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

Dentz, Marco; Gouze, Philippe; Russian, Anna; Dweik, Jalal; Delay, Frédérick

doi:10.1016/j.advwatres.2012.07.015

Cited by 75 publications

(97 citation statements)

References 37 publications

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“…Particle tracking based on a random walk is usually employed for simulating advective-dispersive transport of solutes in the water phase, but not for the soil water phase itself (Delay and Bodin, 2001;Klaus and Zehe, 2011;Dentz et al, 2012). For linear problems, when neither the dispersion coefficient nor the drift term depends on solute concentration and thus particle density, a time domain representation of the random walk is favourable as it maximises computational efficiency .…”

Section: Introductionmentioning

confidence: 99%

A Lagrangian model for soil water dynamics during rainfall-driven conditions

Zehe

Jackisch

2016

Hydrol. Earth Syst. Sci.

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Abstract. Within this study we propose a stochastic approach to simulate soil water dynamics in the unsaturated zone by using a non-linear, space domain random walk of water particles. Soil water is represented by particles of constant mass, which travel according to the Itô form of the Fokker-Planck equation. The model concept builds on established soil physics by estimating the drift velocity and the diffusion term based on the soil water characteristics. A naive random walk, which assumes all water particles to move at the same drift velocity and diffusivity, overestimated depletion of soil moisture gradients compared to a Richards solver. This is because soil water and hence the corresponding water particles in smaller pore size fractions are, due to the non-linear decrease in soil hydraulic conductivity with decreasing soil moisture, much less mobile. After accounting for this subscale variability in particle mobility, the particle model and a Richards solver performed highly similarly during simulated wetting and drying circles in three distinctly different soils. Both models were in very good accordance during rainfall-driven conditions, regardless of the intensity and type of the rainfall forcing and the shape of the initial state. Within subsequent drying cycles the particle model was typically slightly slower in depleting soil moisture gradients than the Richards model.Within a real-world benchmark, the particle model and the Richards solver showed the same deficiencies in matching observed reactions of topsoil moisture to a natural rainfall event. The particle model performance, however, clearly improved after a straightforward implementation of rapid nonequilibrium infiltration, which treats event water as different types of particles, which travel initially in the largest pore fraction at maximum velocity and experience a slow diffusive mixing with the pre-event water particles. The proposed Lagrangian approach is hence a promising, easy-to-implement alternative to the Richards equation for simulating rainfalldriven soil moisture dynamics, which offers straightforward opportunities to account for preferential, non-equilibrium flow.

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Section: Introductionmentioning

confidence: 99%

A Lagrangian model for soil water dynamics during rainfall-driven conditions

Zehe

Jackisch

2016

Hydrol. Earth Syst. Sci.

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“…[1][2][3] It turned out that CTRW is a powerful and efficient method for studying a wide distribution of complex dynamic processes in natural sciences, engineering, social sciences, and in economics. [4][5][6][7][8][9][10][11][12][13] It is natural to utilize CTRW for understanding transport phenomena that cannot be described within classical diffusion framework. 1,2,7 Recent experimental advances in single-molecule techniques that allowed to visualize various chemical and biological processes with high temporal and spatial resolution stimulated the application of CTRW for investigating biological and cellular transport phenomena with anomalous diffusion.…”

Section: Introductionmentioning

confidence: 99%

All-time dynamics of continuous-time random walks on complex networks

Teimouri

Kolomeisky

2013

The Journal of Chemical Physics

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The concept of continuous-time random walks (CTRW) is a generalization of ordinary random walk models, and it is a powerful tool for investigating a broad spectrum of phenomena in natural, engineering, social, and economic sciences. Recently, several theoretical approaches have been developed that allowed to analyze explicitly dynamics of CTRW at all times, which is critically important for understanding mechanisms of underlying phenomena. However, theoretical analysis has been done mostly for systems with a simple geometry. Here we extend the original method based on generalized master equations to analyze all-time dynamics of CTRW models on complex networks. Specific calculations are performed for models on lattices with branches and for models on coupled parallelchain lattices. Exact expressions for velocities and dispersions are obtained. Generalized fluctuations theorems for CTRW models on complex networks are discussed.

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“…In combination with the previous concerns this makes the model computationally very expensive. Due to the self-dependent state, we could not find any option to make use of the more efficient 10 continuous time random walk methodology (Metzler and Klafter, 2000;Delay and Bodin, 2001;Dentz et al, 2012).…”

Section: Numerical Concernsmentioning

confidence: 99%

“…Delay and Bodin, 2001;Metzler and Klafter, 2004;Berkowitz et al, 2006;Koutsoyiannis, 2010). Thus, most random walk applications rely on a continuous time domain representation as it performs well at minimum computational cost (Delay et al, 2008;Dentz et al, 2012). This approach is, however, not feasible when the diffusivity itself depends on the particle density as 5 is the case for water particles.…”

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confidence: 99%

Ecohydrological particle model based on representative domains

Jackisch¹,

Zehe²

2017

Preprint

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Abstract. Non-uniform infiltration and subsurface flow in structured soils is observed in most natural settings. It arises from imperfect lateral mixing of fast advective flow in structures and diffusive flow in the soil matrix and remains one of the most challenging topics with respect to match observation and modelling of water and solutes at the plot scale.This study extends the fundamental introduction of a space-domain random walk of water particles as alternative approach to the Richards equation for diffusive flow (Zehe and Jackisch, 2016) to a stochastic-physical model framework simulating 5 soil water flow in a representative, structured soil domain. The central objective of the proposed model is the simulation of non-uniform flow fingerprints in different ecohydrological settings and antecedent states by making maximum use of field observables for parameterisation. Avoiding non-observable parameters for macropore-matrix exchange, an energy-balance approach to govern film flow in representative flow paths is employed. We present the echoRD model (ecohydrological particle model based on representative domains) and a series of application test cases. 10The model proves as a powerful alternative to existing dual-domain models, driven on experimental data and with selfcontrolled, dynamic macropore-matrix exchange from the topologically semi-explicitly defined structures.

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

Cited by 75 publications

References 37 publications

A Lagrangian model for soil water dynamics during rainfall-driven conditions

A Lagrangian model for soil water dynamics during rainfall-driven conditions

All-time dynamics of continuous-time random walks on complex networks

Ecohydrological particle model based on representative domains

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