Boundary condition sensitivity analysis of the stochastic flow equation

The effect of random vs deterministic boundary conditions on the direct solution of one- and two-dimensional flow systems was examined. The one-dimensional case allows exact analytical solutions for the hydraulic gradient for various boundary conditions. The results demonstrate how a simple modeling choice (i.e. random vs deterministic boundary conditions) can make a significant difference in the mean and variance of the hydraulic gradient. The two-dimensional system models the location of constant head boundaries and no-flow boundaries as random. In the case of steady-state flow in a rectangular domain, a relatively constant increase in head variance was found throughout the domain. Finally, we show that no-flow boundaries whose positions are deterministically known, lower the head variance at points near the boundaries more than at the boundaries themselves.

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