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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
