Subordinated advection‐dispersion equation for contaminant transport

By Boris Baeumer, David A. Benson, Mark M. Meerschaert, S. Wheatcraft. 2001

250 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Environmental Engineering, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/7f4950cef87cf5bb5f77bac8f0805ed85fa54d72

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Civil and Structural Engineering

In Environmental Engineering

In Modeling and Simulation

Citations in the corpus

Finite difference methods for two-dimensional fractional dispersion equation (2006, methodology): “In this paper we discuss a practical alternating directions implicit method to solve a class of two-dimensional initial-boundary value fractional partial differential equations with variable coefficients on a finite domain.”
Finite difference approximations for fractional advection-dispersion flow equations (2004, background): “Fractional derivatives have recently been applied to many problems in physics [3,7,8,10,16,19,20,22, 29,31,36], 5nance [14,25,28], and hydrology [2,4–6,33,34].”
Modeling non‐Fickian transport in geological formations as a continuous time random walk (2006, background): “[225] In contrast to the temporal FDE a spatial FDE assumes a transition time distribution y(t) with a finite first moment and a transition length distribution p(s) with a diverging second moment.”
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].”
On Riesz derivative (2019, background): “Introduction It is widely recognized that Riesz derivative plays a pivotal role in characterizing anomalous diffusion [2, 3, 4, 19, 20, 21, 23, 25, 27, 30].”
Time and space nonlocalities underlying fractional-derivative models: Distinction and literature review of field applications (2009, unknown): “[3].”
Fractional Laplace model for hydraulic conductivity (2004, methodology): “In groundwater hydrology, T(t) has been used to represent the ‘‘operational time’’ a particle experiences, a time that passes more rapidly in high velocity zones [Baeumer et al., 2001].”
Fractal mobile/immobile solute transport (2003, methodology): “…Þ ¼ sg ~C sð Þ C0 xð Þsg 1; and L H t uð Þgg t u buð Þ1=g ! buð Þ 1=g ( ) ¼ e sþbsgð Þu; where H ( ) is the Heaviside function and gg(t) is a stable density with scaling parameter 0 < g < 1 (known as a stable subordinator) so that L gg tð Þ ¼ e sg [Hille and Phillips, 1957; Baeumer et al., 2001].”
TEMPERED FRACTIONAL CALCULUS (2015, background): “They are now used to model a wide variety of problems in physics [24, 35,38,50,51,55,65], finance [23,27,37,42,60,61], biology [2,4,22,26,36], and hydrology [1,7,8,15,17,62].”
Fourier spectral methods for fractional-in-space reaction-diffusion equations (2014, background): “In water resources, fractional models have been used to describe chemical and contaminant transport in heterogeneous aquifers [1, 2, 3].”
VECTOR GRÜNWALD FORMULA FOR FRACTIONAL DERIVATIVES (2004, background): “Introduction Fractional derivatives have been around for centuries [22, 26] but recently they have found new applications in physics [2, 6, 7, 9, 15, 18, 19, 29], hydrology [1, 4, 5, 10, 14, 28], and finance [24, 25, 27].”
Fractional vector calculus for fractional advection–dispersion (2006, background): “Fractional derivatives have recently been applied to many problems in physics [5–18], finance [15,19–22], and hydrology [23–28].”
The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics (2004, background): “…(49) is X(T(t)) where X(t) is the process behind equation (49) when µ = 1 and T(t) is the µ-stable subordinator, compare Bochner 1949; see also the application in Baeumer et al 2001. where the µth power of the Fokker–Planck operator is interpreted in Fourier–Laplace space, i.e., equation (50)…”