A quasi-Monte Carlo method based on the Karhunen–Loeve expansion for groundwater flow simulation

Abstract

To study the effects of spatial variability on groundwater flow simulation, some stochastic methods are proposed in this study. The Karhunen–Loeve expansion is utilized to generate the random field of the parameter conductivity. The conventional and pseudo-random, Latin hypercube, and quasi-random sampling methods are employed to generate random vectors in the Karhunen–Loeve expansion. Various Monte Carlo methods based on different sampling methods are compared and analyzed in groundwater flow simulation. It is shown that the quasi-Monte Carlo method has better convergence and efficiency compared to other methods, especially in cases with large input variance and short correlation length. The Karhunen–Loeve expansion possesses the ability to generate a random field of general type. The type of stochastic input has a great impact on uncertainty in groundwater simulations.