Random walk particle tracking simulations of non-Fickian transport in heterogeneous media

Authors:
G. Srinivasan;D. M. Tartakovsky;M. Dentz;H. Viswanathan;B. Berkowitz;B. A. Robinson
Affiliations:
Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA;Department of Mechanical and Aerospace Engineering, University of California, San Diego, 9500 Gilman Drive, Mail Code 0411, La Jolla, CA 92093, USA;Institute of Environmental Assessment and Water Research (IDíA-CSIC), Barcelona, Spain;Earth and Environmental Sciences Division, Los Alamos National Laboratory, Los Alamos, New Mexico, USA;Department of Environmental Sciences and Energy Research, Weizmann Institute of Science, Rehovot, Israel;Earth and Environmental Sciences Division, Los Alamos National Laboratory, Los Alamos, New Mexico, USA
Venue:
Journal of Computational Physics
Year:
2010

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Abstract

Derivations of continuum nonlocal models of non-Fickian (anomalous) transport require assumptions that might limit their applicability. We present a particle-based algorithm, which obviates the need for many of these assumptions by allowing stochastic processes that represent spatial and temporal random increments to be correlated in space and time, be stationary or non-stationary, and to have arbitrary distributions. The approach treats a particle trajectory as a subordinated stochastic process that is described by a set of Langevin equations, which represent a continuous time random walk (CTRW). Convolution-based particle tracking (CBPT) is used to increase the computational efficiency and accuracy of these particle-based simulations. The combined CTRW-CBPT approach enables one to convert any particle tracking legacy code into a simulator capable of handling non-Fickian transport.