Evaluation of the first-order approximations for transport in heterogeneous media
Nicolae Suciu2006, Water Resources Research
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Abstract
Longitudinal dispersion coefficients in given realizations of the transport computed by two currently used approximations of the first-order in velocity variance are compared with accurate global random walk simulations. The comparisons are performed for the same ensemble of realizations of the Darcy velocity field, approximated by a quasi-periodic random field, for log-normal hydraulic conductivity with small variance and finite correlation lengths. The results show that, at finite times of about one dispersion time scale, the mean coefficient is underestimated by ≈ 20% and the fluctuations are overestimated by ≈ 80%. At larger times the errors decrease monotonously and the first-order approximations yield fairly good predictions for the mean and the fluctuations of the dispersion coefficient.
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