Abstract
We present a diagrammatic method for solving stochastic 1-D and 2-D steady-state flow equations in bounded domains. The diagrammatic method results in explicit solutions for the moments of the hydraulic head. This avoids certain numerical constraints encountered in realization-based methods. The diagrammatic technique also allows for the consideration of finite domains or large fluctuations, and is not restricted by distributional assumptions. The results of the method for 1-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 moments derived by standard analytic methods requiring a linearized form of the flow equation.
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Oliver, L.D., Christakos, G. Diagrammatic solutions for hydraulic head moments in 1-D and 2-D bounded domains. Stochastic Hydrol Hydraul 9, 269–296 (1995). https://doi.org/10.1007/BF01581729
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DOI: https://doi.org/10.1007/BF01581729