Nonstationary stochastic analysis of transient unsaturated flow in randomly heterogeneous media

In this study, a first-order, nonstationary stochastic model of transient f low is developed which is applicable to the entire domain of a bounded vado se zone in the presence of sink/source. We derive general equations governi ng the statistical moments of the flow quantities by perturbation expansion s. Owing to the mathematical complexity of the equations, in general we nee d to solve them numerically. The numerical moment equation approach, howeve r, has the flexibility in handling different boundary conditions, flow conf igurations, input covariance structures, and soil constitutive relationship s. The moment equations presented in this study are simpler and easier to s olve than those in the literature for transient unsaturated how. We solve t hese moment equations by the method of finite differences and demonstrate t he developed model through some one- and two-dimensional examples under var ious transient conditions.