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.
CITATION STYLE
Baeumer, B., Benson, D. A., Meerschaert, M. M., & Wheatcraft, S. W. (2001). Subordinated advection-dispersion equation for contaminant transport. Water Resources Research, 37(6), 1543–1550. https://doi.org/10.1029/2000WR900409
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