A tempered multiscaling stable model to simulate transport in regional-scale fractured media

Accurate and efficient simulation of contaminant transport in fractured rock is practically important, yet current approaches suffer from numerical constraints that limit the full inclusion of fracture network properties at the regional scale. We propose a multidimensional transport model, nonlocal in space and time, which describes complex transport behavior in fractured media at regional scales, without introducing the computational burden of explicitly incorporating individual rock fractures. The model utilizes a direction-dependent tempered stable process to describe the transition of multiscaling anomalous diffusion to asymptotic diffusion limits. Applications show that the model can capture efficiently the transient superdiffusion found in two-dimensional synthetic fracture networks, and suggest that the truncation of leading plume edges is related to fracture network properties. Citation: Zhang, Y., B. Baeumer, and D. M. Reeves (2010), A tempered multiscaling stable model to simulate transport in regional-scale fractured media, Geophys. Res. Lett., 37, L11405, doi: 10.1029/2010GL043609.