A boundary element method for stochastic flow problems in a semiconfined aquifer with random boundary conditions

A boundary element technique will be developed to deal with steady state flows through a shallow aquifer with random boundary conditions. The aquifer is bounded by a leaky layer above, and an impervious stratum below. The flow problem is formulated in terms of a stochastic boundary value problem involving a Helmholtz equation. A formulation of the boundary element method for the stochastic mixed boundary value problem is presented. The moments of unknown random hydraulic head can be obtained by application of an expectation operation to the boundary element formulations. A numerical method to evaluate hydraulic head moments on boundaries and inside the domain is then developed. The influence of the spatial structure of the boundary conditions on the hydraulic head statistics is discussed and the results are compared with some analytical solutions for one-dimensional flow problems for the purpose of verification of the numerical algorithm. The significance of the presence of the leaky layer on the hydraulic head statistics is also investigated. A numerical example for more general steady state flows through a semiconfined aquifer is presented. (C) 1997 Elsevier Science Ltd.