PROBABILISTIC ANALYSIS OF FLOW IN RANDOM POROUS-MEDIA BY STOCHASTIC BOUNDARY ELEMENTS

The mathematical and numerical modeling of groundwater flows in random porous media is studied assuming that the formation's hydraulic log-t ransmissivity is a statistically homogeneous, Gaussian, random field w ith given mean and covariance function. In the model, log-transmissivi ty may be conditioned to take exact field values measured at a few loc ations. Our method first assumes that the log-transmissivity may be ex panded in a Fourier-type series with random coefficients, known as the Karhunen-Loeve (KL) expansion. This expansion has optimal properties and is valid for both homogeneous and nonhomogeneous fields. By combin ing the KL expansion with a small parameter perturbation expansion, we transform the original stochastic boundary value problem into a hiera rchy of deterministic problems. To the first order of perturbation, th e hydraulic head is expanded on the same set of random variables as in the KL representation of log-transmissivity. To solve for the corresp onding coefficients of this expansion, we adopt a boundary integral fo rmulation whose numerical solution is carried out by using boundary el ements and dual reciprocity (DRBEM). To illustrate and validate our sc heme, we solve three test problems and compare the numerical solutions against Monte Carlo simulations based on a finite difference formulat ion of the original flow problem. In all three cases we obtain good qu antitative agreement and the present approach is shown to provide both a more efficient and accurate way of solving the problem. (C) 1997 El sevier Science Ltd.