A stochastic boundary element solution applied to groundwater flow

Abstract

A stochastic boundary element solution for two dimensional, transient groundwater flow in confined aquifers with random diffusivity is presented in this work. In particular, the fundamental solutions for the diffusion equation with a random coefficient are derived using the perturbation method. The resulting expressions for both piezometric head and flow solutions are validated through Monte-Carlo simulations. Subsequently, perturbations are again used for building a boundary integral equation-based solution for the covariance matrix of the response to arbitrarily posed boundary-value problems, with the mean solution being identical to the deterministic one due to the second order expansion used. The entire methodology is defined in the Laplace transform domain, and an efficient inversion scheme is employed for capturing the transient response in terms of a mean solution plus a variance. A series of examples serve to illustrate the methodology and the focus is on simple aquifers with parallel, concave and convex boundaries under piezometric heads with prescribed temporal variations which are arbitrary functions of time. It is shown that the medium stochasticity affects transient flow through the aquifer but has no effect under quasi-static conditions.