Application of a fractional advection‐dispersion equation

By David A. Benson, S. Wheatcraft, Mark M. Meerschaert. 2000

1,257 citations recorded by the source corpus.

Subfields: Computational Mechanics, Environmental Engineering, Modeling and Simulation

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Citations in the corpus

fPINNs: Fractional Physics-Informed Neural Networks (2018, background): “Among these are solute transport in fractured and porous media [2, 3], acoustic wave propagation with frequency-dependent dissipation [4, 5, 6, 7], laminar and turbulent flows [8, 9, 10], viscoelastic constitutive laws [11], just to mention a few.”
Modeling flow and transport in highly heterogeneous three‐dimensional aquifers: Ergodicity, Gaussianity, and anomalous behavior—2. Approximate semianalytical solution (2006, background): “Alternative approaches addressing the same issues are the fractional ADE [Cushman and Ginn, 1993, 2000; Benson et al., 2000] and the mass transfer model [see, e.”
Finite di$erence approximations for fractional advection-dispersion &ow equations (2004, methodology): “Keywords: Finite di$erence approximation; Stability; Backward Euler method; Implicit Euler method; Radial dispersion; Radial advection; Fractional di$usion; Fractional derivative; Fractional advection–dispersion; Numerical fractional ADE”
Comparison of alternative models for simulating anomalous solute transport in a large heterogeneous soil column (2009, methodology): “The spatial FADE broadens the applicability of CDE by describing the super-diffusive rapid transport including heavy leading plume edges and faster-than-Fickian growth rates (Benson et al., 2000a,b, 2001).”
New Fractional Derivatives with Nonlocal and Non-Singular Kernel: Theory and Application to Heat Transfer Model (2016, background): “[7-14] and the references therein) but still there are many thinks to be done in this direction.”
Portfolio Modeling with Heavy Tailed Random Vectors (2003, background): “Benson, et al. [9, 10] model concentration profiles for tracer plumes in groundwater using stochastic models whose heavy tails have 1 < α < 2, so that the mean is finite but the variance is infinite.”
Brownian subordinators and fractional Cauchy problems (2007, background): “Inverse L´evy subordinators occur in scaling limits of continuous time random walks used to model anomalous diﬀusion in physics [43, 44, 61], ﬁnance [27, 42, 57], and hydrology [13, 15, 59].”
A second-order accurate numerical method for the two-dimensional fractional diffusion equation (2007, methodology): “Fractional diffusion equations are used to model problems in physics (see a comprehensive review by Metzler and Klafter [25]), finance [10,16,28,31,30], and hydrology [2,4,5,32,33].”
Numerical solutions of the space‐time fractional advection‐dispersion equation (2008, neutral): “[6] considered space fractional advection-dispersion equation.”
A Fractional Laplace Equation: Regularity of Solutions and Finite Element Approximations (2015, background): “ure [30, 37]; among the several applications of these nonlocal models let us mention image processing [7, 24, 26, 34], nance [10, 12], electromagnetic uids [36], peridynamics [46] and porous media ow [2, 14]. In this work we will be interested in the fractional Laplace operator of order s, which we ”
SDEs Driven by a Time-Changed Lévy Process and Their Associated Time-Fractional Order Pseudo-Differential Equations (2009, methodology): “l FokkerPlanck equations have appeared as an essential tool for the study of dynamics of various complex stochastic processes arising in anomalous diﬀusion in physics [28, 44], ﬁnance [16], hydrology [6], and cell biology [34]. Complexity includes phenomena such as the presence of weak or strong cor”