Numerical approximation of head and flux covariances in three dimensions using mixed finite elements |
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| Institution: | 1. College of Geology and Environment, Xi’an University of Science and Technology, Xi’an 710054, Shaanxi, China;2. College of Life Science, Yan’an University, Yan’an, Shaanxi 716000, China;3. State Key Laboratory of Eco-hydraulics in Northwest Arid Region, Xi’an University of Technology, Xi’an 710048, Shaanxi, China;4. Sichuan Water Resources and Hydroelectric Investigation & Design Institute CO., LTD., Chengdu 610072, Sichuan, China |
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| Abstract: | A numerical method is developed for accurately approximating head and flux covariances and cross-covariances in finite two- and three-dimensional domains using the mixed finite element method. The method is useful for determining head and flux covariances for non-stationary flow fields, for example those induced by injection or extraction wells, impermeable subsurface barriers, or non-stationary hydraulic conductivity fields. Because the numerical approximations to the flux covariances are obtained directly from the solution to the coupled problem rather than having to differentiate head covariances, the approximations are in general more accurate than those obtained from conventional finite difference or finite element methods. Results for uniform flow example problems are consistent with results from previously published finite domain analyses and demonstrate that head variances and covariances are quite sensitive to boundary conditions and the size of the bounded domain. Flux variances and covariances are less sensitive to boundary conditions and domain size. Results comparing approximations from lower-order Raviart–Thomas–Nedelec and higher order Brezzi–Douglas–Marini9] finite element spaces indicate that higher order element space improve the estimate of the flux covariances, but do not significantly affect the estimate of the head covariances. |
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