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Subordinated advection‐dispersion equation for contaminant transport
Author(s) -
Baeumer Boris,
Benson David A.,
Meerschaert Mark M.,
Wheatcraft Stephen W.
Publication year - 2001
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 - 10.1029/2000wr900409
Subject(s) - aquifer , subordinator , dispersion (optics) , advection , skewness , fractal , continuous time random walk , variable (mathematics) , diffusion , statistical physics , fick's laws of diffusion , anomalous diffusion , convection–diffusion equation , mechanics , mathematics , soil science , environmental science , geotechnical engineering , mathematical analysis , physics , thermodynamics , statistics , geology , computer science , random walk , groundwater , knowledge management , optics , innovation diffusion , lévy process
A mathematical method called subordination broadens the applicability of the classical advection‐dispersion equation for contaminant transport. In this method the time variable is randomized to represent the operational time experienced by different particles. In a highly heterogeneous aquifer the operational time captures the fractal properties of the medium. This leads to a simple, parsimonious model of contaminant transport that exhibits many of the features (heavy tails, skewness, and non‐Fickian growth rate) typically seen in real aquifers. We employ a stable subordinator that derives from physical models of anomalous diffusion involving fractional derivatives. Applied to a one‐dimensional approximation of the MADE‐2 data set, the model shows excellent agreement.