Numerical benchmark study for flow in highly heterogeneous aquifers. (April 2020)

• Record Type: Journal Article
• Authors: Alecsa, Cristian D.; Boros, Imre; Frank, Florian; Knabner, Peter; Nechita, Mihai; Prechtel, Alexander; Rupp, Andreas; Suciu, Nicolae
• Is Part Of: Advances in water resources. Volume 138(2020)
• Publication Date: 2020-04
• Subjects: Darcy flow -- Accuracy -- Convergence -- Computational feasibility -- Finite difference -- Finite element -- Discontinuous Galerkin -- Spectral methods -- Global random walk; 65N06 -- 65N30 -- 65N35 -- 65N12 -- 76S05 -- 86A05; Hydrology -- Periodicals; Hydrodynamics -- Periodicals; Hydraulic engineering -- Periodicals; 551.48
• DOI: 10.1016/j.advwatres.2020.103558
• Languages: English
• ISSNs: 0309-1708

Abstract

Highlights: Heterogeneous aquifers are modeled with log-normal random conductivity fields. Numerical schemes are tested on two-dimensional benchmark flow problems. Code verification performed by comparison with analytical manufactured solutions. Validation done through comparisons between MC statistics and first-order results. Limited computational feasibility for exponentially correlated log-conductivity. Abstract: This article presents numerical investigations on accuracy and convergence properties of several numerical approaches for simulating steady state flows in heterogeneous aquifers. Finite difference, finite element, discontinuous Galerkin, spectral, and random walk methods are tested on two-dimensional benchmark flow problems. Realizations of log-normal hydraulic conductivity fields are generated by Kraichnan algorithms in closed form as finite sums of random periodic modes, which allow direct code verification by comparisons with manufactured reference solutions. The quality of the methods is assessed for increasing number of random modes and for increasing variance of the log-hydraulic conductivity fields with Gaussian and exponential correlation. Experimental orders of convergence are calculated from successive refinements of the grid. The numerical methods are further validated by comparisons between statistical inferences obtained from Monte Carlo ensembles of numerical solutions and theoretical first-order perturbation results. It is found that while for Gaussian correlation of the log-conductivity field all the methods perform well, in the exponential case their accuracy deteriorates and, for large variance and number of modes, the benchmark problems are practically not solvable with reasonably large computing resources, for all the methods considered in this study.