Time domain random walks for hydrodynamic transport in heterogeneous media

We derive a general formulation of the time domain random walk (TDRW) approach to model the hydrodynamic transport of inert solutes in complex geometries and heterogeneous media. We demonstrate its formal equivalence with the discretized advection‐dispersion equation and show that the TDRW is equiva...

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Bibliographic Details
Published in:Water resources research 2016-05, Vol.52 (5), p.3309-3323
Main Authors: Russian, Anna, Dentz, Marco, Gouze, Philippe
Format: Article
Language:English
Subjects:
Advection
Boundary conditions
continuous time random walk
Dispersion
Earth Sciences
Equivalence
Geophysics
Hydrodynamics
Initial conditions
Mass transfer
Mathematical models
Media
multirate mass transfer
Random walk
Random walk theory
Sciences of the Universe
Solutes
Solutions
Time domain analysis
time domain random walk
Transition probabilities
Transport
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Summary:We derive a general formulation of the time domain random walk (TDRW) approach to model the hydrodynamic transport of inert solutes in complex geometries and heterogeneous media. We demonstrate its formal equivalence with the discretized advection‐dispersion equation and show that the TDRW is equivalent to a continuous time random walk (CTRW) characterized by space‐dependent transition times and transition probabilities. The transition times are exponentially distributed. We discuss the implementation of different concentration boundary conditions and initial conditions as well as the occurrence of numerical dispersion. Furthermore, we propose an extension of the TDRW scheme to account for mobile‐immobile multirate mass transfer. Finally, the proposed TDRW scheme is validated by comparison to analytical solutions for spatially homogeneous and heterogeneous transport scenarios. Key Points: Equivalence TDRW with discretized ADE Equivalence TDRW with heterogeneous biased CTRW Extension TDRW for multirate mass transfer mechanism
ISSN:0043-1397
1944-7973
DOI:10.1002/2015WR018511