Boundary Element Formulations For Stochastic Flow In Semi-confined Aquifers With Random Boundary Conditions
Free (open access)
M. Satish & J. Zhu
A boundary element technique is developed to solve steady state flow in a shallow aquifer with random boundary conditions. The aquifer is bounded by a leaky aquifer above, and an impervious layer below. The flow problem is formulated in terms of a stochastic boundary value problem involving a Helmholtz equation. The moment of unknown random hydraulic head is obtained by application of an expectation operation to the boundary element formulations. The influence of the spatial structure of the boundary conditions on the hydraulic head statistics is discussed. The significance of the presence of the leaky layer on the hydraulic head statistics is also investigated. Keywords: semi-confined shallow aquifer, stochastic analysis, random boundary conditions. 1 Introduction The traditional approach to modelling of groundwater systems has been deterministic. If a variable, for instance, has been measured at a few locations, its distribution in space was determined by some kind of smooth interpolation, and then the flow problem was solved by using appropriate differential equations. This approach is open to criticism for the following reasons. The variables of interest do not vary in a regular manner in space and smooth interpolations are not able to reproduce their fluctuation, and in practice, measurements are generally scarce, i.e. they are available only at a few points, and values at other points are subject to uncertainty.
semi-confined shallow aquifer, stochastic analysis, random boundary conditions