A GIF-based Stochastic Boundary Element Method for Random Porous Media

Abstract

Using a global interpolation function (GIF) approach, boundary element solutions are obtained for flows in porous media with random hydraulic conductivity. The formulation is based on the indirect approach. The solution field is decomposed into two parts. The first is due to the influence of the constant (or effective) property of the medium. This is represented by a boundary integral term. The second, which is due solely to the random nature of the permeability, is represented by a series of bases functions. Appropriate expressions are obtained for the statistics of the primary flow variables (hydraulic head and flux) in terms of the statistics of the permeability field. Numerical implementations include the use of different families of orthogonal trigonometric, polynomial, and wavelet bases functions. The ensuing code can be used for both the forward solution (i.e., determination of flow field) and the inverse solution (e.g., identification of parameters).