Data from: Multi-level and quasi Monte Carlo methods for uncertainty quantification in particle travel times through random heterogeneous porous media

In this study we apply four Monte Carlo simulation methods, namely, Monte Carlo, quasi Monte Carlo, multilevel Monte Carlo and multilevel quasi Monte Carlo to the problem of uncertainty quantification in the estimation of the average travel time during the transport of particles through random heterogeneous porous media. We apply the four methodologies to a model problem where the only input parameter, the hydraulic conductivity, is modelled as a log Gaussian random field by using direct Karhunen-Lo eve decompositions. The random terms in such expansions represent the coefficients in the equations. Numerical calculations demonstrating the effectiveness of each of the methods are presented. A comparison of the computational cost spent by each of the methods for three different tolerances is provided. The accuracy of the approaches is quantified via the mean square error.