Diffusion and trapping in heterogeneous media: An inhomogeneous continuous time random walk approach

• Published in: Advances in water resources 2012-12, Vol.49, p.13-22
• Main Authors: Dentz, Marco, Gouze, Philippe, Russian, Anna, Dweik, Jalal, Delay, Frederick
• Format: Article
• Language: English
• Subjects: Continuous time random walks; Diffusion; Diffusion in random media; Earth Sciences; Earth, ocean, space; Environmental Sciences; Exact sciences and technology; Formulations; Geophysics; Global Changes; Hydrogeology; Hydrology. Hydrogeology; Mass transfer; Mathematical analysis; Media; Multirate mass transfer; Physics; Random walk; Sciences of the Universe; Stochastic modeling; Time-domain random walks; Trapping; Water resources
• ISSN: 0309-1708; 1872-9657
• DOI: 10.1016/j.advwatres.2012.07.015

► Equivalence of TDRW and the heterogeneous diffusion equation is shown. ► A TDRW method for heterogeneous diffusion with multitrapping is developed. ► Anomalous diffusion on finite domains is studied. We study diffusion in a heterogeneous medium that is characterized by spatially varying diffusion properties from a random walk point of view. We show that an inhomogeneous continuous time random walk (CTRW) with a spatially variable exponential transition time distribution solves the spatially discretized heterogeneous diffusion equation. This demonstrates the equivalence of the widely used time-domain random walk (TDRW) scheme and spatially inhomogeneous CTRW and at the same time provides a demonstration of the formal equivalence of the TDRW particle formulation and the heterogeneous diffusion equation. Based on this equivalence, we develop a TDRW method for heterogeneous diffusion under spatially variable multirate mass transfer properties. We discuss the implementation of these schemes and study the diffusion behavior in the presence of traps that are characterized by a truncated power-law trapping time distribution.