DIAGRAMMATIC SOLUTIONS FOR HYDRAULIC-HEAD MOMENTS IN 1-D AND 2-D BOUNDED DOMAINS

We present a diagrammatic method for solving stochastic 1-D and 2-D st eady-state flow equations in bounded domains. The diagrammatic method results in explicit solutions for the moments of the hydraulic head. T his avoids certain numerical constraints encountered in realization-ba sed methods. The diagrammatic technique also allows for the considerat ion of finite domains or large fluctuations, and is not restricted by distributional assumptions. The results of the method for I-D and 2-D finite domains are compared with those obtained through a realization- based approach. Mean and variance of head are well reproduced for all log-conductivity variances inputted, including those larger than one. The diagrammatic results also compare favorably to hydraulic head mome nts derived by standard analytic methods requiring a linearized form o f the flow equation.