BOUNDARY-CONDITION SENSITIVITY ANALYSIS OF THE STOCHASTIC FLOW EQUATION

The effect of random vs deterministic boundary conditions on the direc t solution of one- and two-dimensional flow systems was examined. The one-dimensional case allows exact analytical solutions for the hydraul ic gradient for various boundary conditions. The results demonstrate h ow a simple modeling choice (i.e. random vs deterministic boundary con ditions) can make a significant difference in the mean and variance of the hydraulic gradient. The two-dimensional system models the locatio n of constant head boundaries and no-flow boundaries as random. In the case of steady-state flow in a rectangular domain, a relatively const ant increase in head variance was found throughout the domain. Finally , we show that no-flow boundaries whose positions are deterministicall y known, lower the head variance at points near the boundaries more th an at the boundaries themselves.