Data from: Multilevel 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–Loéve 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 incurred by each of the methods for
three different tolerances is provided. The accuracy of the approaches is
quantified via the mean square error.