Book ChapterDOI
The Random Walk Method in Pollutant Transport Simulation
Wolfgang Kinzelbach
- pp 227-245
TLDR
In this article, the random walk method is used for the case of an ideal tracer starting out from the Ito-Fokker-Planck equation. But the method suffers from the general roughness of simulated distributions in space and time due to statistical fluctuations and resolution problems.Abstract:
Standard finite difference and finite element solution methods of the pollutant transport equation require restrictive spatial discretization in order to avoid numerical dispersion. The random walk method offers a robust alternative if for reasons of calculational effort discretization requirements cannot be met. The method is discussed for the case of an ideal tracer starting out from the Ito-Fokker-Planck-equation. Features such as chemical reactions and adsorption can be incorporated. Besides being an alternative to other solution methods for the classical transport equation the random walk deserves attention due to its generalizability allowing the incorporation of non-Fickian dispersion. A shortcoming of the method results from the general roughness of simulated distributions in space and time due to statistical fluctuations and resolution problems. The method is applied to a field case of groundwater pollution by chlorohydrocarbons.read more
Citations
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Journal ArticleDOI
Numerical simulation of solute transport in three-dimensional, randomly heterogeneous porous media
TL;DR: In this paper, a three-dimensional solute transport model is developed to study detailed contaminant movements through large heterogeneous flow systems in porous media, based upon a random walk particle method.
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Mixing, spreading and reaction in heterogeneous media: a brief review.
TL;DR: This paper provides a brief review on approaches of non-reactive and reactive transport modeling in geological media and its impact on spreading and mixing of dissolved species.
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Particle tracking and the diffusion-reaction equation
TL;DR: In this paper, a particle tracking algorithm was proposed to model conservative transport in surface and subsurface hydrological systems and rigorously demonstrated that this particle method converges to the diffusion-reaction equation at the limit of infinitely small time step.
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Direct Simulation of Groundwater Age
TL;DR: In this paper, a new method is proposed to simulate groundwater age directly, by use of an advection-dispersion transport equation with a distributed zero-order source of unit strength, corresponding to the rate of aging.
Journal ArticleDOI
Anomalous transport in laboratory-scale, heterogeneous porous media
TL;DR: In this paper, the first-passage time distribution (FPTD) of migrating contaminants in random media, developed with the use of a continuous time random walk (CTRW) formalism, is analyzed.
References
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The Fractal Geometry of Nature
TL;DR: This book is a blend of erudition, popularization, and exposition, and the illustrations include many superb examples of computer graphics that are works of art in their own right.
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TL;DR: In this paper, the Milieux poreux Reference Record was created on 2004-09-07, modified on 2016-08-08 and the reference record was updated in 2016.
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TL;DR: In this article, the authors present the definitive work on the subject by one of the world's foremost hydrologists, designed primarily for advanced undergraduate and graduate students of ground water hydrology, soil mechanics, soil physics, drainage and irrigation engineering and sanitary, petroleum and chemical engineering.
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Mass transfer studies in sorbing porous media. I. Analytical solutions
TL;DR: An analytical solution for the movement of chemicals through a sorbing porous medium with lateral or intra-aggregate diffusion is presented in this paper, where the liquid phase in the porous medium is divided into mobile and immobile regions.