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Numerical investigations on ergodicity of solute transport in heterogeneous aquifers
Author(s) -
Suciu N.,
Vamoş C.,
Vanderborght J.,
Hardelauf H.,
Vereecken H.
Publication year - 2006
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/2005wr004546
Subject(s) - ergodicity , ergodic theory , advection , statistical physics , random walk , turbulence , mathematics , convergence (economics) , realization (probability) , stochastic process , dispersion (optics) , mechanics , physics , mathematical analysis , statistics , thermodynamics , optics , economics , economic growth
Darcy velocities for lognormal hydraulic conductivity with small variance and finite correlation length were approximated by periodic random fields. Accurate simulations of two‐dimensional advection‐dispersion processes were achieved with the global random walk algorithm, using 10 10 particles in every transport realization. Reliable statistical estimations were obtained by averaging over 256 realizations. The main result is a numerical evidence for the mean square convergence of the actual concentrations to the macrodispersion process predicted by a known limit theorem. For small initial plumes the ergodic behavior can be expected after thousands of advection timescales, when the deviation from the theoretical prediction of the cross‐section space‐averaged concentration monotonously decays and falls under 20%. The increase of the transverse dimension of the initial plume slows down the approach to the quasi‐ergodic state and has a nonlinear effect on the variability of the actual concentrations and dispersivities.