Simulating Scale-Dependent Solute Transport in Soils with the Fractional Advective–Dispersive Equation

By Yakov A. Pachepsky, David A. Benson, Walter J. Rawls. 2000

143 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Computational Mechanics, Environmental Engineering

View Paper: https://www.semanticscholar.org/paper/2fdbdf9017e275f00489e3d8d50557e1e37f7630

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In Civil and Structural Engineering

In Computational Mechanics

In Environmental Engineering

Citations in the corpus

Information content and complexity of simulated soil water fluxes (2006, methodology): “…commonly used performance measures such as the root-mean square error, the lack-of-fit root mean square error (Whitmore, 1991), Williams–Kloot test (Pachepsky et al., 2000), modeling efficiency (Loague and Green, 1991), use the statistics or probability distribution functions of the set of…”
A finite element solution for the fractional advection–dispersion equation (2008, methodology): “The MIM based approach seems make a big improvement over ADE, but the disadvantage of this approach is also apparent as reviewed by many researchers [34,35,52,53,11].”
A variable-order time-fractional derivative model for chloride ions sub-diffusion in concrete structures (2012, background): “However, the chloride transport in saturated concrete is a quite complicated diffusion-binding process and characterizes time and concentration dependency, which is quite difficult to be described only by a constant-order fractional diffusion equation model [5, 24].”
Multiscaling fractional advection‐dispersion equations and their solutions (2003, methodology): “[3] One-dimensional fractional ADEs have been used to model the heavy leading edges and nonlinear scaling of conservative plumes observed in both laboratory and field solute transport experiments [Benson, 1998; Pachepsky et al., 2000; Benson et al., 2001].”
Possible problems of scale dependency in applications of the three‐dimensional fractional advection‐dispersion equation to natural porous media (2002, background): “, 1999, 2001], most hydrological applications to date have been one-dimensional [Benson et al., 2000, 2001; Pachepshy et al., 2000].”
Non‐Fickian transport in homogeneous unsaturated repacked sand (2004, methodology): “…media [de Smedt and Wierenga, 1984; Wierenga and van Genuchten, 1989], however most often this model is unable to capture the early breakthrough and long tailing characteristic of unsaturated transport [de Smedt et al., 1986; Bond and Wierenga, 1990; Padilla et al., 1999; Pachepsky et al., 2000].”
Comparison of alternative models for simulating anomalous solute transport in a large heterogeneous soil column (2009, methodology): “…the symmetric u-stable probability function (Pachepsky et al., 2000): FuðyÞ ¼ CðuÞ þ signð1 uÞ 2 Z 1 0 exp y u 1 uUuðvÞ dv ð14Þ where v is the integration variable, C(u) and Uu(v) can be expressed as (Pachepsky et al., 2000): CðuÞ ¼ 1 u > 1 1 2 u < 1 ( and UuðvÞ ¼ sin puv=2ð Þ cosðpu=2Þ u 1 u ð15Þ”