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SPECIAL SECTION: ZNS'03 VADOSE ZONE RESEARCH

Simulation of Tracer Dispersion in Porous Media Using Lattice Boltzmann and Random Walk Models

^a Dep. of Agronomy, University of Córdoba, P.O. Box 3048, 14080 Córdoba, Spain
^b Dep. of Agronomy, University of Córdoba and Institute of Sustainable Agriculture, CSIC, P.O. Box 3048, 14080 Córdoba, Spain
^c Dep. of Applied Physics, University of Córdoba, P.O. Box 3048, 14080 Córdoba, Spain
^* Corresponding author (jihof{at}arrakis.es)

Received 16 June 2004.

Pore-scale flow and transport processes are generally difficult to simulate using conventional models. Two state-of-the-art approaches are adopted in this study of solute transport in porous media. The first approach is a lattice Boltzmann model with the Bhatnagar, Gross, and Krook simplification (BGK) to determine both the advection and diffusion components of the transport process, while the second approach uses the BGK model to calculate the velocity field in conjunction with a random walk (RW) model to characterize diffusion (BGK/RW). Both approaches yield similar results. The BGK/RW model is an attractive alternative to the BGK model when it is necessary to simulate small values of the diffusion coefficient so as to avoid instabilities in the numerical solution. Nevertheless, the BGK/RW model is less accurate than the BGK model alone when compared with the analytic solution of the well-known Taylor–Aris dispersion model.

Abbreviations: BGK, Bhatnagar, Gross, and Krook model • BGK/RW, Bhatnagar, Gross, and Krook model, with a random walk model • LBM, lattice Boltzmann model • l.u., lattice units • RW, random walk model