Numerical benchmark study for flow in highly heterogeneous aquifers

Alecsa CD, Boros I, Frank F, Knabner P, Nechita M, Prechtel A, Rupp A, Suciu N (2020)

Publication Type: Journal article

Publication year: 2020

Journal

Advances in Water Resources Elsevier

Pages Range: 103558

Article Number: 103558

DOI: 10.1016/j.advwatres.2020.103558

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.

Authors with CRIS profile

Florian Frank Professur für Wissenschaftliches Rechnen Peter Knabner Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik) Alexander Prechtel Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik) Andreas Rupp Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik) Nicolae Suciu Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik)

Involved external institutions

Tiberiu Popoviciu Institute of Numerical Analysis (Romanian Academy) RO Romania (RO)

How to cite

APA:

Alecsa, C.D., Boros, I., Frank, F., Knabner, P., Nechita, M., Prechtel, A.,... Suciu, N. (2020). Numerical benchmark study for flow in highly heterogeneous aquifers. Advances in Water Resources, 103558. https://doi.org/10.1016/j.advwatres.2020.103558

MLA:

Alecsa, Cristian D., et al. "Numerical benchmark study for flow in highly heterogeneous aquifers." Advances in Water Resources (2020): 103558.

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