of the permeability in multiscale heterogeneous porous medium. The method is based on the application of the multiscale finite element method within the framework of Monte Carlo simulation and an efficient preprocessing construction of the multiscale basis functions. We focus our quantities of interest on the Darcy velocity and the breakthrough time and quantify their uncertainty by constructing the cumulative distribution functions. We provide a number of numerical examples to illustrate the performance of the method.